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## Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2023 2023.

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

## Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

## Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

## Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

## Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

## Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

## Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

## Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

## Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field , Nolberto Rezola

ALGEBRA 1 STUDENTS’ ABILITY TO RELATE THE DEFINITION OF A FUNCTION TO ITS REPRESENTATIONS , Sarah A. Thomson

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## Mathematics Graduate Projects and Theses

Theses/dissertations from 2022 2022.

Relationships Between COVID-19 Infection Rates, Healthcare Access, Socioeconomic Status, and Cultural Diversity , MarGhece P.J. Barnes

The Matrix Sortability Problem , Seth Cleaver

Cognitive Demand of Teacher-Created Mathematics Assessments , Megan Marie Schmidt

Waring Rank and Apolarity of Some Symmetric Polynomials , Max Brian Sullivan

Security Analysis of Lightweight Cryptographic Primitives , William Unger

Regression Analysis of Resilience and COVID-19 in Idaho Counties , Ishrat Zaman

## Theses/Dissertations from 2021 2021

Tukey Morphisms Between Finite Binary Relations , Rhett Barton

A Data Adaptive Model for Retail Sales of Electricity , Johanna Marcelia

Exploring the Beginnings of Algebraic K-Theory , Sarah Schott

Zariski Geometries and Quantum Mechanics , Milan Zanussi

## Theses/Dissertations from 2020 2020

The Directed Forest Complex of Cayley Graphs , Kennedy Courtney

Beliefs About Effective Instructional Practices Among Middle Grades Teachers of Mathematics , Lauren A. Dale

Analytic Solutions for Diffusion on Path Graphs and Its Application to the Modeling of the Evolution of Electrically Indiscernible Conformational States of Lysenin , K. Summer Ware

## Theses/Dissertations from 2019 2019

Dynamic Sampling Versions of Popular SPC Charts for Big Data Analysis , Samuel Anyaso-Samuel

Computable Reducibility of Equivalence Relations , Marcello Gianni Krakoff

On the Fundamental Group of Plane Curve Complements , Mitchell Scofield

Radial Basis Function Finite Difference Approximations of the Laplace-Beltrami Operator , Sage Byron Shaw

Formally Verifying Peano Arithmetic , Morgan Sinclaire

## Theses/Dissertations from 2018 2018

Selective Strong Screenability , Isaac Joseph Coombs

Mathematics Student Achievement in the Context of Idaho’s Advanced Opportunities Initiative , Nichole K. Hall

Secure MultiParty Protocol for Differentially-Private Data Release , Anthony Harris

## Theses/Dissertations from 2017 2017

A Stable Algorithm for Divergence-Free and Curl-Free Radial Basis Functions in the Flat Limit , Kathryn Primrose Drake

The Classification Problem for Models of ZFC , Samuel Dworetzky

Joint Inversion of Compact Operators , James Ford

Trend and Return Level of Extreme Snow Events in New York City , Mintaek Lee

Multi-Rate Runge-Kutta-Chebyshev Time Stepping for Parabolic Equations on Adaptively Refined Meshes , Talin Mirzakhanian

Investigating College Instructors’ Methods of Differentiation and Derivatives in Calculus Classes , Wedad Mubaraki

The Random Graph and Reciprocity Laws , Spencer M. Nelson

Classification of Vertex-Transitive Structures , Stephanie Potter

## Theses/Dissertations from 2016 2016

On the Conjugacy Problem for Automorphisms of Trees , Kyle Douglas Beserra

The Density Topology on the Reals with Analogues on Other Spaces , Stuart Nygard

Latin Squares and Their Applications to Cryptography , Nathan O. Schmidt

Solution Techniques and Error Analysis of General Classes of Partial Differential Equations , Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe

Numerical Computing with Functions on the Sphere and Disk , Heather Denise Wilber

## Theses/Dissertations from 2015 2015

The Classical Theory of Rearrangements , Monica Josue Agana

Nonlinear Partial Differential Equations, Their Solutions, and Properties , Prasanna Bandara

The Impact of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables on Student Achievement and Student Thinking About Linearity , Paul Thomas Belue

Student Understanding of Function and Success in Calculus , Daniel I. Drlik

Monodromy Representation of the Braid Group , Phillip W. Hart

The Frobenius Problem , Anna Marie Megale

## Theses/Dissertations from 2014 2014

Pi-1-1-determinacy and Sharps , Shehzad Ahmed

A Radial Basis Function Partition of Unity Method for Transport on the Sphere , Kevin Aiton

Diagrammatically Reducible 2-Complexes , Tyler Allyn

A Stochastic Parameter Regression Model for Long Memory Time Series , Rose Marie Ocker

## Theses/Dissertations from 2013 2013

The Assignment Packet Grading System , Sarah Nichole Bruce

Using Learner-Generated Examples to Support Student Understanding of Functions , Martha Ottelia Dinkelman

Computing Curvature and Curvature Normals on Smooth Logically Cartesian Surface Meshes , John Thomas Hutchins

Schur's Theorem and Related Topics in Ramsey Theory , Summer Lynne Kisner

## Theses/Dissertations from 2012 2012

On the Geometry of Virtual Knots , Rachel Elizabeth Byrd

A Stochastic Parameter Regression Approach for Time-Varying Relationship between Gold and Silver Prices , Birsen Canan-McGlone

Uncertainty Analysis of RELAP5-3D© , Alexandra E. Gertman and George L. Mesina

A Statistical Method for Regularizing Nonlinear Inverse Problems , Chad Clifton Hammerquist

Perfect Stripes from a General Turing Model in Different Geometries , Jean Tyson Schneider

Stability and Convergence for Nonlinear Partial Differential Equations , Oday Mohammed Waheeb

Regular Homotopy of Closed Curves on Surfaces , Katherine Kylee Zebedeo

## Theses/Dissertations from 2011 2011

Coloring Problems , Thomas Antonio Charles Chartier

Modules Over Localized Group Rings for Groups Mapping Onto Free Groups , Nicholas Davidson

How Do We Help Students Interpret Contingency Tables? A Study on the Use of Proportional Reasoning as an Intervention , Kathleen M. Isaacson

A Fictitious Point Method for Handling Boundary Conditions in the RBF-FD Method , Joseph Lohmeier

## Theses/Dissertations from 2010 2010

Developmental Understanding of the Equals Sign and Its Effects on Success in Algebra , Ryan W. Brown

The Inquiry Learning Model as an Approach to Mathematics Instruction , Michael C. Brune

Galois Theory for Differential Equations , Soheila Eghbali

Stably Free Modules Over the Klein Bottle , Andrew Misseldine

Combinatorics and Topology of Curves and Knots , Bailey Ann Ross

## Theses/Dissertations from 2009 2009

Concept Booklets: Examining the Performance Effects of Journaling of Mathematics Course Concepts , Todd Stephen Fogdall

Effective Sample Size in Order Statistics of Correlated Data , Neill McGrath

Transparency in Formal Proof , Cap Petschulat

Weight Selection by Misfit Surfaces for Least Squares Estimation , Garrett Saunders

The Effects of a Standards-Based Mathematics Curriculum on the Self-Efficacy and Academic Achievement of Previously Unsuccessful Students , Cindy Chesley Shaw

Analytical Upstream Collocation Solution of a Quadratic Forced Steady-State Convection-Diffusion Equation , Eric Paul Smith

Solvability Characterizations of Pell Like Equations , Jason Smith

## Theses/Dissertations from 2008 2008

Tube-Equivalence of Spanning Surfaces and Seifert Surfaces , Thomas Glass

Simple Tests for Short Memory in ARFIMA Models , Timothy A. C. Hughes

Incomparable Metrics on the Cantor Space , Trevor Jack

Richards' Equation and Its Constitutive Relations as a System of Differential-Algebraic Equations , Shannon K. Murray

## Theses/Dissertations from 2007 2007

Theorem Proving in Elementary Analysis , Joanna Porter Guild

An Investigation of Lucas Sequences , Dustin E. Hinkel

A Canonical Countryman Line , William Russell Hudson

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Modern computational methods for finitely presented monoids , finiteness conditions on semigroups relating to their actions and one-sided congruences , on constructing topology from algebra , interpolating between hausdorff and box dimension , solving decision problems in finitely presented groups via generalized small cancellation theory .

## Senior Thesis

This page is for Undergraduate Senior Theses. For Ph.D. Theses, see here .

So that Math Department senior theses can more easily benefit other undergraduate, we would like to exhibit more senior theses online (while all theses are available through Harvard University Archives , it would be more convenient to have them online). It is absolutely voluntary, but if you decide to give us your permission, please send an electronic version of your thesis to cindy@math. The format can be in order of preference: DVI, PS, PDF. In the case of submitting a DVI format, make sure to include all EPS figures. You can also submit Latex or MS word source files.

If you are looking for information and advice from students and faculty about writing a senior thesis, look at this document . It was compiled from comments of students and faculty in preparation for, and during, an information session. Let Wes Cain ([email protected]) know if you have any questions not addressed in the document.

## BYU ScholarsArchive

Home > Physical and Mathematical Sciences > Mathematics Education > Theses and Dissertations

## Mathematics Education Theses and Dissertations

Theses/dissertations from 2024 2024.

New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting

## Theses/Dissertations from 2023 2023

Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales

Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff

Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley

Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson

## Theses/Dissertations from 2022 2022

Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll

Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon

Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena

The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper

Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby

Structural Reasoning with Rational Expressions , Dana Steinhorst

Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong

## Theses/Dissertations from 2021 2021

Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams

You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer

Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens

## Theses/Dissertations from 2020 2020

Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway

Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen

Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe

## Theses/Dissertations from 2019 2019

Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson

Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson

Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis

“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross

Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark

## Theses/Dissertations from 2018 2018

Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason

How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job

Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau

Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky

## Theses/Dissertations from 2017 2017

Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard

Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard

Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville

Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga

## Theses/Dissertations from 2016 2016

The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis

Insight into Student Conceptions of Proof , Steven Daniel Lauzon

## Theses/Dissertations from 2015 2015

Teacher Participation and Motivation inProfessional Development , Krystal A. Hill

Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet

English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill

Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich

Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts

Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson

Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke

Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise

## Theses/Dissertations from 2014 2014

The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams

Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch

Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd

Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton

An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen

## Theses/Dissertations from 2013 2013

Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo

Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau

Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc

Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele

Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk

## Theses/Dissertations from 2012 2012

Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call

Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons

Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson

Mathematics Teacher Time Allocation , Ashley Martin Jones

## Theses/Dissertations from 2011 2011

How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell

Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce

A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams

## Theses/Dissertations from 2010 2010

Growth in Students' Conceptions of Mathematical Induction , John David Gruver

Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart

Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon

Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams

## Theses/Dissertations from 2009 2009

A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick

The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling

Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak

## Theses/Dissertations from 2008 2008

Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon

How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks

Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill

Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson

Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb

## Theses/Dissertations from 2007 2007

Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff

What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff

Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow

One Problem, Two Contexts , Danielle L. Gigger

The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry

Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer

## Theses/Dissertations from 2006 2006

How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras

Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz

The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze

Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb

## Theses/Dissertations from 2005 2005

Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff

An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen

## Theses/Dissertations from 2004 2004

Reasoning About Motion: A Case Study , Tiffini Lynn Glaze

## Theses/Dissertations from 2003 2003

An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford

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## Dissertations and Placements 2010-Present

Kimoi Kemboi Thesis: Full exceptional collections of vector bundles on linear GIT quotients Advisor: Daniel Halpern-Leistner First Position: Postdoc at the Institution for Advanced Study and Princeton

Max Lipton Thesis: Dynamical Systems in Pure Mathematics Advisor: Steven Strogatz First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology

Elise McMahon Thesis: A simplicial set approach to computing the group homology of some orthogonal subgroups of the discrete group Advisor: Inna Zakharevich First Position: Senior Research Scientist at Two Six Technologies

Peter Uttenthal Thesis: Density of Selmer Ranks in Families of Even Galois Representations Advisor: Ravi Kumar Ramakrishna First Position: Visiting Assistant Professor at Cornell University

Liu Yun Thesis: Towers of Borel Fibrations and Generalized Quasi-Invariants Advisor: Yuri Berest First Position: Postdoc at Indiana University Bloomington

Romin Abdolahzadi Thesis: Anabelian model theory Advisor: Anil Nerode First Position: Quantitative Analyst, A.R.T. Advisors, LLC

Hannah Cairns Thesis: Abelian processes, and how they go to sleep Advisor: Lionel Levine First Position: Visiting Assistant Professor, Cornell University

Shiping Cao Thesis: Topics in scaling limits on some Sierpinski carpet type fractals Advisor: Robert Strichartz (Laurent Saloff-Coste in last semester) First Position: Postdoctoral Scholar, University of Washington

Andres Fernandes Herrero Thesis: On the boundedness of the moduli of logarithmic connections Advisor: Nicolas Templier First Position: Ritt Assistant Professor, Columbia University

Max Hallgren Thesis: Ricci Flow with a Lower Bound on Ricci Curvature Advisor: Xiaodong Cao First Position: NSF Postdoctoral Research Fellow, Rutgers University

Gautam Krishnan Thesis: Degenerate series representations for symplectic groups Advisor: Dan Barbasch First Position: Hill Assistant Professor, Rutgers University

Feng Liang Thesis: Mixing time and limit shapes of Abelian networks Advisor: Lionel Levine

David Mehrle Thesis: Commutative and Homological Algebra of Incomplete Tambara Functors Advisor: Inna Zakharevich First Position: Postdoctoral Scholar, University of Kentucky

Itamar Sales de Oliveira Thesis: A new approach to the Fourier extension problem for the paraboloid Advisor: Camil Muscalu First Position: Postdoctoral Researcher, Nantes Université

Brandon Shapiro Thesis: Shape Independent Category Theory Advisor: Inna Zakharevich First Position: Postdoctoral Fellow, Topos Institute

Ayah Almousa Thesis: Combinatorial characterizations of polarizations of powers of the graded maximal ideal Advisor: Irena Peeva First position: RTG Postdoctoral Fellow, University of Minnesota

Jose Bastidas Thesis: Species and hyperplane arrangements Advisor: Marcelo Aguiar First position: Postdoctoral Fellow, Université du Québec à Montréal

Zaoli Chen Thesis: Clustered Behaviors of Extreme Values Advisor: Gennady Samorodnitsky First Position: Postdoctoral Researcher, Department of and Statistics, University of Ottawa

Ivan Geffner Thesis: Implementing Mediators with Cheap Talk Advisor: Joe Halpern First Position: Postdoctoral Researcher, Technion – Israel Institute of Technology

Ryan McDermott Thesis: Phase Transitions and Near-Critical Phenomena in the Abelian Sandpile Model Advisor: Lionel Levine

Aleksandra Niepla Thesis: Iterated Fractional Integrals and Applications to Fourier Integrals with Rational Symbol Advisor: Camil Muscalu First Position: Visiting Assistant Professor, College of the Holy Cross

Dylan Peifer Thesis: Reinforcement Learning in Buchberger's Algorithm Advisor: Michael Stillman First Position: Quantitative Researcher, Susquehanna International Group

Rakvi Thesis: A Classification of Genus 0 Modular Curves with Rational Points Advisor: David Zywina First Position: Hans Rademacher Instructor, University of Pennsylvania

Ana Smaranda Sandu Thesis: Knowledge of counterfactuals Advisor: Anil Nerode First Position: Instructor in Science Laboratory, Computer Science Department, Wellesley College

Maru Sarazola Thesis: Constructing K-theory spectra from algebraic structures with a class of acyclic objects Advisor: Inna Zakharevich First Position: J.J. Sylvester Assistant Professor, Johns Hopkins University

Abigail Turner Thesis: L2 Minimal Algorithms Advisor: Steven Strogatz

Yuwen Wang Thesis: Long-jump random walks on finite groups Advisor: Laurent Saloff-Coste First Position: Postdoc, University of Innsbruck, Austria

Beihui Yuan Thesis: Applications of commutative algebra to spline theory and string theory Advisor: Michael Stillman First Position: Research Fellow, Swansea University

Elliot Cartee Thesis: Topics in Optimal Control and Game Theory Advisor: Alexander Vladimirsky First Position: L.E. Dickson Instructor, Department of , University of Chicago

Frederik de Keersmaeker Thesis: Displaceability in Symplectic Geometry Advisor: Tara Holm First Position: Consultant, Addestino Innovation Management

Lila Greco Thesis: Locally Markov Walks and Branching Processes Advisor: Lionel Levine First Position: Actuarial Assistant, Berkshire Hathaway Specialty Insurance

Benjamin Hoffman Thesis: Polytopes And Hamiltonian Geometry: Stacks, Toric Degenerations, And Partial Advisor: Reyer Sjamaar First Position: Teaching Associate, Department of , Cornell University

Daoji Huang Thesis: A Bruhat Atlas on the Wonderful Compactification of PS O(2 n )/ SO (2 n -1) and A Kazhdan-Lusztig Atlas on G/P Advisor: Allen Knutson First Position: Postdoctoral Associate, University of Minnesota

Pak-Hin Li Thesis: A Hopf Algebra from Preprojective Modules Advisor: Allen Knutson First position: Associate, Goldman Sachs

Anwesh Ray Thesis: Lifting Reducible Galois Representations Advisor: Ravi Ramakrishna First Position: Postdoctoral Fellowship, University of British Columbia

Avery St. Dizier Thesis: Combinatorics of Schubert Polynomials Advisor: Karola Meszaros First Position: Postdoctoral Fellowship, Department of , University of Illinois at Urbana-Champaign

Shihao Xiong Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences Advisor: Justin Moore First Position: Algorithm Developer, Hudson River Trading

Swee Hong Chan Thesis: Nonhalting abelian networks Advisor: Lionel Levine First Position: Hedrick Adjunct Assistant Professor, UCLA

Joseph Gallagher Thesis: On conjectures related to character varieties of knots and Jones polynomials Advisor: Yuri Berest First Position: Data Scientist, Capital One

Jun Le Goh Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems Advisor: Richard Shore First Position: Van Vleck Assistant Professor, University of Wisconsin-Madison

Qi Hou Thesis: Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces Advisor: Laurent Saloff-Coste First Position: Visiting Assistant Professor, Department of , Cornell University

Jingbo Liu Thesis: Heat kernel estimate of the Schrodinger operator in uniform domains Advisor: Laurent Saloff-Coste First Position: Data Scientist, Jet.com

Ian Pendleton Thesis: The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds Advisor: Tara Holm

Amin Saied Thesis: Stable representation theory of categories and applications to families of (bi)modules over symmetric groups Advisor: Martin Kassabov First Position: Data Scientist, Microsoft

Yujia Zhai Thesis: Study of bi-parameter flag paraproducts and bi-parameter stopping-time algorithms Advisor: Camil Muscalu First Position: Postdoctoral Associate, Université de Nantes

Tair Akhmejanov Thesis: Growth Diagrams from Polygons in the Affine Grassmannian Advisor: Allen Knutson First position: Arthur J. Krener Assistant Professor, University of California, Davis

James Barnes Thesis: The Theory of the Hyperarithmetic Degrees Advisor: Richard Shore First position: Visiting Lecturer, Wellesley College

Jeffrey Bergfalk Thesis: Dimensions of ordinals: set theory, homology theory, and the first omega alephs Advisor: Justin Moore Postdoctoral Associate, UNAM - National Autonomous University of Mexico

TaoRan Chen Thesis: The Inverse Deformation Problem Advisor: Ravi Ramakrishna

Sergio Da Silva Thesis: On the Gorensteinization of Schubert varieties via boundary divisors Advisor: Allen Knutson First position: Pacific Institute for the Mathematical Sciences (PIMS) postdoctoral fellowship, University of Manitoba

Eduard Einstein Thesis: Hierarchies for relatively hyperbolic compact special cube complexes Advisor: Jason Manning First position: Research Assistant Professor (Postdoc), University of Illinois, Chicago (UIC)

Balázs Elek Thesis: Toric surfaces with Kazhdan-Lusztig atlases Advisor: Allen Knutson First position: Postdoctoral Fellow, University of Toronto

Kelsey Houston-Edwards Thesis: Discrete Heat Kernel Estimates in Inner Uniform Domains Advisor: Laurent Saloff-Coste First position: Professor of Math and Science Communication, Olin College

My Huynh Thesis: The Gromov Width of Symplectic Cuts of Symplectic Manifolds. Advisor: Tara Holm First position: Applied Mathematician, Applied Research Associates Inc., Raleigh NC.

Hossein Lamei Ramandi Thesis: On the minimality of non-σ-scattered orders Advisor: Justin Moore First position: Postdoctoral Associate at UFT (University Toronto)

Christine McMeekin Thesis: A density of ramified primes Advisor: Ravi Ramakrishna First position: Researcher at Max Planck Institute

Aliaksandr Patotski Thesis: Derived characters of Lie representations and Chern-Simons forms Advisor: Yuri Berest First position: Data Scientist, Microsoft

Ahmad Rafiqi Thesis: On dilatations of surface automorphisms Advisor: John Hubbard First position: Postdoctoral Associate, Sao Palo, Brazil

Ying-Ying Tran Thesis: Computably enumerable boolean algebras Advisor: Anil Nerode First position: Quantitative Researcher

Drew Zemke Thesis: Surfaces in Three- and Four-Dimensional Topology Advisor: Jason Manning First position: Preceptor in , Harvard University

Heung Shan Theodore Hui Thesis: A Radical Characterization of Abelian Varieties Advisor: David Zywina First position: Quantitative Researcher, Eastmore Group

Daniel Miller Thesis: Counterexamples related to the Sato–Tate conjecture Advisor: Ravi Ramakrishna First position: Data Scientist, Microsoft

Lihai Qian Thesis: Rigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions Advisor: Xiaodong Cao First position: Quantitative Associate, Wells Fargo

Valente Ramirez Garcia Luna Thesis: Quadratic vector fields on the complex plane: rigidity and analytic invariants Advisor: Yulij Ilyashenko First position: Lebesgue Post-doc Fellow, Institut de Recherche Mathématique de Rennes

Iian Smythe Thesis: Set theory in infinite-dimensional vector spaces Advisor: Justin Moore First position: Hill Assistant Professor at Rutgers, the State University of New Jersey

Zhexiu Tu Thesis: Topological representations of matroids and the cd-index Advisor: Edward Swartz First position: Visiting Professor - Centre College, Kentucky

Wai-kit Yeung Thesis: Representation homology and knot contact homology Advisor: Yuri Berest First position: Zorn postdoctoral fellow, Indiana University

Lucien Clavier Thesis: Non-affine horocycle orbit closures on strata of translation surfaces: new examples Advisor: John Smillie First position: Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg

Voula Collins Thesis: Crystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space Advisor: Allen Knutson FIrst position: Postdoctoral Associate, University of Connecticut

Pok Wai Fong Thesis: Smoothness Properties of symbols, Calderón Commutators and Generalizations Advisor: Camil Muscalu First position: Quantitative researcher, Two Sigma

Tom Kern Thesis: Nonstandard models of the weak second order theory of one successor Advisor: Anil Nerode First position: Visiting Assistant Professor, Cornell University

Robert Kesler Thesis: Unbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators Advisor: Camil Muscalu First position: Postdoctoral Associate, Georgia Institute of Technology

Yao Liu Thesis: Riesz Distributions Assiciated to Dunkl Operators Advisor: Yuri Berest First position: Visiting Assistant Professor, Cornell University

Scott Messick Thesis: Continuous atomata, compactness, and Young measures Advisor: Anil Nerode First position: Start-up

Aaron Palmer Thesis: Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity Advisor: Timothy J. Healey First position: Postdoctoral fellow, University of British Columbia

Kristen Pueschel Thesis: On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups Advisor: Timothy Riley First position: Postdoctoral Associate, University of Arkansas

Chenxi Wu Thesis: Translation surfaces: saddle connections, triangles, and covering constructions. Advisor: John Smillie First position: Postdoctoral Associate, Max Planck Institute of

David Belanger Thesis: Sets, Models, And Proofs: Topics In The Theory Of Recursive Functions Advisor: Richard A. Shore First position: Research Fellow, National University of Singapore

Cristina Benea Thesis: Vector-Valued Extensions for Singular Bilinear Operators and Applications Advisor: Camil Muscalu First position: University of Nantes, France

Kai Fong Ernest Chong Thesis: Face Vectors and Hilbert Functions Advisor: Edward Swartz First position: Research Scientist, Agency for Science, Technology and Research, Singapore

Laura Escobar Vega Thesis: Brick Varieties and Toric Matrix Schubert Varieties Advisor: Allen Knutson First position: J. L. Doob Research Assistant Professor at UIUC

Joeun Jung Thesis: Iterated trilinear fourier integrals with arbitrary symbols Advisor: Camil Muscalu First position: Researcher, PARC (PDE and Functional Analysis Research Center) of Seoul National University

Yasemin Kara Thesis: The laplacian on hyperbolic Riemann surfaces and Maass forms Advisor: John H. Hubbard Part Time Instructor, Faculty of Engineering and Natural Sciences, Bahcesehir University

Chor Hang Lam Thesis: Homological Stability Of Diffeomorphism Groups Of 3-Manifolds Advisor: Allen Hatcher

Yash Lodha Thesis: Finiteness Properties And Piecewise Projective Homeomorphisms Advisor: Justin Moore and Timothy Riley First position: Postdoctoral fellow at Ecole Polytechnique Federale de Lausanne in Switzerland

Radoslav Zlatev Thesis: Examples of Implicitization of Hypersurfaces through Syzygies Advisor: Michael E. Stillman First position: Associate, Credit Strats, Goldman Sachs

Margarita Amchislavska Thesis: The geometry of generalized Lamplighter groups Advisor: Timothy Riley First position: Department of Defense

Hyungryul Baik Thesis: Laminations on the circle and hyperbolic geometry Advisor: John H. Hubbard First position: Postdoctoral Associate, Bonn University

Adam Bjorndahl Thesis: Language-based games Advisor: Anil Nerode and Joseph Halpern First position: Tenure Track Professor, Carnegie Mellon University Department of Philosophy

Youssef El Fassy Fihry Thesis: Graded Cherednik Algebra And Quasi-Invariant Differential Forms Advisor: Yuri Berest First position: Software Developer, Microsoft

Chikwong Fok Thesis: The Real K-theory of compact Lie groups Advisor: Reyer Sjamaar First position: Postdoctoral fellow in the National Center for Theoretical Sciences, Taiwan

Kathryn Lindsey Thesis: Families Of Dynamical Systems Associated To Translation Surfaces Advisor: John Smillie First position: Postdoctoral Associate, University of Chicago

Andrew Marshall Thesis: On configuration spaces of graphs Advisor: Allan Hatcher First position: Visiting Assistant Professor, Cornell University

Robyn Miller Thesis: Symbolic Dynamics Of Billiard Flow In Isosceles Triangles Advisor: John Smillie First position: Postdoctoral Researcher at Mind Research Network

Diana Ojeda Aristizabal Thesis: Ramsey theory and the geometry of Banach spaces Advisor: Justin Moore First position: Postdoctoral Fellow, University of Toronto

Hung Tran Thesis: Aspects of the Ricci flow Advisor: Xiaodong Cao First position: Visiting Assistant Professor, University of California at Irvine

Baris Ugurcan Thesis: LPLP-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs Advisor: Robert S. Strichartz First position: Postdoctoral Fellowship, University of Western Ontario

Anna Bertiger Thesis: The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space Advisor: Allen Knutson First position: University of Waterloo, Postdoctoral Fellow

Mariya Bessonov Thesis: Probabilistic Models for Population Dynamics Advisor: Richard Durrett First position: CUNY City Tech, Assistant Professor, Tenure Track

Igors Gorbovickis Thesis: Some Problems from Complex Dynamical Systems and Combinatorial Geometry Advisor: Yulij Ilyashenko First position: Postdoctoral Fellow, University of Toronto

Marisa Hughes Thesis: Quotients of Spheres by Linear Actions of Abelian Groups Advisor: Edward Swartz First position: Visiting Professor, Hamilton College

Kristine Jones Thesis: Generic Initial Ideals of Locally Cohen-Macaulay Space Curves Advisor: Michael E. Stillman First position: Software Developer, Microsoft

Shisen Luo Thesis: Hard Lefschetz Property of Hamiltonian GKM Manifolds Advisor: Tara Holm First position: Associate, Goldman Sachs

Peter Luthy Thesis: Bi-parameter Maximal Multilinear Operators Advisor: Camil Muscalu First position: Chauvenet Postdoctoral Lecturer at Washington University in St. Louis

Remus Radu Thesis: Topological models for hyperbolic and semi-parabolic complex Hénon maps Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Jenna Rajchgot Thesis: Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane Advisor: Allen Knutson First position: Research member at the Mathematical Sciences Research Institute (fall 2012); postdoc at the University of Michigan

Raluca Tanase Thesis: Hénon maps, discrete groups and continuity of Julia sets Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Ka Yue Wong Thesis: Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories Advisor: Dan M. Barbasch First position: Postdoctoral fellow at Hong Kong University of Science and Technology

Tianyi Zheng Thesis: Random walks on some classes of solvable groups Advisor: Laurent Saloff-Coste First position: Postdoctoral Associate, Stanford University

Juan Alonso Thesis: Graphs of Free Groups and their Measure Equivalence Advisor: Karen Vogtmann First position: Postdoc at Uruguay University

Jason Anema Thesis: Counting Spanning Trees on Fractal Graphs Advisor: Robert S. Strichartz First position: Visiting assistant professor of mathematics at Cornell University

Saúl Blanco Rodríguez Thesis: Shortest Path Poset of Bruhat Intervals and the Completecd-Index Advisor: Louis Billera First position: Visiting assistant professor of mathematics at DePaul University

Fatima Mahmood Thesis: Jacobi Structures and Differential Forms on Contact Quotients Advisor: Reyer Sjamaar First position: Visiting assistant professor at University of Rochester

Philipp Meerkamp Thesis: Singular Hopf Bifurcation Advisor: John M. Guckenheimer First position: Financial software engineer at Bloomberg LP

Milena Pabiniak Thesis: Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Advisor: Tara Holm First position: Postdoctoral associate at the University of Toronto

Peter Samuelson Thesis: Kauffman Bracket Skein Modules and the Quantum Torus Advisor: Yuri Berest First position: Postdoctoral associate at the University of Toronto

Mihai Bailesteanu Thesis: The Heat Equation under the Ricci Flow Advisor: Xiaodong Cao First position: Visiting assistant professor at the University of Rochester

Owen Baker Thesis: The Jacobian Map on Outer Space Advisor: Karen Vogtmann First position: Postdoctoral fellow at McMaster University

Jennifer Biermann Thesis: Free Resolutions of Monomial Ideals Advisor: Irena Peeva First position: Postdoctoral fellow at Lakehead University

Mingzhong Cai Thesis: Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties Advisor: Richard A. Shore First position: Van Vleck visiting assistant professor at the University of Wisconsin at Madison

Ri-Xiang Chen Thesis: Hilbert Functions and Free Resolutions Advisor: Irena Peeva First position: Instructor at Shantou University in Guangdong, China

Denise Dawson Thesis: Complete Reducibility in Euclidean Twin Buildings Advisor: Kenneth S. Brown First position: Assistant professor of mathematics at Charleston Southern University

George Khachatryan Thesis: Derived Representation Schemes and Non-commutative Geometry Advisor: Yuri Berest First position: Reasoning Mind

Samuel Kolins Thesis: Face Vectors of Subdivision of Balls Advisor: Edward Swartz First position: Assistant professor at Lebanon Valley College

Victor Kostyuk Thesis: Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups Advisor: Karen Vogtmann First position: Knowledge engineering at Reasoning Mind

Ho Hon Leung Thesis: K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory Advisor: Reyer Sjamaar First position: Assistant professor at the Canadian University of Dubai

Benjamin Lundell Thesis: Selmer Groups and Ranks of Hecke Rings Advisor: Ravi Ramakrishna First position: Acting assistant professor at the University of Washington

Eyvindur Ari Palsson Thesis: Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator Advisor: Camil Muscalu First position: Visiting assistant professor at the University of Rochester

Paul Shafer Thesis: On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Advisor: Richard A. Shore First position: Lecturer at Appalachian State University

Michelle Snider Thesis: Affine Patches on Positroid Varieties and Affine Pipe Dreams Advisor: Allen Knutson First position: Government consulting job in Maryland

Santi Tasena Thesis: Heat Kernel Analysis on Weighted Dirichlet Spaces Advisor: Laurent Saloff-Coste First position: Lecturer professor at Chiang Mai University, Thailand

Russ Thompson Thesis: Random Walks and Subgroup Geometry Advisor: Laurent Saloff-Coste First position: Postdoctoral fellow at the Mathematical Sciences Research Institute

Gwyneth Whieldon Thesis: Betti Numbers of Stanley-Reisner Ideals Advisor: Michael E. Stillman First position: Assistant professor of mathematics at Hood College

Andrew Cameron Thesis: Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations Advisor: Alfred H. Schatz First position: Adjunct instructor of mathematics at Tompkins Cortland Community College

Timothy Goldberg Thesis: Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry Advisor: Reyer Sjamaar First position: Visiting assistant professor of mathematics at Lenoir-Rhyne University

Gregory Muller Thesis: The Projective Geometry of Differential Operators Advisor: Yuri Berest First position: Assistant professor at Louisiana State University

Matthew Noonan Thesis: Geometric Backlund transofrmation in homogeneous spaces Advisor: John H. Hubbard

Sergio Pulido Niño Thesis: Financial Markets with Short Sales Prohibition Advisor: Philip E. Protter First position: Postdoctoral associate in applied probability and finance at Carnegie Mellon University

Home > FACULTIES > Applied Mathematics > APMATHS-ETD

## Applied Mathematics Theses and Dissertations

This collection contains theses and dissertations from the Department of Applied Mathematics, collected from the Scholarship@Western Electronic Thesis and Dissertation Repository

## Theses/Dissertations from 2023 2023

Visual Cortical Traveling Waves: From Spontaneous Spiking Populations to Stimulus-Evoked Models of Short-Term Prediction , Gabriel B. Benigno

Spike-Time Neural Codes and their Implication for Memory , Alexandra Busch

Study of Behaviour Change and Impact on Infectious Disease Dynamics by Mathematical Models , Tianyu Cheng

Series Expansions of Lambert W and Related Functions , Jacob Imre

Data-Driven Exploration of Coarse-Grained Equations: Harnessing Machine Learning , Elham Kianiharchegani

Pythagorean Vectors and Rational Orthonormal Matrices , Aishat Olagunju

The Magnetic Field of Protostar-Disk-Outflow Systems , Mahmoud Sharkawi

A Highly Charged Topic: Intrinsically Disordered Proteins and Protein pKa Values , Carter J. Wilson

Population Dynamics and Bifurcations in Predator-Prey Systems with Allee Effect , Yanni Zeng

## Theses/Dissertations from 2022 2022

A Molecular Dynamics Study Of Polymer Chains In Shear Flows and Nanocomposites , Venkat Bala

On the Spatial Modelling of Biological Invasions , Tedi Ramaj

Complete Hopf and Bogdanov-Takens Bifurcation Analysis on Two Epidemic Models , Yuzhu Ruan

A Theoretical Perspective on Parasite-Host Coevolution with Alternative Modes of Infection , George N. Shillcock

## Theses/Dissertations from 2021 2021

Mathematical Modelling & Simulation of Large and Small Scale Structures in Star Formation , Gianfranco Bino

Mathematical Modelling of Ecological Systems in Patchy Environments , Ao Li

Credit Risk Measurement and Application based on BP Neural Networks , Jingshi Luo

Coevolution of Hosts and Pathogens in the Presence of Multiple Types of Hosts , Evan J. Mitchell

SymPhas: A modular API for phase-field modeling using compile-time symbolic algebra , Steven A. Silber

Population and Evolution Dynamics in Predator-prey Systems with Anti-predation Responses , Yang Wang

## Theses/Dissertations from 2020 2020

The journey of a single polymer chain to a nanopore , Navid Afrasiabian

Exploration Of Stock Price Predictability In HFT With An Application In Spoofing Detection , Andrew Day

Multi-Scale Evolution of Virulence of HIV-1 , David W. Dick

Contraction Analysis of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria and Plasmodium within Mosquitoes. , Nickolas Goncharenko

Phage-Bacteria Interaction and Prophage Sequences in Bacterial Genomes , Amjad Khan

The Effect of the Initial Structure on the System Relaxation Time in Langevin Dynamics , Omid Mozafar

Mathematical modelling of prophage dynamics , Tyler Pattenden

Hybrid Symbolic-Numeric Computing in Linear and Polynomial Algebra , Leili Rafiee Sevyeri

Abelian Integral Method and its Application , Xianbo Sun

## Theses/Dissertations from 2019 2019

Algebraic Companions and Linearizations , Eunice Y. S. Chan

Algorithms for Mappings and Symmetries of Differential Equations , Zahra Mohammadi

Algorithms for Bohemian Matrices , Steven E. Thornton

A Survey Of Numerical Quadrature Methods For Highly Oscillatory Integrals , Jeet Trivedi

## Theses/Dissertations from 2018 2018

Properties and Computation of the Inverse of the Gamma function , Folitse Komla Amenyou

Optimization Studies and Applications: in Retail Gasoline Market , Daero Kim

Models of conflict and voluntary cooperation between individuals in non-egalitarian social groups , Cody Koykka

Investigation of chaos in biological systems , Navaneeth Mohan

Bifurcation Analysis of Two Biological Systems: A Tritrophic Food Chain Model and An Oscillating Networks Model , Xiangyu Wang

Ecology and Evolution of Dispersal in Metapopulations , Jingjing Xu

Selected Topics in Quantization and Renormalization of Gauge Fields , Chenguang Zhao

Three Essays on Structural Models , Xinghua Zhou

## Theses/Dissertations from 2017 2017

On Honey Bee Colony Dynamics and Disease Transmission , Matthew I. Betti

Simulation of driven elastic spheres in a Newtonian fluid , Shikhar M. Dwivedi

Feasible Computation in Symbolic and Numeric Integration , Robert H.C. Moir

Modelling Walleye Population and Its Cannibalism Effect , Quan Zhou

## Theses/Dissertations from 2016 2016

Dynamics of Discs in a Nematic Liquid Crystal , Alena Antipova

Modelling the Impact of Climate Change on the Polar Bear Population in Western Hudson Bay , Nicole Bastow

A comparison of solution methods for Mandelbrot-like polynomials , Eunice Y. S. Chan

A model-based test of the efficacy of a simple rule for predicting adaptive sex allocation , Joshua D. Dunn

Universal Scaling Properties After Quantum Quenches , Damian Andres Galante

Modeling the Mass Function of Stellar Clusters Using the Modified Lognormal Power-Law Probability Distribution Function , Deepakshi Madaan

Bacteria-Phage Models with a Focus on Prophage as a Genetic Reservoir , Alina Nadeem

A Sequence of Symmetric Bézout Matrix Polynomials , Leili Rafiee Sevyeri

Study of Infectious Diseases by Mathematical Models: Predictions and Controls , SM Ashrafur Rahman

The survival probability of beneficial de novo mutations in budding viruses, with an emphasis on influenza A viral dynamics , Jennifer NS Reid

Essays in Market Structure and Liquidity , Adrian J. Walton

Computation of Real Radical Ideals by Semidefinite Programming and Iterative Methods , Fei Wang

Studying Both Direct and Indirect Effects in Predator-Prey Interaction , Xiaoying Wang

## Theses/Dissertations from 2015 2015

The Effect of Diversification on the Dynamics of Mobile Genetic Elements in Prokaryotes: The Birth-Death-Diversification Model , Nicole E. Drakos

Algorithms to Compute Characteristic Classes , Martin Helmer

Studies of Contingent Capital Bonds , Jingya Li

Determination of Lie superalgebras of supersymmetries of super differential equations , Xuan Liu

Edge states and quantum Hall phases in graphene , Pavlo Piatkovskyi

Evolution of Mobile Promoters in Prokaryotic Genomes. , Mahnaz Rabbani

Extensions of the Cross-Entropy Method with Applications to Diffusion Processes and Portfolio Losses , Alexandre Scott

## Theses/Dissertations from 2014 2014

A Molecular Simulation Study on Micelle Fragmentation and Wetting in Nano-Confined Channels , Mona Habibi

Study of Virus Dynamics by Mathematical Models , Xiulan Lai

Applications of Stochastic Control in Energy Real Options and Market Illiquidity , Christian Maxwell

Options Pricing and Hedging in a Regime-Switching Volatility Model , Melissa A. Mielkie

Optimal Contract Design for Co-development of Companion Diagnostics , Rodney T. Tembo

Bifurcation of Limit Cycles in Smooth and Non-smooth Dynamical Systems with Normal Form Computation , Yun Tian

Understanding Recurrent Disease: A Dynamical Systems Approach , Wenjing Zhang

## Theses/Dissertations from 2013 2013

Pricing and Hedging Index Options with a Dominant Constituent Stock , Helen Cheyne

On evolution dynamics and strategies in some host-parasite models , Liman Dai

Valuation of the Peterborough Prison Social Impact Bond , Majid Hasan

Sensitivity Analysis of Minimum Variance Portfolios , Xiaohu Ji

Eigenvalue Methods for Interpolation Bases , Piers W. Lawrence

Hybrid Lattice Boltzmann - Molecular Dynamics Simulations With Both Simple and Complex Fluids , Frances E. Mackay

Ecological Constraints and the Evolution of Cooperative Breeding , David McLeod

A single cell based model for cell divisions with spontaneous topology changes , Anna Mkrtchyan

Analysis of Re-advanceable Mortgages , Almas Naseem

Modeling leafhopper populations and their role in transmitting plant diseases. , Ji Ruan

Topological properties of modular networks, with a focus on networks of functional connections in the human brain , Estefania Ruiz Vargas

Computation Sequences for Series and Polynomials , Yiming Zhang

## Theses/Dissertations from 2012 2012

A Real Options Valuation of Renewable Energy Projects , Natasha Burke

Approximate methods for dynamic portfolio allocation under transaction costs , Nabeel Butt

Optimal clustering techniques for metagenomic sequencing data , Erik T. Cameron

Phase Field Crystal Approach to the Solidification of Ferromagnetic Materials , Niloufar Faghihi

Molecular Dynamics Simulations of Peptide-Mineral Interactions , Susanna Hug

Molecular Dynamics Studies of Water Flow in Carbon Nanotubes , Alexander D. Marshall

Valuation of Multiple Exercise Options , T. James Marshall

Incomplete Market Models of Carbon Emissions Markets , Walid Mnif

Topics in Field Theory , Alexander Patrushev

Pricing and Trading American Put Options under Sub-Optimal Exercise Policies , William Wei Xing

Further applications of higher-order Markov chains and developments in regime-switching models , Xiaojing Xi

## Theses/Dissertations from 2011 2011

Bifurcations and Stability in Models of Infectious Diseases , Bernard S. Chan

Real Options Models in Real Estate , Jin Won Choi

Models, Techniques, and Metrics for Managing Risk in Software Engineering , Andriy Miranskyy

Thermodynamics, Hydrodynamics and Critical Phenomena in Strongly Coupled Gauge Theories , Christopher Pagnutti

Molecular Dynamics Studies of Interactions of Phospholipid Membranes with Dehydroergosterol and Penetrating Peptides , Amir Mohsen Pourmousa Abkenar

Socially Responsible Investment in a Changing World , Desheng Wu

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- Discuss the binomial theorem
- The math behind encryption
- Game theory and its real-life applications
- Analyze the Bernoulli scheme
- What are holomorphic functions and how do they work?
- Describe big numbers
- Solving the Tower of Hanoi problem

## Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

- Methods to count discrete objects
- The origins of Greek symbols in mathematics
- Methods to solve simultaneous equations
- Real-world applications of the theorem of Pythagoras
- Discuss the limits of diffusion
- Use math to analyze the abortion data in the UK over the last 100 years
- Discuss the Knot theory
- Analyze predictive models (take meteorology as an example)
- In-depth analysis of the Monte Carlo methods for inverse problems
- Squares vs. rectangles (compare and contrast)

## Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

- Discuss the greatest common divisor
- Explain the extended Euclidean algorithm
- What are RSA numbers?
- Discuss Bézout’s lemma
- In-depth analysis of the square-free polynomial
- Discuss the Stern-Brocot tree
- Analyze Fermat’s little theorem
- What is a discrete logarithm?
- Gauss’s lemma in number theory
- Analyze the Pentagonal number theorem

## Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

- Discuss Brun’s constant
- An in-depth look at the Brahmagupta–Fibonacci identity
- What is derivative algebra?
- Describe the Symmetric Boolean function
- Discuss orders of approximation in limits
- Solving Regiomontanus’ angle maximization problem
- What is a Quadratic integral?
- Define and describe complementary angles
- Analyze the incircle and excircles of a triangle
- Analyze the Bolyai–Gerwien theorem in geometry
- Math in our everyday life

## Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

- Mathematics and its appliance in Artificial Intelligence
- Try to solve an unsolved problem in math
- Discuss Kolmogorov’s zero-one law
- What is a discrete random variable?
- Analyze the Hewitt–Savage zero-one law
- What is a transferable belief model?
- Discuss 3 major mathematical theorems
- Describe and analyze the Dempster-Shafer theory
- An in-depth analysis of a continuous stochastic process
- Identify and analyze Gauss-Markov processes

## Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

- Define the hyperbola
- Do we need to use a calculator during math class?
- The binomial theorem and its real-world applications
- What is a parabola in geometry?
- How do you calculate the slope of a curve?
- Define the Jacobian matrix
- Solving matrix problems effectively
- Why do we need differential equations?
- Should math be mandatory in all schools?
- What is a Hessian matrix?

## Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

- Discuss the reductio ad absurdum approach
- Discuss Boolean algebra
- What is consistency proof?
- Analyze Trakhtenbrot’s theorem (the finite model theory)
- Discuss the Gödel completeness theorem
- An in-depth analysis of Morley’s categoricity theorem
- How does the Back-and-forth method work?
- Discuss the Ehrenfeucht–Fraïssé game technique
- Discuss Aleph numbers (Aleph-null and Aleph-one)
- Solving the Suslin problem

## Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

- Discuss the differential equation
- Analyze the Jacobson density theorem
- The 4 properties of a binary operation in algebra
- Analyze the unary operator in depth
- Analyze the Abel–Ruffini theorem
- Epimorphisms vs. monomorphisms: compare and contrast
- Discuss the Morita duality in algebraic structures
- Idempotent vs. nilpotent in Ring theory
- Discuss the Artin-Wedderburn theorem
- What is a commutative ring in algebra?
- Analyze and describe the Noetherian ring

## Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

- What are the goals a mathematics professor should have?
- What is math anxiety in the classroom?
- Teaching math in UK schools: the difficulties
- Computer programming or math in high school?
- Is math education in Europe at a high enough level?
- Common Core Standards and their effects on math education
- Culture and math education in Africa
- What is dyscalculia and how does it manifest itself?
- When was algebra first thought in schools?
- Math education in the United States versus the United Kingdom

## Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

- What is a multiplication table?
- Analyze the Scholz conjecture
- Explain exponentiating by squaring
- Analyze the Myhill-Nerode theorem
- What is a tree automaton?
- Compare and contrast the Pushdown automaton and the Büchi automaton
- Discuss the Markov algorithm
- What is a Turing machine?
- Analyze the post correspondence problem
- Discuss the linear speedup theorem
- Discuss the Boolean satisfiability problem

## Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

- What is two-element Boolean algebra?
- The life of Gauss
- The life of Isaac Newton
- What is an orthodiagonal quadrilateral?
- Tessellation in Euclidean plane geometry
- Describe a hyperboloid in 3D geometry
- What is a sphericon?
- Discuss the peculiarities of Borel’s paradox
- Analyze the De Finetti theorem in statistics
- What are Martingales?
- The basics of stochastic calculus

## Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

- Discuss Newton’s laws of motion
- Analyze the perpendicular axes rule
- How is a Galilean transformation done?
- The conservation of energy and its applications
- Discuss Liouville’s theorem in Hamiltonian mechanics
- Analyze the quantum field theory
- Discuss the main components of the Lorentz symmetry
- An in-depth look at the uncertainty principle

## Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

- Most useful trigonometry functions in math
- The life of Archimedes and his achievements
- Trigonometry in computer graphics
- Using Vincenty’s formulae in geodesy
- Define and describe the Heronian tetrahedron
- The math behind the parabolic microphone
- Discuss the Japanese theorem for concyclic polygons
- Analyze Euler’s theorem in geometry

## Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

- Finding critical points in a graph
- The basics of calculus
- What makes a graph ultrahomogeneous?
- How do you calculate the area of different shapes?
- What contributions did Euclid have to the field of mathematics?
- What is Diophantine geometry?
- What makes a graph regular?
- Analyze a full binary tree

## Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

- What are extremal problems and how do you solve them?
- Discuss an unsolvable math problem
- How can supercomputers solve complex mathematical problems?
- An in-depth analysis of fractals
- Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
- Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
- An in-depth look at Einstein’s field equation
- The math behind computer vision and object recognition

## Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

- When do we need to apply the L’Hôpital rule?
- Discuss the Leibniz integral rule
- Calculus in ancient Egypt
- Discuss and analyze linear approximations
- The applications of calculus in real life
- The many uses of Stokes’ theorem
- Discuss the Borel regular measure
- An in-depth analysis of Lebesgue’s monotone convergence theorem

## Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

- The life and work of the famous Pierre de Fermat
- What are limits and why are they useful in calculus?
- Explain the concept of congruency
- The life and work of the famous Jakob Bernoulli
- Analyze the rhombicosidodecahedron and its applications
- Calculus and the Egyptian pyramids
- The life and work of the famous Jean d’Alembert
- Discuss the hyperplane arrangement in combinatorial computational geometry
- The smallest enclosing sphere method in combinatorics

## Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

- Is paying a loan with another loan a good approach?
- Discuss the major causes of a stock market crash
- Best debt amortization methods in the US
- How do bank loans work in the UK?
- Calculating interest rates the easy way
- Discuss the pros and cons of annuities
- Basic business math skills everyone should possess
- Business math in United States schools
- Analyze the discount factor

## Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

- What is the autoregressive conditional duration?
- Applying the ANOVA method to ranks
- Discuss the practical applications of the Bates distribution
- Explain the principle of maximum entropy
- Discuss Skorokhod’s representation theorem in random variables
- What is the Factorial moment in the Theory of Probability?
- Compare and contrast Cochran’s C test and his Q test
- Analyze the De Moivre-Laplace theorem
- What is a negative probability?

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## Mathematics MSc dissertations

The Department of Mathematics and Statistics was host until 2014 to the MSc course in the Mathematics of Scientific and Industrial Computation (previously known as Numerical Solution of Differential Equations) and the MSc course in Mathematical and Numerical Modelling of the Atmosphere and Oceans. A selection of dissertation titles are listed below, some of which are available online:

2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

## 2014: Mathematics of Scientific and Industrial Computation

Amanda Hynes - Slow and superfast diffusion of contaminant species through porous media

## 2014: Applicable and Numerical Mathematics

Emine Akkus - Estimating forecast error covariance matrices with ensembles

Rabindra Gurung - Numerical solution of an ODE system arising in photosynthesis

## 2013: Mathematics of Scientific and Industrial Computation

Zeinab Zargar - Modelling of Hot Water Flooding as an Enhanced Oil Recovery Method

Siti Mazulianawati Haji Majid - Numerical Approximation of Similarity in Nonlinear Diffusion Equations

## 2013: Mathematical and Numerical Modelling of the Atmosphere and Oceans

Yu Chau Lam - Drag and Momentum Fluxes Produced by Mountain Waves

Josie Dodd - A Moving Mesh Approach to Modelling the Grounding Line in Glaciology

## 2012: Mathematics of Scientific and Industrial Computation

Chris Louder - Mathematical Techniques of Image Processing

Jonathan Muir - Flux Modelling of Polynyas

Naomi Withey - Computer Simulations of Dipolar Fluids Using Ewald Summations

## 2012: Mathematical and Numerical Modelling of the Atmosphere and Oceans

Jean-Francois Vuillaume - Numerical prediction of flood plains using a Lagrangian approach

## 2011: Mathematics of Scientific and Industrial Computation

Tudor Ciochina - The Closest Point Method

Theodora Eleftheriou - Moving Mesh Methods Using Monitor Functions for the Porous Medium Equation

Melios Michael - Self-Consistent Field Calculations on a Variable Resolution Grid

## 2011: Mathematical and Numerical Modelling of the Atmosphere and Oceans

Peter Barnet - Rain Drop Growth by Collision and Coalescence

Matthew Edgington - Moving Mesh Methods for Semi-Linear Problems

Samuel Groth - Light Scattering by Penetrable Convex Polygons

Charlotte Kong - Comparison of Approximate Riemann Solvers

Amy Jackson - Estimation of Parameters in Traffic Flow Models Using Data Assimilation

Bruce Main - Solving Richards' Equation Using Fixed and Moving Mesh Schemes

Justin Prince - Fast Diffusion in Porous Media

Carl Svoboda - Reynolds Averaged Radiative Transfer Model

## 2010: Mathematics of Scientific and Industrial Computation

Tahnia Appasawmy - Wave Reflection and Trapping in a Two Dimensional Duct

Nicholas Bird - Univariate Aspects of Covariance Modelling within Operational Atmospheric Data Assimilation

Michael Conland - Numerical Approximation of a Quenching Problem

Katy Shearer - Mathematical Modelling of the regulation and uptake of dietary fats

Peter Westwood - A Moving Mesh Finite Element Approach for the Cahn-Hilliard Equation

Kam Wong - Accuracy of a Moving Mesh Numerical Method applied to the Self-similar Solution of Nonlinear PDEs

## 2010: Mathematical and Numerical Modelling of the Atmosphere and Oceans

James Barlow - Computation and Analysis of Baroclinic Rossby Wave Rays in the Atlantic and Pacific Oceans

Martin Conway - Heat Transfer in a Buried Pipe

Simon Driscoll - The Earth's Atmospheric Angular Momentum Budget and its Representation in Reanalysis Observation Datasets and Climate Models

George Fitton - A Comparative Study of Computational Methods in Cosmic Gas Dynamics Continued

Fay Luxford - Skewness of Atmospheric Flow Associated with a Wobbling Jetstream

Jesse Norris - A Semi-Analytic Approach to Baroclinic Instability on the African Easterly Jet

Robert J. Smith - Minimising Time-Stepping Errors in Numerical Models of the Atmosphere and Ocean

Amandeep Virdi - The Influence of the Agulhas Leakage on the Overturning Circulation from Momentum Balances

## 2009: Mathematics of Scientific and Industrial Computation

Charlotta Howarth - Integral Equation Formulations for Scattering Problems

David Fairbairn - Comparison of the Ensemble Transform Kalman Filter with the Ensemble Transform Kalman Smoother

Mark Payne - Mathematical Modelling of Platelet Signalling Pathways Mesh Generation and its application to Finite Element Methods

Mary Pham - Mesh Generation and its application to Finite Element Methods

Sarah Cole - Blow-up in a Chemotaxis Model Using a Moving Mesh Method

## 2009: Mathematical and Numerical Modelling of the Atmosphere and Oceans

Danila Volpi - Estimation of parameters in traffic flow models using data assimilation

Dale Partridge - Analysis and Computation of a Simple Glacier Model using Moving Grids

David MacLeod - Evaluation of precipitation over the Middle East and Mediterranean in high resolution climate models

Joanne Pocock - Ensemble Data Assimilation: How Many Members Do We Need?

Neeral Shah - Impact and implications of climate variability and change on glacier mass balance in Kenya

Tomos Roberts - Non-oscillatory interpolation for the Semi-Lagrangian scheme

Zak Kipling - Error growth in medium-range forecasting models

Zoe Gumm - Bragg Resonance by Ripple Beds

## 2008: Mathematics of Scientific and Industrial Computation

Muhammad Akram - Linear and Quadratic Finite Elements for a Moving Mesh Method

Andrew Ash - Examination of non-Time Harmonic Radio Waves Incident on Plasmas

Cassandra Moran - Harbour modelling and resonances

Elena Panti - Boundary Element Method for Heat Transfer in a Buried Pipe

Juri Parrinello - Modelling water uptake in rice using moving meshes

Ashley Twigger - Blow-up in the Nonlinear Schrodinger Equation Using an Adaptive Mesh Method

Chloe Ward - Numerical Evaluation of Oscillatory Integrals

Christopher Warner - Forward and Inverse Water-Wave Scattering by Topography

## 2008: Mathematical and Numerical Modelling of the Atmosphere and Oceans

Fawzi Al Busaidi - Fawzi Albusaidi

Christopher Bowden - A First Step Towards the Calculation of a Connectivity Matrix for the Great Barrier Reef

Evangelia-Maria Giannakopoulou - Flood Prediction and Uncertainty

Victoria Heighton - 'Every snowflake is different'

Thomas Jordan - Does Self-Organised Criticality Occur in the Tropical Convective System?

Gillian Morrison - Numerical Modelling of Tidal Bores using a Moving Mesh

Rachel Pritchard - Evaluation of Fractional Dispersion Models

## 2007: Numerical solution of differential equations

Tamsin Lee - New methods for approximating acoustic wave transmission through ducts (PDF 2.5MB)

Lee Morgan - Anomalous diffusion (PDF-1.5MB)

Keith Pham - Finite element modelling of multi-asset barrier options (PDF-3MB)

Alastair Radcliffe - Finite element modelling of the atmosphere using the shallow water equations (PDF-2.5MB)

Sanita Vetra - The computation of spectral representations for evolution PDE (PDF-3.2MB)

## 2007: Mathematical and numerical modelling of the atmosphere and oceans

Laura Baker - Properties of the ensemble Kalman filter (PDF-3.8MB)

Alison Brass - A moving mesh method for the discontinuous Galerkin finite element technique (PDF-916KB)

Daniel Lucas - Application of the phase/amplitude method to the study of trapped waves in the atmosphere and oceans (PDF-1.1MB)

Duduzile Nhlengethwa - Petrol or diesel (PDF-1MB)

Rhiannon Roberts - Modelling glacier flow (PDF-406KB)

David Skinner - A moving mesh finite element method for the shallow water equations (PDF-4.3MB)

Jovan Stojsavljevic - Investigation of waiting times in non-linear diffusion equations using a moving mesh method (PDF-538KB)

## 2006: Numerical solution of differential equations

Bonhi Bhattacharya - A moving finite element method for high order nonlinear diffusion problems

Jonathan Coleman - High frequency boundary element methods for scattering by complex polygons

Rachael England - The use of numerical methods in solving pricing problems for exotic financial derivatives with a stochastic volatility

Stefan King - Best fits with adjustable nodes and scale invariance

Edmund Ridley - Analysis of integral operators from scattering problems

Nicholas Robertson - A moving Lagrangian mesh model of a lava dome volcano and talus slope

## 2006: Mathematical and numerical modelling of the atmosphere and oceans

Iain Davison - Scale analysis of short term forecast errors

Richard Silveira - Electromagnetic scattering by simple ice crystal shapes

Nicola Stone - Development of a simplified adaptive finite element model of the Gulf Stream

Halina Watson - The behaviour of 4-D Var for a highly nonlinear system

## 2005: Numerical solution of differential equations

Jonathan Aitken - Data dependent mesh generation for peicewise linear interpolation

Stephen Arden - A collocation method for high frequency scattering by convex polygons

Shaun Benbow - Numerical methods for american options

Stewart Chidlow - Approximations to linear wave scattering by topography using an integral equation approach

Philip McLaughlin - Outdoor sound propagation and the boundary element method

Antonis Neochoritis - Numerical modelling of islands and capture zone size distributions in thin film growth

Kylie Osman - Numerical schemes for a non-linear diffusion problem

Shaun Potticary - Efficient evaluation of highly oscillatory integrals

Martyn Taylor - Investigation into how the reduction of length scales affects the flow of viscoelastic fluid in parallel plate geometries

Aanand Venkatramanan - American spread option pricing

## 2005: Mathematical and numerical modelling of the atmosphere and oceans

Richard Fruehmann - Ageostrophic wind storms in the central Caspian sea

Gemma Furness - Using optimal estimation theory for improved rainfall rates from polarization radar

Edward Hawkins - Vorticity extremes in numerical simulations of 2-D geostrophic turbulence

Robert Horton - Two dimensional turbulence in the atmosphere and oceans

David Livings - Aspects of the ensemble Kalman filter

David Sproson - Energetics and vertical structure of the thermohaline circulation

## 2004: Numerical solution of differential equations

Rakhib Ahmed - Numerical schemes applied to the Burgers and Buckley-Leverett equations

James Atkinson - Embedding methods for the numerical solution of convolution equations

Catherine Campbell-Grant - A comparative study of computational methods in cosmic gas dynamics

Paresh Prema - Numerical modelling of Island ripening

Mark Webber - The point source methods in inverse acoustic scattering

## 2004: Mathematical and numerical modelling of the atmosphere and oceans

Oliver Browne - Improving global glacier modelling by the inclusion of parameterised subgrid hypsometry within a three-dimensional, dynamical ice sheet model

Petros Dalakakis - Radar scattering by ice crystals

Eleanor Gosling - Flow through porous media: recovering permeability data from incomplete information by function fitting .

Sarah Grintzevitch - Heat waves: their climatic and biometeorological nature in two north american reigions

Helen Mansley - Dense water overflows and cascades

Polly Smith - Application of conservation laws with source terms to the shallow water equations and crowd dynamics

Peter Taylor - Application of parameter estimation to meteorology and food processing

## 2003: Numerical solution of differential equations

Kate Alexander - Investigation of a new macroscopic model of traffic flow

Luke Bennetts - An application of the re-iterated Galerkin approximation in 2-dimensions

Peter Spence - The Position of the free boundary formed between an expanding plasma and an electric field in differing geometries

Daniel Vollmer - Adaptive mesh refinement using subdivision of unstructured elements for conservation laws

## 2003: Mathematical and numerical modelling of the atmosphere and oceans

Clare Harris - The Valuation of weather derivatives using partial differential equations

Sarah Kew - Development of a 3D fractal cirrus model and its use in investigating the impact of cirrus inhomogeneity on radiation

Emma Quaile - Rotation dominated flow over a ridge

Jemma Shipton - Gravity waves in multilayer systems

## 2002: Numerical solution of differential equations

Winnie Chung - A Spectral Method for the Black Scholes Equations

Penny Marno - Crowded Macroscopic and Microscopic Models for Pedestrian Dynamics

Malachy McConnell - On the numerical solution of selected integrable non-linear wave equations

Stavri Mylona - An Application of Kepler's Problem to Formation Flying using the Störmer-Verlet Method

## 2002: Mathematical and numerical modelling of the atmosphere and oceans

Sarah Brodie - Numerical Modelling of Stratospheric Temperature Changes and their Possible Causes

Matt Sayer - Upper Ocean Variability in the Equatorial Pacific on Diurnal to Intra-seasonal Timescales

Laura Stanton - Linearising the Kepler problem for 4D-var Data Assimilation

## 2001: Numerical solution of differential equations

R.B. Brad - An Implementation of the Box Scheme for use on Transcritical Problems

D. Garwood - A Comparison of two approaches for the Approximating of 2-D Scattered Data, with Applications to Geological Modelling

R. Hawkes - Mesh Movement Algorithms for Non-linear Fisher-type Equations

P. Jelfs - Conjugate Gradients with Rational and Floating Point Arithmetic

M. Maisey - Vorticity Preserving Lax-Wendroff Type Schemes

C.A. Radcliffe - Positive Schemes for the Linear Advection Equation

## 2000: Numerical solution of differential equations

D. Brown - Two Data Assimilation Techniques for Linear Multi-input Systems.

S. Christodoulou - Finite Differences Applied to Stochastic Problems in Pricing Derivatives.

C. Freshwater - The Muskingum-Cunge Method for Flood Routing.

S.H. Man - Galerkin Methods for Coupled Integral Equations.

A. Laird - A New Method for Solving the 2-D Advection Equation.

T. McDowall - Finite Differences Applied to Joint Boundary Layer and Eigenvalue Problems.

M. Shahrill - Explicit Schemes for Finding Soliton Solutions of the Korteweg-de Vries Equation.

B. Weston - A Marker and Cell Solution of the Incompressible Navier-Stokes Equations for Free Surface Flow.

## 1999: Numerical solution of differential equations

M. Ariffin - Grid Equidistribution via Various Algorithmic Approaches.

S.J. Fletcher - Numerical Approximations to Bouyancy Advection in the Eddy Model.

N.Fulcher - The Finite Element Approximation of the Natural Frequencies of a Circular Drum.

V. Green - A Financial Model and Application of the Semi-Lagrangian Time-Stepping Scheme.

D.A. Parry - Construction of Symplectic Runge-Kutta Methods and their Potential for Molecular Dynamics Application.

S.C. Smith - The Evolution of Travelling Waves in a Simple Model for an Ionic Autocatalytic System

P. Swain - Numerical Investigations of Vorticity Preserving Lax-Wendroff Type Schemes.

M. Wakefield - Variational Methods for Upscaling.

## 1998: Numerical solution of differential equations

C.C. Anderson - A dual-porosity model for simulating the preferential movement of water in the unsaturated zone of a chalk aquifer.

K.W. Blake - Contour zoning.

M.R. Garvie - A comparison of cell-mapping techniques for basins of attraction.

W. Gaudin - HYDRA: a 3-d MPP Eulerian hydrocode.

D. Gnandi - Alternating direction implicit method applied to stochastic problems in derivative finance.

J. Hudson - Numerical techniques for conservation laws with source terms. .

H.S. Khela - The boundary integral method.

K. Singh - A comparison of numerical schemes for pricing bond options.

## 1997: Numerical solution of differential equations

R.V. Egan - Chaotic response of the Duffing equation. A numerical investigation into the dynamics of the non-linear vibration equation.

R.G. Higgs - Nonlinear diffusion in reservoir simulation.

P.B. Horrocks - Fokker-Planck model of stochastic acceleration: a study of finite difference schemes.

M.A. Wlasek - Variational data assimilation: a study.

## 1996: Numerical solution of differential equations

A. Barnes - Reaction-diffusion waves in an isothermal chemical system with a general order of autocatalysis.

S.J. Leary - Mesh movement and mesh subdivision.

S. McAllister - First and second order complex differential equations.

R.K. Sadhra - Investigating dynamical systems using the cell-to-cell mapping.

J.P. Wilson - A refined numerical model of sediment deposition on saltmarshes.

## 1995: Numerical solution of differential equations

M. Bishop - The modelling and analysis of the equations of motion of floating bodies on regular waves.

J. Olwoch - Isothermal autocatalytic reactions with an immobilized autocatalyst.

S. Stoke - Eulerian methods with a Lagrangian phase in gas dynamics.

R. Coad - 1-D and 2-D simulations of open channel flows using upwinding schemes.

## 1994: Numerical solution of differential equations

M. Ali - Application of control techniques to solving linear systems of equations .

M.H. Brookes - An investigation of a dual-porosity model for the simulation of unsaturated flow in a porous medium .

A.J. Crossley - Application of Roe's scheme to the shallow water equations on the sphere .

D.A. Kirkland - Huge singular values and the distance to instability. .

B.M. Neil - An investigation of the dynamics of several equidistribution schemes .

## 1993: Numerical solution of differential equations

P.A. Burton - Re-iterative methods for integral equations .

J.M. Hobbs - A moving finite element approach to semiconductor process modelling in 1-D. .

L.M. Whitfield - The application of optimal control theory to life cycle strategies .

S.J. Woolnough - A numerical model of sediment deposition on saltmarshes .

## 1992: Numerical solution of differential equations

I. MacDonald - The numerical solution of free surface/pressurized flow in pipes. .

A.D. Pollard - Preconditioned conjugate gradient methods for serial and parallel computers. .

C.J. Smith - Adaptive finite difference solutions for convection and convection-diffusion problems .

## 1991: Numerical solution of differential equations

K.J. Neylon - Block iterative methods for three-dimensional groundwater flow models .

Thesis Helpers

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## 202 Math Research Topics: List To Vary Your Ideas

Mathematics is an exceptional field of study dealing primarily with numbers. It also deals with structures, formulas, shapes, spaces, and quantities of where they are contained.

Maths encompasses different types of computations that are applied in the real world.

Math requires a lot of analysis. This is why there are different types of maths. They all encompass different subjects and deal with different things. What are the types of maths?

Arithmetic This is perhaps the commonest type or branch of maths. It is one of the oldest and it encompasses basic numbers operations. These are addition, subtraction, multiplication, and divisions; in some schools, the short word for it is BODMAS. This is known as the Bracket of Division, Multiplication, Addition, and Subtraction. Algebra This is where unknown quantities are represented by alphabets and used along with numbers. The letters these unknown quantities are represented by are usually A, B, X, and Y, and they could also be symbols. Geometry This is considered one of the practical branches of maths as it examines sizes, shapes, figures, and the features of these entities. The most common parts of geometry are lines, points, solids, surfaces, and angles.

There are many other types but the above are the most popular. Others are trigonometry, topology, mathematical analysis, calculus, probability, statistics, and a few others.

As many students find it hard to develop maths research topics on their own, this is a chance for you. It’s okay to be worked up when you can’t find undergraduate math research topics that fit your project, essay or paper choices. This article will provide custom maths education research topics for your use. Before that, how do you structure your math essay or paper?

## How to Structure Your Math Essay or Paper

Structuring your essay or paper may require that you’ve been reading critical math journals. Reading them could have made it easy to understand how to structure your paper. However, you don’t have to worry if you haven’t. Structuring your paper as expected is an essential part of writing and you’ll know about it in this section. Before you learn that, how do you choose a topic?

## Choosing a Topic to Discuss

One of the difficult yet significant parts of any math essay or paper is choosing your topic. This is because you need to solve a problem or engage in a subject that has got less attention. You also need to understand the background to the subject you want to discuss as you can’t write blindly.

You must also be able to articulate your thoughts well as you must show visible knowledge before you commence the research and writing. How do you go about this? You can consider reading existing research. You can even take notes during classes to see the areas you think more work needs to be done.

After choosing your topic, conduct your research to see if you can investigate the sphere. If you can, you need to structure your research thus:

The Background This includes the discussion on what the essay is about. Depending on what you’re writing about, you need to discuss the primary concepts, including the history of some terms, where essential, in this section. This section is more like general information about the subject you want to discuss with your paper. This helps your readers familiarize themselves with your intended discussion. The Introduction This is where the main ideas behind your essays (and the solutions you hope to proffer) are tended to the readers. This is where you also explain the symbols you’ll use and the principles which are required in your essay. Aside from this, you need to state the basic issues, the solutions you could offer, the laws which are essential to discuss to make your work comprehensible. The Main Body This is where you elaborate on your findings. You need to state the research problem, the formulas, the theories you’ll use in tackling the problem, and many other things. You also need to introduce different sections of maths into the main body which is divided by paragraphs and/or chapters as well as mathematical analysis where needed. Implications This is the last part of your essay or paper. This is where you share the insights of your research with your readers. You offer short explanations of the things you have discussed. If you have treated a subject in applied mathematics, this is where you give summaries of how math is connected to human life and the strategic importance of these to people.

By adhering to this structure, you would have crafted the best rated and high-quality maths paper. Furthermore, remember you always have an option to get help with dissertations and save your time. Since it is sometimes challenging to choose cool maths topics to research on your own, these are some for you:

## Research Topics in Math

Math is a broad subject. There is a study of the history of math as well as its influence in education, amongst many other sub-sections. If you’d like to create stunning research, you may choose to discuss any of these research topics in math to fulfill one of your academic requirements:

- What are the distinctions between commutative and noncommutative algebra?
- Discuss the methods of factoring quadratics
- Types of sequences and your understanding of them
- Partial fractions: what are they and how do they work?
- Logarithms: what are they and how do they work?
- An overview of Gaussian elimination
- An overview of Brun’s constant relevant
- A description of the effect of dyscalculia on daily student lives
- Describe Descartes’s Dukes of Signs and their application
- Greeks and geometry: discuss
- Describe Euler’s formula
- The progression in the study of math
- Congruence meaning and methods
- Describe the correlation of CT scans to geometry
- Hypercubes and how they work
- The basis of Cramer’s rule
- The examination of Archimedean solids
- Projective geometry and why it’s studied
- Types of Transformations and the available types
- Picasso’s works and the application of geometry
- Difference between the conventional and unconventional approaches to teaching
- Math education and the process of Improvement in the US
- Rhombicosidodecahedron and how it operates in real life
- What are the STEM career fields and why are they important?
- Why women are needed in STEM
- The goals of teaching maths
- How to teach maths to special students
- The correlation between maths and accounting
- The distinction between computer programming and applied maths
- Applied maths and its dynamics
- Processes of solving Heesch’s problem
- Why should kids learn equations?
- History of calculus
- Why there is a need for math camps in schools
- The need for more maths competition in the US
- Methods of draining flight schedule for a country
- Why are some math problems unsolved?
- Discuss the consequences of the gender gap in math students
- Encryption and prime numbers: how do they apply?
- The significance of maths in day to day living.

## Undergraduate Math Research Topics

As an undergraduate, you may also have a difficult time wrapping your head around math research topics. You may need to offer both practical and theoretical assessments while writing your paper or essay. The following are undergraduate math research topics:

- Show the proofs of what F-algebras are used
- Abstract algebra, what does it mean?
- Algebra and geometry: discuss
- Acute square triangulation: how it works
- Right triangles: discuss their importance
- Discuss number problems
- Why every math student should study non-Euclidean geometry
- Dirac manifolds and what it means
- Influence of geometry in physics, chemistry, and others
- The application of Riemannian manifolds in the Euclidean space
- How to improve your mathematical thinking ability
- Technology in maths: how is it used?
- Studies of maths in Europe
- Math anxiety and what it truly means
- Standardized testing and the goals of such
- Challenges of learning maths from public schools
- The significance of circles in maths
- The political and social significance of learning maths
- Research into how to increase student interest in maths
- How painting and drawing could help with maths
- Relationship of culture and maths
- History of algebra
- Role of maths in everyday life
- How math is used in Artificial intelligence
- The transferable belief model and its application
- An analysis of the Dempster-Shafer theory
- The role of continuous stochastic process in mathematics
- The major math theorems: discuss how they work
- Understanding the Gauss-Markov: The Evolution of maths
- Discrete random variable: an in-depth understanding of what it means in math and how to identify one.

## Math Research Topics for High School Students

As a high school student writing a research paper, one way to get high grades is to write what you know. If you know any math research paper topics for high school, they are the topics you should pick. You can consider:

- Hyperbola: what it is and how it’s used in math
- When to use a calculator in class
- How to find solutions to linear equations
- The need for Pythagoras theorem in maths
- The role of art in maths and vice versa
- Role of philosophy in maths
- An overview of numerical data
- Egyptian mathematics explained
- Binomial theorem and its importance
- Probability, and how to solve a question on dice
- Why is math made compulsory in schools?
- Why do students hate maths?
- Why do students hate math teachers?
- How is math applied in the workplace?
- What are imaginary numbers and why are they needed
- How to calculate the interest rate and what is their importance in the banking sector?
- Discount factor: how is it achieved and why is it important for students?
- Types of techniques to be used while finding solutions to mathematical and finance gaps
- Solving a matrix: what are the important formulas and principles to embrace?
- How to create a chart on a company’s financial analysis for the past 5 years.

## Interesting Math Research Topics

Writing a mathematical essay may seem complex to you if you can’t find simple topics to write about. There are many easy topics which are also general in maths. If you want to choose a relaxing topic for your math essay or paper, you can write about the following:

- The basic elements of Boolean algebra
- The life, time, and contribution of Isaac Newton to maths
- Sphericon and what it means
- Martingales and what they mean
- Hyperboloid and importance in geometry
- Describe the life, times, and contribution of Gauss to maths
- The most famous work of Jakob Bernoulli
- The most famous work of Jean d’Alembert
- Meaning and application of calculus in the banking field
- The meaning of congruence in math
- Analysis of De Finetti theorem in probability and statistics
- Describe Egyptian pyramids in concert with calculus
- Describe the enclosing sphere technique as used in combinatorics
- Tree automation meaning
- Pushdown automaton and Buchi automaton: differences and similarities
- What is the Markov algorithm?
- Describe what a Turing machine is
- What is the linear speedup theory in math?
- The Boolean satisfiability problem and what it means for students
- Why is the multiplication table important?
- Computational maths and its classes
- What does the post correspondence problem mean?
- What does the Scholz conjecture mean?
- How to calculate mean, median, and mode
- A study of the most difficult equations in math.

## Cool Math Topics to Research

As a student of any level, you may love to create math topics that are not exactly complex. These are topics that lean on the history of maths, math education research topics, and others. Consider these math research topics for college students for your next essay or paper:

- Discuss what the Golden Ratio means in the paintings of the Renaissance period
- How to learn math
- An overview of the multiple ideas to probability
- How chess and checkers is essential in understanding mathematics
- How Pythagorean theorem is applied in real-life maths
- How to measure infinity
- The features of Mobius strip in geometry
- Describe what is meant by the Pascal’s Triangle
- Evaluate the Georg Cantor set theory
- What is the history of the number types?
- How does probability relate to card tricks?
- Compare and contrast abstract and universal algebra
- Describe Euclid’s role in the evolution of maths
- Evaluate the role of Indians in maths
- Explain the limits of calculus
- Discuss what predictive and prescriptive statistical analysis means
- What does chaos theory mean?
- Explain how to solve the Rubik’s Cube
- Why are some math equations so complex?
- How is geometry used in contemporary architectural designs?

## Math Research Topics for Middle School

It’s okay to be worried about math topics for your research as a middle school student. There are still different unique topics that are rebranded from existing ones. You can find some of the right math research paper topics for you here:

- The role of statistics in business
- Definition of economic lot scheduling
- Why stock market crash
- The contribution of many traders in the New York Stock Exchange
- Revenue management and its history
- What are the financial indicators of a good investment?
- What are the odds of depreciation?
- How can any country benefit from the poor currency?
- Describe debt amortization and how math helps
- How to calculate net worth
- Distinctions in calculus, trigonometry, and algebra
- How did calculus start?
- How did trigonometry start?
- Why is Ito stochastic important in math?
- What do limits in math mean?
- How to know critical points in graphs
- What does nonstandard analysis in the probability theory mean?
- Describe continuous function
- The main principles of calculus
- The main principles of Pythagoras theorem
- Application of calculus in finance
- Value theorem in math
- Ratio and root test definition
- Linear approximations and how they work
- What is the Jacobson density theorem?
- Similarities and differences between epimorphisms and monopolists
- What does the Artin-Wedderburn theorem mean?
- Commutative ring and its meaning in algebra
- How difficult is it to teach maths?
- How standards examination curriculum affects math education.

## Applied Math Research Topics

Applied math is a branch which deals with the application of mathematical methods in real life. These are manifested by applications in finance, physics, engineering, biology, medicine, and others. Through specialized knowledge, applied math is made possible. These are some topics for you in this area:

- How discovering genes can help determine healthy and unhealthy patients
- Role of algorithms in probabilistic modeling
- The need for mathematicians in developing robots
- The role of mathematicians in crime data analysis and prevention
- How did Isaac’s Laws of Motion help in real life?
- How math helped with energy conservation
- The role of math in quantum theory
- Analyze the features of the Lorentz symmetry
- Evaluate statistical signal processing in details
- Discuss how Galilean Transformation was achieved
- Examine nonlinear models
- Elucidate on the importance of data mining in banking
- The importance of step-stress modeling
- The significance of computer tomography
- What are the dimensions used in examining fingerprints?

## Math Research Topics for College Students

As college students, you are at a critical level. You need maths topics for your essays and paper. You may also need them to prepare for your exams. These are some math research topics for you:

- Evolution of mathematics
- Explore the varieties of the Tower of Hanoi solutions
- Discuss how to use Napier’s bones
- Give examples of chaos theory and explain
- Discuss the important mathematical equations of all times
- Examine the nitty-gritty of barcodes
- What is the Traveling Salesman Problem?
- Natural selection and Fisher’s fundamental theorem of understanding it
- The Influence of math in biology
- The Influence of math in chemistry
- What is quantum computing?
- How to solve extremal problems in maths
- Analyze the meaning of fractals
- Discuss Einstein’s field equation theory
- Who created computer vision and object recognition?
- Five formulas and how they are applied
- Give three approaches to understanding maths
- Explain the origin and importance of algebra
- What do you know about the Fibonacci sequence?
- Trace the origin of math
- How does math help in geography?
- What does the operator spaces notion mean?

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Home > USC Columbia > Arts and Sciences > Mathematics > Mathematics Theses and Dissertations

## Mathematics Theses and Dissertations

Theses/dissertations from 2023 2023.

Extreme Covering Systems, Primes Plus Squarefrees, and Lattice Points Close to a Helix , Jack Robert Dalton

On the Algebraic and Geometric Multiplicity of Zero as a Hypergraph Eigenvalue , Grant Ian Fickes

Widely Digitally Delicate Brier Primes and Irreducibility Results for Some Classes of Polynomials , Thomas David Luckner

Deep Learning Methods for Some Problems in Scientific Computing , Yuankai Teng

## Theses/Dissertations from 2022 2022

Covering Systems and the Minimum Modulus Problem , Maria Claire Cummings

The Existence and Quantum Approximation of Optimal Pure State Ensembles , Ryan Thomas McGaha

Structure Preserving Reduced-Order Models of Hamiltonian Systems , Megan Alice McKay

Tangled up in Tanglegrams , Drew Joseph Scalzo

Results on Select Combinatorial Problems With an Extremal Nature , Stephen Smith

Poset Ramsey Numbers for Boolean Lattices , Joshua Cain Thompson

Some Properties and Applications of Spaces of Modular Forms With ETA-Multiplier , Cuyler Daniel Warnock

## Theses/Dissertations from 2021 2021

Simulation of Pituitary Organogenesis in Two Dimensions , Chace E. Covington

Polynomials, Primes and the PTE Problem , Joseph C. Foster

Widely Digitally Stable Numbers and Irreducibility Criteria For Polynomials With Prime Values , Jacob Juillerat

A Numerical Investigation of Fractional Models for Viscoelastic Materials With Applications on Concrete Subjected to Extreme Temperatures , Murray Macnamara

Trimming Complexes , Keller VandeBogert

Multiple Frailty Model for Spatially Correlated Interval-Censored , Wanfang Zhang

## Theses/Dissertations from 2020 2020

An Equivariant Count of Nodal Orbits in an Invariant Pencil of Conics , Candace Bethea

Finite Axiomatisability in Nilpotent Varieties , Joshua Thomas Grice

Rationality Questions and the Derived Category , Alicia Lamarche

Counting Number Fields by Discriminant , Harsh Mehta

Distance Related Graph Invariants in Triangulations and Quadrangulations of the Sphere , Trevor Vincent Olsen

Diameter of 3-Colorable Graphs and Some Remarks on the Midrange Crossing Constant , Inne Singgih

Two Inquiries Related to the Digits of Prime Numbers , Jeremiah T. Southwick

Windows and Generalized Drinfeld Kernels , Robert R. Vandermolen

Connections Between Extremal Combinatorics, Probabilistic Methods, Ricci Curvature of Graphs, and Linear Algebra , Zhiyu Wang

An Ensemble-Based Projection Method and Its Numerical Investigation , Shuai Yuan

Variable-Order Fractional Partial Differential Equations: Analysis, Approximation and Inverse Problem , Xiangcheng Zheng

## Theses/Dissertations from 2019 2019

Classification of Non-Singular Cubic Surfaces up to e-invariants , Mohammed Alabbood

On the Characteristic Polynomial of a Hypergraph , Gregory J. Clark

A Development of Transfer Entropy in Continuous-Time , Christopher David Edgar

Moving Off Collections and Their Applications, in Particular to Function Spaces , Aaron Fowlkes

Finding Resolutions of Mononomial Ideals , Hannah Melissa Kimbrell

Regression for Pooled Testing Data with Biomedical Applications , Juexin Lin

Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries , Shuang Liu

An Implementation of the Kapustin-Li Formula , Jessica Otis

A Nonlinear Parallel Model for Reversible Polymer Solutions in Steady and Oscillating Shear Flow , Erik Tracey Palmer

A Few Problems on the Steiner Distance and Crossing Number of Graphs , Josiah Reiswig

Successful Pressing Sequences in Simple Pseudo-Graphs , Hays Wimsatt Whitlatch

On The Generators of Quantum Dynamical Semigroups , Alexander Wiedemann

An Examination of Kinetic Monte Carlo Methods with Application to a Model of Epitaxial Growth , Dylana Ashton Wilhelm

Dynamical Entropy of Quantum Random Walks , Duncan Wright

Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State , Chenfei Zhang

## Theses/Dissertations from 2018 2018

Theory, Computation, and Modeling of Cancerous Systems , Sameed Ahmed

Turán Problems and Spectral Theory on Hypergraphs and Tensors , Shuliang Bai

Quick Trips: On the Oriented Diameter of Graphs , Garner Paul Cochran

Geometry of Derived Categories on Noncommutative Projective Schemes , Blake Alexander Farman

A Quest for Positive Definite Matrices over Finite Fields , Erin Patricia Hanna

Comparison of the Performance of Simple Linear Regression and Quantile Regression with Non-Normal Data: A Simulation Study , Marjorie Howard

Special Fiber Rings of Certain Height Four Gorenstein Ideals , Jaree Hudson

Graph Homomorphisms and Vector Colorings , Michael Robert Levet

Local Rings and Golod Homomorphisms , Thomas Schnibben

States and the Numerical Range in the Regular Algebra , James Patrick Sweeney

Thermodynamically Consistent Hydrodynamic Phase Field Models and Numerical Approximation for Multi-Component Compressible Viscous Fluid Mixtures , Xueping Zhao

## Theses/Dissertations from 2017 2017

On the Existence of Non-Free Totally Reflexive Modules , J. Cameron Atkins

Subdivision of Measures of Squares , Dylan Bates

Unconditionally Energy Stable Numerical Schemes for Hydrodynamics Coupled Fluids Systems , Alexander Yuryevich Brylev

Convergence and Rate of Convergence of Approximate Greedy-Type Algorithms , Anton Dereventsov

Covering Subsets of the Integers and a Result on Digits of Fibonacci Numbers , Wilson Andrew Harvey

Nonequispaced Fast Fourier Transform , David Hughey

Deep Learning: An Exposition , Ryan Kingery

A Family of Simple Codimension Two Singularities with Infinite Cohen-Macaulay Representation Type , Tyler Lewis

Polynomials Of Small Mahler Measure With no Newman Multiples , Spencer Victoria Saunders

## Theses/Dissertations from 2016 2016

On Crown-free Set Families, Diffusion State Difference, and Non-uniform Hypergraphs , Edward Lawrence Boehnlein

Structure of the Stable Marriage and Stable Roommate Problems and Applications , Joe Hidakatsu

Binary Quartic Forms over Fp , Daniel Thomas Kamenetsky

On a Constant Associated with the Prouhet-Tarry-Escott Problem , Maria E. Markovich

Some Extremal And Structural Problems In Graph Theory , Taylor Mitchell Short

Chebyshev Inversion of the Radon Transform , Jared Cameron Szi

Modeling of Structural Relaxation By A Variable-Order Fractional Differential Equation , Su Yang

## Theses/Dissertations from 2015 2015

Modeling, Simulation, and Applications of Fractional Partial Differential Equations , Wilson Cheung

The Packing Chromatic Number of Random d-regular Graphs , Ann Wells Clifton

Commutator Studies in Pursuit of Finite Basis Results , Nathan E. Faulkner

Avoiding Doubled Words in Strings of Symbols , Michael Lane

A Survey of the Kinetic Monte Carlo Algorithm as Applied to a Multicellular System , Michael Richard Laughlin

Toward the Combinatorial Limit Theory of free Words , Danny Rorabaugh

Trees, Partitions, and Other Combinatorial Structures , Heather Christina Smith

Fast Methods for Variable-Coefficient Peridynamic and Non-Local Diffusion Models , Che Wang

Modeling and Computations of Cellular Dynamics Using Complex-fluid Models , Jia Zhao

## Theses/Dissertations from 2014 2014

The Non-Existence of a Covering System with all Moduli Distinct, Large and Square-Free , Melissa Kate Bechard

Explorations in Elementary and Analytic Number Theory , Scott Michael Dunn

Independence Polynomials , Gregory Matthew Ferrin

Turán Problems on Non-uniform Hypergraphs , Jeremy Travis Johnston

On the Group of Transvections of ADE-Diagrams , Marvin Jones

Fake Real Quadratic Orders , Richard Michael Oh

## Theses/Dissertations from 2013 2013

Shimura Images of A Family of Half-Integral Weight Modular Forms , Kenneth Allan Brown

Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients , Morgan Cole

Deducing Vertex Weights From Empirical Occupation Times , David Collins

Analysis and Processing of Irregularly Distributed Point Clouds , Kamala Hunt Diefenthaler

Generalizations of Sperner's Theorem: Packing Posets, Families Forbidding Posets, and Supersaturation , Andrew Philip Dove

Spectral Analysis of Randomly Generated Networks With Prescribed Degree Sequences , Clifford Davis Gaddy

Selected Research In Covering Systems of the Integers and the Factorization of Polynomials , Joshua Harrington

The Weierstrass Approximation Theorem , LaRita Barnwell Hipp

The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations , Meshack K. Kiplagat

Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs , Austin Tyler Mohr

Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations , Rosalia Tatano

Coloring Pythagorean Triples and a Problem Concerning Cyclotomic Polynomials , Daniel White

## Theses/Dissertations from 2012 2012

A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices , Jonathan Brett Barwick

Mathematical Modeling and Computational Studies for Cell Signaling , Kanadpriya Basu

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- Grade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations : a case of selected schools in Gauteng North District Mothudi, Teresa Ntsae ( 2022-12-10 ) The purpose of this research was to look into Grade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations. The study was intrigued by the performance of learners in ...
- Grade 6 mathematics teachers’ development of learner mathematical proficiency in addition and subtraction of common fractions, in the Tshwane South District of Gauteng Lendis, Ashley Pearl ( 2022-11-30 ) The study was motivated by the fact that learners are not performing well in the topic of fractions due to the lack of conceptual understanding of the concept. The purpose of this qualitative study based on an interpretive ...
- The performance and learning difficulties of Grade 10 learners in solving euclidean geometry problems in Tshwane West District Olabode, Adedayo Abosede ( 2023-01-31 ) There is a growing trend of declining performance in the final year (Grade 12) mathematics examinations in the South African public school system. The study aimed to evaluate Grade 10 learners in the Tshwane West District ...
- A collaborative model for teaching and learning mathematics in secondary schools Ngwenya, Vusani ( 2021-11 ) Mathematics pass rates in South African schools, as in many developing nations, continue to be a source of concern for educators and policymakers alike. Improving mathematics performance is non-negotiable if Africa is to ...
- Teachers improvement of mathematics achievements in rural schools of Mopani District : implications for professional development Sambo, Sosa Isaac ( 2023-01-01 ) Throughout the globe, there is an outcry that learners’ performance in mathematics is below the expected standard. Hence, teachers need teacher development to improve their skills and knowledge in the subject. The purpose ...
- Grade 10 learners’ academic experiences of learning parabolic functions in schools of Vhembe district of Limpopo Province Mudau, Takalani Lesley ( 2022-11-22 ) The objective of this study was to determine Grade 10 learners' academic performance in learning parabola functions. Furthermore, the study sought to unearth errors that learners make when learning parabola functions and ...
- An exploration of learning difficulties experienced by grade 12 learners in euclidean geometry : a case of Ngaka Modiri Molema district Mudhefi, Fungirai ( 2022-08-20 ) The purpose of this study was to investigate the learning difficulties experienced by Grade 12 learners in Euclidean geometry. Despite the efforts exerted in terms of time, material and human resources in the teaching and ...
- The relationship between anxiety, working memory and achievement in mathematics in grade 5 learners : a case study of Tshepisong schools Mnguni, Maria Tebogo ( 2022-01-21 ) This study investigated the relationship between anxiety, working memory and achievement in mathematics in grade 5 learners at Tshepisong schools. A sample of 300 grade 5 learners from Tshepisong schools was selected using ...
- The effects of using a graphic calculator as a cognitive tool in learning grade 10 data handling Rambao, Mpho ( 2022-09 ) The integration of technology in the mathematics classroom is believed to have an influence on how the learners learn and change their perception of mathematics. Therefore, technology tools are developed to enhance the ...
- Integration of ethnomathematics in the teaching of probability in secondary school mathematics in Zimbabwe Turugari, Munamato ( 2022-06 ) Underpinned by the social constructivism theory and the praxis of integrating ethnomathematics in the teaching of probability, this PAR developed a policy framework for facilitating the integration of ethno-mathematics in ...
- Evaluating Grade 10 learners’ change in understanding of similar triangles following a classroom intervention Maweya, Amokelo Given ( 2022 ) Geometry, in particular Euclidean geometry, has been highlighted as a subject in mathematics that presents a variety of challenges to many secondary school learners. Many students struggle to gain appropriate knowledge of ...
- The impact of technology integration in teaching grade 11 Euclidean geometry based on van Hiele’s model Bediako, Adjei ( 2021-10-10 ) This quantitative study reports on the impact of using GeoGebra software to teach Grade 11 geometry through van Hieles’ levels theory, merged with some elements of the Technological Pedagogical Content Knowledge framework. ...
- A framework towards improved instruction of probability to grade seven students : a case of South African schools in Mpumalanga province Kodisang, Sophy Mamanyena ( 2022-02-03 ) This empirical phenomenological study explored teachers’ conceptual understanding of probability to gain insights into how this understanding enhanced their instructional classroom practice. The study was motivated by the ...
- The use and effect of Geogebra software in Calculus at Wachemo University, Ethiopia : an investigation Tola Bekene Bedada ( 2021-08 ) With the rapid growth of technology in the 21st century, traditional teaching and learning methods are considered outdated and not suitable for the active learning processes of the constructivist learning approach. The ...
- Exploration of Grade 8 learners’ misconceptions in learning surface area and volume of prisms at a high school in Johannesburg East District Sibanda, Edwin ( 2021-01-29 ) This study was conducted in order to explore Grade 8 learners’ perceptions through misconceptions they display when learning surface area and volume of prisms, which hinder conceptual understanding. A case study was used ...
- Exploring learning difficulties experienced by Grade 9 mathematics learners in understanding 3D shapes in Geometry Kgopane, Khomotso Welcome ( 2021-07 ) This study aimed to explore learning difficulties experienced by Grade 9 Mathematics learners in understanding 3D shapes in Geometry. To achieve that aim, the study focused on achieving three objectives, namely to: identify ...
- Relationship between learners’ proficiency in common and algebraic fractions : a case of grade 10 learners at a Limpopo high school Mangwende, Lina ( 2021-06 ) In Mathematics, the topic of fractions is one of the most difficult topics for both teachers and learners. The primary focus of the study was to examine how pedagogical strategies could be used in the teaching of common ...
- Using ubuntu values to enhance disruptive pedagogies for effective and meaningful teaching of grade 12 Euclidean geometry Chidziva, Justine ( 2021-06 ) Using a convergent mixed-methods parallel research design, this study explored how the use of Ubuntu values can enhance disruptive pedagogies for effective and meaningful teaching of Grade 12 Euclidean geometry. It employed ...
- Exploring the grade 11 mathematics learners' experiences and challenges in solving probability problems in selected Soshanguve schools Zhou, Tinevimbo ( 2019-11 ) This study explored the challenges experienced by Grade 11 mathematics learners in solving probability problems in selected Soshanguve Township Schools in the Gauteng Province of South Africa. The aim of the study was to ...
- Teachers’ perceptions of problem solving in mathematics : a case of Manzini Region in Eswatini Nhlabatsi, Nkosikhona Calvin ( 2019-11 ) Problem solving is an innovative instructional practice currently receiving attention and advocacy in mathematics education. It may support learners to develop knowledge to employ ideas in real world situations. It motivates ...

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## 100+ Amazing Algebra Topics for Research Papers

Many students seek algebra topics when writing research papers in this mathematical field. Algebra is the study field that entails studying mathematical symbols and rules for their manipulation. Algebra is the unifying thread for most mathematics, including solving elementary equations to learning abstractions like rings, groups, and fields. In most cases, people use algebra when unsure about the exact numbers. Therefore, they replace those numbers with letters. In business, algebra helps with sales prediction. While many students dislike mathematics, avoiding algebra research paper topics is almost impossible at an advanced study level. Therefore, this article lists topics to consider when writing a research paper in this academic field. It’s helpful because many learners struggle to find suitable topics when writing research papers in this field.

## How to Write Theses on Advanced Algebra Topics

A thesis on an algebra topic is an individual project that the learner writes after investigating and studying a specific idea. Here’s a step-by-step guide for writing a thesis on an algebra topic.

Pick a topic: Start by selecting a title for your algebra thesis. Your topic should relate to your research interests and your supervisor’s guidelines. Investigate your topic: Once you’ve chosen a topic, research it extensively to know the relevant theories, formulas, and texts. Your thesis should be an extension of a particular topic’s analysis and a report on your research. Write the thesis: Once you’ve explored the topic extensively, start writing your paper. Your dissertation should have an abstract, an introduction, the body, and a conclusion.

The abstract should summarise your thesis’ aims, scope, and conclusions. The introduction should introduce the topic, size, and significance while providing relevant literature and outlining the logical structure. The body should have several chapters with details and proofs of numerical implementations, while the conclusion should restate your main arguments and tell readers the effects. Also, it should suggest future work.

## College Algebra Topics

You may need topics to consider if you’re in college and want to write an algebra research paper. Here’s a list of titles worth considering for your essay.

- Exploring the relationship between Rubik’s cube and the group theory
- Comparing the relationship between various equation systems
- Finding the most appropriate way to solve mathematical word problems
- Investigating the distance formula and its origin
- Exploring the things you can achieve with determinants
- Explaining what “domain” and “range” mean in algebra
- A two-dimension analysis of the Gram-Schmidt process
- Exploring the differences between eigenvalues and eigenvectors
- What the Cramer’s rule states, and why does it matter
- Describing the Gaussian elimination
- Provide an induction-proof example
- Describe the uses of F-algebras
- Understanding the number problems in algebra
- What’s the essence of abstract algebra?
- Investigating Fermat’s last theorem peculiarities
- Exploring the algebra essentials
- Investigating the relationship between geometry and algebra

These are exciting topics in college algebra. However, writing a winning paper about any of them requires careful research and analysis. Therefore, prepare to spend sufficient time working on any of these titles.

## Cool Topics in Algebra

Perhaps, you want to write about an excellent topic in this mathematical field. If so, consider the following ideas for your algebra paper.

- Discussing a differential equation with illustrations
- Describing and analysing the Noetherian ring
- Explain the commutative ring from an algebra viewpoint
- Describe the Artin-Weddderburn theorem
- Studying the Jacobson density theorem
- Describe the four properties of any binary operation from an algebra viewpoint
- A detailed analysis of the unary operator
- Analysing the Abel-Ruffini theorem
- Monomorphisms versus Epimorphisms: Contrast and comparison
- Discus Morita duality with algebraic structures in mind
- Nilpotent versus Idempotent in Ring theory

Pick any idea from this list and develop it into a research topic. Your educator will love your paper and award you a good grade if you research it and write an informative essay.

## Linear Algebra Topics

Linear algebra covers vector spaces and the linear mapping between them. Linear equation systems have unknowns, and mathematicians use vectors and matrices to represent them. Here are exciting topics in linear algebra to consider for your research paper.

- Decomposition of singular value
- Investigating linear independence and dependence
- Exploring projections in linear algebra
- What are linear transformations in linear algebra?
- Describe positive definite matrices
- What are orthogonal matrices?
- Describe Euclidean vector spaces with examples
- Explain how you can solve equation systems with matrices
- Determinants versus matrix inverses
- Describe mathematical operations using matrices
- Functional analysis of linear algebra
- Exploring linear algebra and its fundamentals

These are some of the exciting project topics in linear algebra. Nevertheless, prepare sufficient resources and time to investigate any of these titles to write a winning paper.

## Pre Algebra Topics

Are you interested in a pre-algebra research topic? If so, this category has some of the most exciting ideas to explore.

- Investigating the importance of pre-algebra
- The best way to start pre-algebra for a beginner
- Pre-algebra and algebra- Which is the hardest and why?
- Core lessons in pre-algebra
- What follows pre-algebra?
- The first things to learn in pre-algebra
- Investigating the standard form in pre-algebra
- Provide pre-algebra examples using the basic rules to evaluate expressions
- Differentiate pre-algebra and algebra
- Describe five pre-algebra formulas

Consider exploring any of these ideas if you’re interested in pre-algebra. Nevertheless, choose a title you’re comfortable with to develop a winning paper.

## Intermediate Algebra Topics for Research

Perhaps, you’re interested in intermediate algebra. If so, consider any of these ideas for your research paper.

- Reviewing absolute value and real numbers
- Investigating real numbers’ operations
- Exploring the cube and square roots of real numbers
- Analysing algebraic formulas and expressions
- What are the rules of scientific notation and exponents?
- How to solve a linear inequality with a single variable
- Exploring relations, functions, and graphics from an algebraic viewpoint
- Investigating linear systems with two variables and solutions
- How to solve a linear system with two variables
- Exploring linear systems applications with two variables
- How to solve a linear system with three variables
- Gaussian elimination and matrices
- How to simplify a radical expression
- How to add and subtract a radical expression
- How to multiply and divide a radical expression
- How to extract a square root and complete the square
- Investigating quadratic functions and graphs
- How to solve a polynomial and rational inequality
- How to solve logarithmic and exponential equations
- Exploring arithmetic series and sequences

These are exciting topics in intermediate algebra to consider for research papers. Nevertheless, learners should prepare to solve equations in their work.

## Algebra Topics High School Students Can Explore

Are you in high school and want to explore algebra? If yes, consider these topics for your research, they could be a great coursework help to you.

- Crucial principles and formulas to embrace when solving a matrix
- Ways to create charts on a firm’s financial analysis for the past five years
- How to find solutions to finance and mathematical gaps
- Ways to solve linear equations
- What is a linear equation- Provide examples
- Describe the substitution and elimination methods for solving equations
- How to solve logarithmic equations
- What are partial fractions?
- Describe linear inequalities with examples
- How to solve a quadratic equation by factoring
- How to solve a quadratic equation by formula
- How to solve a quadratic equation with a square completion method
- How to frame a worksheet for a quadratic equation
- Explain the relationship between roots and coefficients
- Describe rational expressions and ways to simplify them
- Describe a cubic equation roots
- What is the greatest common factor- Provide examples
- What is the least common multiple- Provide examples
- Describe the remainder theorem with examples

Explore any of these titles for your high school paper. However, pick a title you’re comfortable working with from the beginning to the end to make your work easier.

## Advanced Topics in Algebra and Geometry

Maybe you want to explore something more advanced in your paper. In that case, the following list has advanced topics in geometry and algebra worth considering.

- Arithmetical structures and their algorithmic aspects
- Fractional thermoentropy spaces in topological quantum fields
- Fractional thermoentripy spaces in large-scale systems
- Eigenpoints configurations
- Investigating the higher dimension aperiodic domino problem
- Exploring math anxiety, executive functions, and math performance
- Coherent quantiles and lifting elements
- Absolute values extension on two subfields
- Reviewing the laws of form and Majorana fermions
- Studying the specialisation and rational maps degree
- Investigating mathematical-pedagogical knowledge of prospective teachers in ECD programs
- The adeles I model theory
- Exploring logarithmic vector fields, arrangements, and divisors’ freeness
- How to reconstruct curves from Hodge classes
- Investigating Eigen points configuration

These are advanced topics in algebra and geometry worth investigating. However, please prepare to explore your topic extensively to write a strong essay.

## Abstract Algebra Topics

Most people study abstract algebra in college. If you’re interested in research in this area, consider these topics for your project.

- Describe abstract algebra applications
- Why is abstract algebra essential?
- Describe ring theory and its application
- What is group theory, and why does it matter?
- Describe the critical conceptual algebra levels
- Describe the fundamental theorem of the finite Abelian groups
- Describe Sylow’s theorems
- What is Polya counting?
- Describe the RSA algorithm
- What are the homomorphisms and ideals of Rings?
- Describe integral domains and factorisation
- Describe Boolean algebra and its importance
- State and explain Cauchy’s Theorem- Why is it important?

This algebra topics list is not exhaustive. You can find more ideas worth exploring in your project. Nevertheless, pick an idea you will work with comfortably to deliver a winning paper.

## Get Professional Math Homework Help!

Perhaps, you don’t have the time to find accurate algebra homework solutions. Maybe you need math thesis help from an expert. If so, you’ve no reason to search further. Our thesis writing services in USA can help you write a winning assignment. We offer custom help with math assignments at cheap prices. If you want to get a quality algebra dissertation without sweating, place an order with us. We’re an online team providing homework help to students across educational levels. We guarantee you a top-notch service once you approach us, saying, “Please do my math assignment.” We’re fast and can beat even a tight deadline without compromising quality. And whether you’re in high school, university, or college, we will write a paper that will compel your teacher to award you the best grade in your class. Contact us now!

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## Pure Mathematics Research

Pure mathematics fields.

- Algebra & Algebraic Geometry
- Algebraic Topology
- Analysis & PDEs
- Geometry & Topology
- Mathematical Logic & Foundations
- Number Theory
- Probability & Statistics
- Representation Theory

## Pure Math Committee

## [100+] Mathematics Research Topics With Free [Thesis Pdf] 2023

Are You Searching Research Topics For Mathematics , Topics For Mathematics Research Paper, Mathematics Research Topics For Students, Research Topics Ideas For Mathematics, Mathematics Research Topics For PhD, Mathematics PhD Topics. So You are in right place.

In this article, we provide you latest research topics for Mathematics with a full Phd thesis. By these research topics for Mathematics you can get idea for your research work. On this website, you can get lots of Mathematics Research Topics for College Students, PhD, Mphil, Dissertations, Thesis, Project, Presentation, Seminar or Workshop. Check the suggestions below that can help you choose the right research topics for Mathematics: You can also Free Download Mathematics Research PhD Thesis in Pdf by the given link.

Now Check 100+ Mathematics Research Topics List

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## Research Topic For Mathematics 2023

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Mathematics Theses, Projects, and Dissertations Jump to: Theses/Projects/Dissertations from 2023 PDF DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS, Hytham Abdelkarim PDF An Exposition of the Curvature of Warped Product Manifolds, Angelina Bisson PDF Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves, Anton Butenko PDF

Possible thesis topics: Investigate various aspects of virtual knots, a generalization of knots. Consider hyperbolicity of virtual knots, building on previous SMALL work. For which virtual knots can you prove hyperbolicity? Investigate why certain virtual knots have the same hyperbolic volume.

1. Candidacy for Honors A senior thesis is required for high or highest honors in Mathematics, where-as for straight honors (neither high nor highest), a senior thesis can be submit or four extra courses in Mathematics or approved related fields can be taken (above the required twelve courses).

Most Harvard PhD dissertations from 2012 forward are available online in DASH, Harvard's central open-access repository and are linked below. Many older dissertations can be found on ProQuest Dissertation and Theses Search which many university libraries subscribe to. Admissions.

A selection of Mathematics PhD thesis titles is listed below, some of which are available online: 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 2023 Melanie Kobras - Low order models of storm track variability

The Senior Thesis in Mathematical Sciences course allows students to engage in independent mathematical work in an active and modern subject area of the mathematical sciences, guided by an official research faculty member in the department of mathematics and culminating in a written thesis presented in an appropriate public forum.

The Department of Mathematics offers Bachelor's degrees in Mathematics and Mathematics with Secondary Education option. A student's course of study can be tailored to suit a particular interest in pure mathematics, applied mathematics, mathematics teaching, or statistics. ... Schur's Theorem and Related Topics in Ramsey Theory, Summer Lynne ...

Diameters of graphs related to groups and base sizes of primitive groups . Freedman, Saul Daniel (2022-11-29) - Thesis. In this thesis, we study three problems. First, we determine new bounds for base sizes b (G,Ω) of primitive subspace actions of finite almost simple classical groups G. Such base sizes are useful statistics in ...

Doing research? Consider browsing through our Harvard University archives for Online Senior Thesis. They are easy to find and will save you lots of time.

Theses/Dissertations from 2022. PDF. Understanding College Students' Use of Written Feedback in Mathematics, Erin Loraine Carroll. PDF. Identity Work to Teach Mathematics for Social Justice, Navy B. Dixon. PDF. Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus, Leilani Camille Heaton Fonbuena.

First Position: Postdoc at the Institution for Advanced Study and Princeton. Max Lipton. Thesis: Dynamical Systems in Pure Mathematics. Advisor: Steven Strogatz. First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology. Elise McMahon. Thesis: A simplicial set approach to computing the group homology ...

A Highly Charged Topic: Intrinsically Disordered Proteins and Protein pKa Values, Carter J. Wilson PDF Population Dynamics and Bifurcations in Predator-Prey Systems with Allee Effect, Yanni Zeng Theses/Dissertations from 2022 PDF A Molecular Dynamics Study Of Polymer Chains In Shear Flows and Nanocomposites, Venkat Bala PDF

Stability Analysis of Implicit Explicit Runge-Kutta Discontinous Galerkin Methods for Convection-Dispersion Equations. Xing, Yulong. 2021. Mussmann, Thomas. Data Driven Learning of Dynamical Systems Using Neural Networks. Xiu, Dongbin. 2020. Chen, Yidi. A Numerical Study of Multi-class Traffic Flow Models.

181 Mathematics Research Topics From PhD Experts If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is).

Peter Barnet - Rain Drop Growth by Collision and Coalescence Matthew Edgington - Moving Mesh Methods for Semi-Linear Problems Samuel Groth - Light Scattering by Penetrable Convex Polygons Charlotte Kong - Comparison of Approximate Riemann Solvers Amy Jackson - Estimation of Parameters in Traffic Flow Models Using Data Assimilation

Math requires a lot of analysis. This is why there are different types of maths. They all encompass different subjects and deal with different things. What are the types of maths? Arithmetic This is perhaps the commonest type or branch of maths. It is one of the oldest and it encompasses basic numbers operations.

Master's Theses 2022. Funmilayo Adeku. Sensitivity of the Thermal Structure and Circulation Patterns of a Simple Idealized Lake and Lake Erie to External Driving Forces. Darian McLaren. On the evaluation of quantum instruments with a consideration to measurements in trapped ion systems. Oluyemi Momoiyioluwa.

Theses/Dissertations from 2022. PDF. Covering Systems and the Minimum Modulus Problem, Maria Claire Cummings. PDF. The Existence and Quantum Approximation of Optimal Pure State Ensembles, Ryan Thomas McGaha. PDF. Structure Preserving Reduced-Order Models of Hamiltonian Systems, Megan Alice McKay. PDF.

advice about writing any mathematics paper, not just a thesis, is provided in [3], and also [2, 4, 5].) 1. Basic requirements Your thesis must make a contribution to some eld of mathematics, and also report what was previously known about the topic. A Ph.D. thesis is expected to have a signi cant amount of original mathematical research.

In Mathematics, the topic of fractions is one of the most difficult topics for both teachers and learners. The primary focus of the study was to examine how pedagogical strategies could be used in the teaching of common ...

College Algebra Topics. You may need topics to consider if you're in college and want to write an algebra research paper. Here's a list of titles worth considering for your essay. Exploring the relationship between Rubik's cube and the group theory. Comparing the relationship between various equation systems.

External Thesis Advisor Info; Teacher Training; Thesis Proposal; Graduation Deadlines; Thesis Defense; After Graduate School; Prospective Undergrads; Class Schedule; Online Classes; Services. ... Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue Cambridge, MA 02139-4307 Campus Map (617 ...

November 1, 2022 by Research Scholar Share This: Are You Searching Research Topics For Mathematics, Topics For Mathematics Research Paper, Mathematics Research Topics For Students, Research Topics Ideas For Mathematics, Mathematics Research Topics For PhD, Mathematics PhD Topics. So You are in right place.