Recent Master's Theses - Applied Mathematics

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Master's Theses 2023

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What is expected in a masters thesis of a mathematics student?

What is the level of work expected in the masters thesis of a student of maths?

I know some people's works are worthy of publications while some involve only studying some topic in detail from a book and submitting a summary (since this is akin to a couple of courses, a year worth of work, in that topic in terms of content covered, I would consider this,which I believe is called a literature review thesis , as an extreme opposite of independent research work thesis).

But what is the "average" level of a MS thesis of a mathematics student? Is it usually closer to a literature review thesis or a research work thesis?

In particular, I would also like to know:

How much is it valued (if at all) when one applies for PhD? I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to absence of GRE like criterion there. Is this true?

Edit : After the wonderful existing answer explaining the case in Germany, I would really like to know the situation in US too. I expect a drastic difference due to the presence of GRE system but would like to know how much importance the thesis has, there.

PS: Please excuse me if one can find answers to some of these questions in already existing questions. I have searched, but couldn't find them. Please provide the links in those cases.

Also, anecdotal details will also be greatly appreciated. Thanks!

Community's user avatar

3 Answers 3

I think this varies a lot. But for Germany your first question can be answers succinctly: In a Master's thesis you should show that you have potential for research .

On the other hand, expectations vary a lot between advisors. But certainly you do not have to prove a new theorem or develop a new theory.

How much is it valued (if at all) when one applies for PhD?

I can only answer for the situation where you apply in Germany. The thesis can be a door opener if it is topic closely related to the field where you want to do a PhD. Also a good mark is important. But also in Germany hiring professors will often contact your advisors or request a reference letter and this is much more important.

I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to no GRE like criterion. Is this true?

Not sure on this point since I can't provide a comparison with the US and also I am not sure if the situation is uniform with the EU.

Dirk's user avatar

From my knowledge of the US system (I did my graduate work in the US, and am currently a professor in the US), the average level of a masters thesis is relatively low. (That said, it usually does involve at least some original research).

The reason for this is the structure of Ph.D. programs in the US. Usually students are admitted to Ph.D. programs directly as undergraduates, and the first two years of the Ph.D. are similar to an MS program in Europe. Students who complete a Ph.D. don't generally write a masters thesis along the way. Rather, masters theses are usually written by students who decide in their second year not to continue with our Ph.D. program, but would still like to earn some sort of degree for their efforts. These theses are often weak (but sometimes are quite good).

Some students do use an MS as a stepping stone to Ph.D. programs elsewhere; indeed, I personally know students who successfully transferred to much stronger programs. Their MS-level work was much better than average.

In short: The degree itself won't be highly valued in the US, but doing an MS can lead to strong letters from your professors and research advisors, and these will be highly valued.

Anonymous's user avatar

A great resource I have used to understand the quality of final thesis work for my primary focus is the Open Access Theses and Dissertations which has thousands of master's and Ph. D. final publications. Research this website using your topic and you will see what amount of research is involved, differences and similarities between schools, methodologies, etc.

In addition, a great site for further publications is . Many thesis in the U.S. are 'sandwich' publications, involving an assortment of publications published while student is performing research.

J. Roibal - BlockchainEng's user avatar

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Home > College of Science > Mathematics and Statistics > Master's Theses

Master’s Theses and Graduate Research

Theses/dissertations from 2021 2021.

Blue Red Hackenbush Spiders , Ravi Cho

Linear Inverse Problems and Neural Networks , Jasjeet Dhaliwal

Theses/Dissertations from 2020 2020

Determination of a Graph's Chromatic Number for Part Consolidation in Axiomatic Design , Jeffery Anthony Cavallaro

The Disk Complex and Topologically Minimal Surfaces , Luis Torres

Theses/Dissertations from 2019 2019

Preserving Ideals of Chemical Reaction Networks , Mark Curiel

Investigations and Analysis of Dynamical and Steady State Properties of Chemical Reaction Systems , Diego Ortega Hernandez

Theses/Dissertations from 2018 2018

A Numerical Study of the van Roosbroeck System for Semiconductors , Alan Ghazarians

Lenstra-Hurwitz Cliques In Real Quadratic Fields , Daniel S. Lopez

Theses/Dissertations from 2017 2017

A Method for Detection of Local Dimension in Point Cloud Data , Catherine Boersma

Knight's Tours and Zeta Functions , Alfred James Brown

Gauge Theory, Connections, and Holonomy: Background for the Ambrose-Singer Theorem , Joseph Fluegemann

The Geometry of Möbius Transformations and an Introduction to Riemann Surfaces , David Peter Goulette

A Boundary-Based Measure for Gerrymandering , Carson Sprock

Theses/Dissertations from 2016 2016

Drawing place field diagrams of neural codes using toric ideals , Nida K. Obatake

A Study on the Sparsity Property of the Jordan Canonical Form , MinhNhat Vu

Geometric Control Theory: Nonlinear Dynamics and Applications , Geoffrey A. Zoehfeld

Theses/Dissertations from 2015 2015

Preservation of Periodicity in Variational Integrators , Jian-Long Liu

Generic Polynomials , Lucas Spencer Mattick

Series and Their Applications to Boundary Value Problems , Jiayin Wang

Computation in a Localization of the Free Group Algebra , Olga Zamoruyeva

Theses/Dissertations from 2014 2014

Hittingtime and PageRank , Shanthi Kannan

A Square Sequence for Constructing a Subset of Aleph-(omega+1) , Robert Joseph Sanders

Theses/Dissertations from 2013 2013

Galois Theory and the Hilbert Irreducibility Theorem , Damien Adams

Mathematical Inequalities , Amy Dreiling

Geometric Algebra: An Introduction with Applications in Euclidean and Conformal Geometry , Richard Alan Miller

Theses/Dissertations from 2011 2011

Teaching and learning of proof in the college curriculum , Maja Derek

Construction and Simplicity of the Large Mathieu Groups , Robert Peter Hansen

Brockett's necessary conditions and the stabilization of nonlinear control systems , Marc Michot

Integrability vs Non-Integrability of Distributions : Frobenius vs Chow , Khanh Quoc Ngo

African American Community College Student Perceptions of Mathematics Instructor Immediacy Behaviors and Perceived Cognitive Learning , Georgia Lynne Toland

Integer Factorization Methods , Stephanie Faith Vergara

Integral Cayley Graphs Over a Direct Sum of Cyclic Groups of Order 2 and 2p , Usha Ganesh Watson

Theses/Dissertations from 2010 2010

Applications of Boundary Value Problems , Annie Nguyen

Family of Circulant Graphs and Its Expander Properties , Vinh Kha Nguyen Tran Nguyen

An Iterated Forcing Extension In Which All Aleph-1 Dense Sets of Reals Are Isomorphic , Michael Haig Vartanian

Elliptic Curves and Cryptography , Senorina Ramos Vazquez

The Friendship Theorem , David Sawyer Zimmermann

Theses/Dissertations from 2009 2009

Integral and non-integral dimension of modules over non-commutative rings. , Sejal K. Dharia

Theses/Dissertations from 2008 2008

The search of graphs equienergetic with edge deleted subgraph , Wilson A. Florero

Laurent polynomial representations of sl(n) , Hélène M. Payne

Theses/Dissertations from 2007 2007

The eigenvalues of compact self-adjoint operators on Hilbert spaces , Mitra Bandari

The Lanczos algorithm and fermat's factoring method , Parvaneh Darafshi

Neural networks and differential equations , Kathleen J. Freitag

Investigation of repeated measures linear regression methodologies , Tracy N. Holsclaw

Continued fraction patterns for numbers related to Carlitz-Drinfeld exponential , Diana L. Mecum

Contour integration with applications , Misako van der Poel

Matchwebs , Katherine Shelley

Effects of pre-processing and postprocessing on the watershed transform , Padmavati Tanniru

Adding a club subset of w₂ without collapsing either w₁ or w₂ , Ivan G. Zaigralin

Theses/Dissertations from 2006 2006

Applications of regularization techniques to data fitting with PDE models , Alina Alt

Integral circulant graphs with the spectral Ádám property , Christopher F. Cusanza

Estimating and forming confidence intervals for extrema of random polynomials , Sandra DeSousa

Construction of symmetric matrices with prescribed spectra , Viet H. Nguyen

Understanding the Cayley-Hamilton Theorem , Tue Saxon Rust

Theses/Dissertations from 2005 2005

Fermat numbers : historical view with applications related to fermat primes , Faun C. Maddux

Inductive reasoning in the algebra classroom , Mihad Mahmoud Mourad

Fibonacci and Lucas series with elliptic functions , TuAnh Gia Nguyen

A numerical method for solving double integral equations , Afshin Tiraie

Theses/Dissertations from 2004 2004

Analysis on vector product spaces , Claude Michael Cassano

The isoperimetric problem in finitely presented groups , James E. Kittock

Positivity of eigenvalues of words in two positive definite letters , Ruchi Pratap

Eigenvalues of graphs : algebraic connectivity and acyclic matrices , Wafa Yacoub

Theses/Dissertations from 2003 2003

Results on chromatic sum of graphs , Sundararajan Arabhi

Special boundary value problems , Graciela Pousa Cochran

A new approach to primary decomposition , Pamela R. Kochman

Theses/Dissertations from 2002 2002

Algorithms to efficiently partition Poisson distributed data , David Foster Barnes

On deciding whether a surface is parabolic or hyperbolic , Dean Kenneth Leonardi

Image compression using wavelet transforms , Ramanjit K. Sahi

Quantum factoring , Amy D. Vu

Theses/Dissertations from 2001 2001

Fibonacci sequences and the golden section , Medha A. Bodas

The Banach-Tarski paradox in euclidean spaces , Kenneth R. Hoover

The geometry of third degree curves , Richard Jones

On Turan's pure power sum problem , Andrew H. Ledoan

The irrationality of zeta (2) and zeta (3) , Victor Legge

Closed unbounded subset problems , Parisa Safa

A decade of ethnic enrollment and achievement trends in mathematics , Barbara L. Schallau

Scheduling and weighted coloring , Sandy Weihong Zhang

Theses/Dissertations from 2000 2000

Using granules to find association rules , Eric Wah Louie

Odd perfect numbers , Anh Minh Nguyen

Poncelet's closure theorem , Loretta H. Silverman

The LU-factorization of totally positive and strictly totally positive matrices , Anna Cooper Strong

Perron-Frobenius theory and Perron Complementation , Angela Hang Tran

Theses/Dissertations from 1999 1999

A visualization of a quantum mechanical search algorithm , Terrance Bing-Parks

Algebraic theory of differential equations , Thomas J. Little

Using the Frechet derivative to improve Arnoldi's method , Huai-An Sun

Theses/Dissertations from 1998 1998

An examination of the nature of a single-sex mathematics class , Amy Burns

On analyzing GMRES from the view of geometry and an application to Haar wavelets , Mei-Wern Cheng

Approximate in inverse preconditioners for the conjugate gradient method , Chieko Honma

Self-affine wavelets , Randy S. Pencin

Theses/Dissertations from 1997 1997

Rank revealing QR factorizations , Lily L. Dalton

Traffic management methodologies for ATM networks : a new approach , Asha G. Dinesh

Attitudes and experiences of Mexican-American females in mathematics , Gretchen Ann Ehlers

The failure of GCH at a measurable cardinal , John F. Freno

A Comparison of genetic and other algorithms for the traveling salesman problem , Martin F. Schlapfer

An application of rough sets to economic and stock market data / c by Joseph A. Tremba , Joseph A. Tremba

Theses/Dissertations from 1996 1996

Heuristic algorithms for the terminal assignment problem , Teresa Li-Pei Chiu

Exploring the Poincare ́models of hyperbolic geometry using Geometer's Sketchpad , Marlene Chiaramonte Dwyer

Object-Oriented Design and Literate Programming , Glen D. Finston

An object-oriented diagram editor and code generator , Glenn Fung

Mathematical systems and their stability , Marc Steven Knobel

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Home > Mathematics and Statistics > MathStat TDs > Masters Theses

Mathematics and Statistics Masters Theses

Theses from 2022 2022.

Several problems in nonlinear Schrödinger equations , Tim Van Hoose

Theses from 2020 2020

Decoupled finite element methods for general steady two-dimensional Boussinesq equations , Lioba Boveleth

Quantifying effects of sleep deprivation on cognitive performance , Quang Nghia Le

The application of machine learning models in the concussion diagnosis process , Sujit Subhash

Theses from 2019 2019

Less is more: Beating the market with recurrent reinforcement learning , Louis Kurt Bernhard Steinmeister

Theses from 2018 2018

Models for high dimensional spatially correlated risks and application to thunderstorm loss data in Texas , Tobias Merk

An investigation of the influence of the 2007-2009 recession on the day of the week effect for the S&P 500 and its sectors , Marcel Alwin Trick

Theses from 2017 2017

The pantograph equation in quantum calculus , Thomas Griebel

Comparing region level testing methods for differential DNA methylation analysis , Arnold Albert Harder

A review of random matrix theory with an application to biological data , Jesse Aaron Marks

Family-based association studies of autism in boys via facial-feature clusters , Luke Andrew Settles

Theses from 2016 2016

Pricing of geometric Asian options in general affine stochastic volatility models , Johannes Ruppert

On the double chain ladder for reserve estimation with bootstrap applications , Larissa Schoepf

Theses from 2015 2015

Some combinatorial applications of Sage, an open source program , Jessica Ruth Chowning

Day of the week effect in returns and volatility of the S&P 500 sector indices , Juan Liu

Application of loglinear models to claims triangle runoff data , Netanya Lee Martin

Theses from 2014 2014

Adaptive wavelet discretization of tensor products in H-Tucker format , Mazen Ali

An iterative algorithm for variational data assimilation problems , Xin Shen

Statistical analysis of sleep patterns in Drosophila melanogaster , Luyang Wang

Theses from 2013 2013

Statistical analysis of microarray data in sleep deprivation , Stephanie Marie Berhorst

Immersed finite element method for interface problems with algebraic multigrid solver , Wenqiang Feng

Theses from 2012 2012

Abel dynamic equations of the first and second kind , Sabrina Heike Streipert

Lattice residuability , Philip Theodore Thiem

Theses from 2011 2011

A time series approach to electric load modelling , Matthias Benjamin Noller

Theses from 2010 2010

Closed-form solutions to discrete-time portfolio optimization problems , Mathias Christian Goeggel

Inverse limits with upper semi-continuous set valued bonding functions: an example , Christopher David Jacobsen

Theses from 2009 2009

The analogue of the iterated logarithm for quantum difference equations , Karl Friedrich Ulrich

Theses from 2008 2008

Modeling particulate matter emissions indices at the Hartsfield-Jackson Atlanta International Airport , Lu Gan

The dynamic multiplier-accelerator model in economics , Julius Severi Heim

Dynamic equations with piecewise continuous argument , Christian Keller

Theses from 2007 2007

Ostrowski and Grüss inequalities on time scales , Thomas Matthews

The Black-Scholes equation in quantum calculus , Christian Müttel

Computerized proofs of hypergeometric identities: Methods, advances, and limitations , Paul Nathaniel Runnion

Screening for noise variables , Lisa Trautwein

Theses from 2006 2006

Distance function applications of object comparison in artificial vision systems , Christina Michelle Ayres

Sensitivity analysis on the relationship between alcohol abuse or dependence and wages , Tim Jensen

Sensitivity analysis on the relationship between alcohol abuse or dependence and annual hours worked , Stefan Koerner

Endogeneity bias and two-stage least squares: a simulation study , Xujun Wang

Theses from 2005 2005

Local compactness of the hyperspace of connected subsets , Robbie A. Beane

A sequential approach to supersaturated design , Angela Marie Jugan

Tests for gene-treatment interaction in microarray data analysis , Wanrong Yin

Theses from 2003 2003

Pricing of European options , Dirk Rohmeder

Prediction intervals for the binomial distribution with dependent trials , Florian Sebastian Rueck

Theses from 2002 2002

The use of a Marakov dependent Bernoulli process to model the relationship between employment status and drug use , Kathrin Koetting

Theses from 2000 2000

Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps , Brian Edward Raines

Theses from 1998 1998

A two-stage step-stress accelerated life testing scheme , Phyllis E. Pound Singer

Theses from 1997 1997

Some properties of hereditarily indecomposable chainable continua , Thomas John Kacvinsky

Theses from 1996 1996

The Axiom of Choice, well-ordering property, Continuum Hypothesis, and other meta-mathematical considerations , Daniel Collins

Theses from 1994 1994

Approximate distributional results for tolerance limits and confidence limits on reliability based on the maximum likelihood estimators for the logistic distribution , Teriann Collins

Theses from 1986 1986

Investigating the output angular acceleration extrema of the planar four bar mechanism , Matthew H. Koebbe

Theses from 1984 1984

Approximating distributions in order restricted inference : the simple tree ordering , Tuan Anh Tran

Theses from 1982 1982

Goodness-of-fit for the Weibull distribution with unknown parameters and censored sampling. , Michael Edward Aho

Theses from 1979 1979

On L convergence of Fourier series. , William O. Bray

Theses from 1977 1977

Characterizations of inner product spaces. , John Lee Roy Williams

Theses from 1975 1975

A study of several substitution ciphers using mathematical models. , Wanda Louise Garner

Theses from 1974 1974

Models for molecular vibration , Allan Bruce Capps

The completions of local rings and their modules. , Christopher Scott Taber

Linear geometry , Phyllis L. Thomas

Theses from 1971 1971

Integrability of the sums of the trigonometric series 1/2 aₒ + ∞ [over] Σ [over] n=1 a n cos nΘ and ∞ [over] Σ [over] n=1 a n sin nΘ , John William Garrett

Inclusion theorems for boundary value problems for delay differential equations , Leon M. Hall

Theses from 1965 1965

A study of certain conservative sets for parameters in the linear statistical model , Roger Alan Chapin

Comparison of methods to select a probability model , Howard Lyndal Colburn

Latent class analysis and information retrieval , George Loyd Jensen

Linear and quadratic programming with more than one objective function , William John Lodholz

Tschebyscheff fitting with polynomials and nonlinear functions , George F. Luffel

Theses from 1964 1964

The effect of matrix condition in the solution of a system of linear algebraic equations. , Herbert R. Alcorn

Estimation and tabulation of bias coefficients for regression analysis in incompletely specified linear models. , Harry Kerry Edwards

A study of a method for selecting the best of two or more mathematical models , August J. Garver

A study of methods for estimating parameters in the model y(t) = A₁e -p₁t + A₂e -p₂t + ϵ , Gerald Nicholas Haas

A parameter perturbation procedure for obtaining a solution to systems of nonlinear equations. , James Carlton Helm

A study of stability of numerical solution for parabolic partial differential equations. , Tsang-Chi Huang

A numerical study of Van Der Pol's nonlinear differential equation for various values of the parameter E. , Charles C. Limbaugh

A study on estimating parameters restricted by linear inequalities , William Lawrence May

Minimization of Boolean functions. , Don Laroy Rogier

A method to give the best linear combination of order statistics to estimate the mean of any symmetric population , Robert M. Smith

On a numerical solution of Dirichlet type problems with singularity on the boundary. , Randall Loran Yoakum

Theses from 1963 1963

A study of methods for estimating parameters in rational polynomial models , Thomas B. Baird

Investigation of measures of ill-conditioning , Thomas D. Calton

A numerical approach to a Sturm-Liouville type problem with variable coefficients and its application to heat transfer and temperature prediction in the lower atmosphere. , Troyce Don Jones

A study of methods for determining confidence intervals for the mean of a normal distribution with unknown varience by comparison of average lengths , Karl Richard Kneile

Stability properties of various predictor corrector methods for solving ordinary differential equations numerically. , Charles Edward. Leslie

Mathematical techniques in the solution of boundary value problems. , Vincent Paul Pusateri

A modified algorithm for Henrici's solution of y' ' = f (x,y) , Frank Garnett Walters

Theses from 1962 1962

An investigation of Lehmer's method for finding the roots of polynomial equations using the Royal-McBee LGP-30 , James W. Joiner

Theses from 1931 1931

The spinning top , Aaron Jefferson Miles

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Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2022 2022.


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


Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez



Verifying Sudoku Puzzles , Chelsea Schweer


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


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


Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder


Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila


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.



Theses/Projects/Dissertations from 2018 2018


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


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

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN


Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager


Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari


Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley



Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova



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



LIFE EXPECTANCY , Ali R. Hassanzadah


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


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

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


The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015


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



Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz


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


Progenitors Related to Simple Groups , Elissa Marie Valencia

The Gelfand Theorem for Commutative Banach Algebras , Nhan H. Zuick

Theses/Projects/Dissertations from 2014 2014

Radio Number for Fourth Power Paths , Linda V. Alegria

The Linear Cutwidth and Cyclic Cutwidth of Complete n-Partite Graphs , Stephanie A. Creswell


Homormophic Images and their Isomorphism Types , Diana Herrera



On the Evolution of Virulence , Thi Nguyen

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Master's Thesis

Information for thesis students (2023-2024) .

Information for thesis students (2022-2023) 

Information for thesis students (2021-2022) 

General information.

Program director:  prof. J. Van der Veken

Department of Mathematics

Celestijnenlaan 200B

3001 Heverlee - Belgium

tel: +32 (16) 32 70 17 

In the spotlight

Power to the particles , joining forces with tae technologies, eos event: geometry minicourses, local forms in singular symplectic geometry (tianqi liu), the ingham-karamata tauberian theorem (gregory debruyne - ghent university), the syz conjecture for families of hypersurfaces (léonard pille-schneider), joint sparse principal component analysis (prof. dr katrijn van deun, tilburg university), methusalem colloquium: isometric actions on symmetric spaces (alberto rodríguez vázquez, ku leuven).

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Master of Science (M.S.) Major in Mathematics (Applied Mathematics Concentration Thesis Option)

Program overview.

Texas State offers opportunities to work with outstanding faculty in a collegial atmosphere where mathematicians and mathematics educators collaborate closely. The multi-faceted program offers a strong foundation and research opportunities in mathematics, applied math, and mathematics education, preparing students for further graduate study, teaching, or industry positions. The M.S. in mathematics prepares students with the applied mathematical knowledge and critical thinking abilities needed to pursue doctoral degrees, teaching careers or leadership positions in industry.

Application Requirements

The items listed below are required for admission consideration for applicable semesters of entry during the current academic year. Submission instructions, additional details, and changes to admission requirements for semesters other than the current academic year can be found on The Graduate College's website . International students should review the International Admission Documents webpage for additional requirements.



Non-native English speakers who do not qualify for an English proficiency waiver:

This program does  not  offer admission if the scores above are not met.

Degree Requirements

The Master of Science (M.S.) degree with a major in Mathematics concentration in applied mathematics requires 30 semester credit hours, including a thesis. Students who do not have the appropriate background course work may be required to complete leveling courses.

Course Requirements

Comprehensive examination requirement.

All candidates for graduate degrees must pass a comprehensive examination consisting of three parts. A student may fail up to two times on one or more of the three parts of the comprehensive exam. After failing any given part of the comprehensive exam twice, a student will then be advised to retake the course(s). Provided they earn at least a C in each retaken class, they will then be permitted one final attempt at passing the corresponding part(s) of the comprehensive exam.

Students who do not successfully complete the requirements for the degree within the timelines specified will be dismissed from the program.

If a student elects to follow the thesis option for the degree, a committee to direct the written thesis will be established. The thesis must demonstrate the student’s capability for research and independent thought. Preparation of the thesis must be in conformity with the  Graduate College Guide to Preparing and Submitting a Thesis or Dissertation .

Thesis Proposal

The student must submit an official  Thesis Proposal Form  and proposal to his or her thesis committee. Thesis proposals vary by department and discipline. Please see your department for proposal guidelines and requirements. After signing the form and obtaining committee members’ signatures, the graduate advisor’s signature if required by the program and the department chair’s signature, the student must submit the Thesis Proposal Form with one copy of the proposal attached to the dean of The Graduate College for approval before proceeding with research on the thesis. If the thesis research involves human subjects, the student must obtain exemption or approval from the Texas State Institutional Review Board prior to submitting the proposal form to The Graduate College. The IRB approval letter should be included with the proposal form. If the thesis research involves vertebrate animals, the proposal form must include the Texas State IACUC approval code. It is recommended that the thesis proposal form be submitted to the dean of The Graduate College by the end of the student’s enrollment in 5399A. Failure to submit the thesis proposal in a timely fashion may result in delayed graduation.

Thesis Committee

The thesis committee must be composed of a minimum of three approved graduate faculty members.

Thesis Enrollment and Credit

The completion of a minimum of six hours of thesis enrollment is required. For a student's initial thesis course enrollment, the student will need to register for thesis course number 5399A.  After that, the student will enroll in thesis B courses, in each subsequent semester until the thesis is defended with the department and approved by The Graduate College. Preliminary discussions regarding the selection of a topic and assignment to a research supervisor will not require enrollment for the thesis course.

Students must be enrolled in thesis credits if they are receiving supervision and/or are using university resources related to their thesis work.  The number of thesis credit hours students enroll in must reflect the amount of work being done on the thesis that semester.  It is the responsibility of the committee chair to ensure that students are making adequate progress toward their degree throughout the thesis process.  Failure to register for the thesis course during a term in which supervision is received may result in postponement of graduation. After initial enrollment in 5399A, the student will continue to enroll in a thesis B course as long as it takes to complete the thesis. Thesis projects are by definition original and individualized projects.  As such, depending on the topic, methodology, and other factors, some projects may take longer than others to complete.  If the thesis requires work beyond the minimum number of thesis credits needed for the degree, the student may enroll in additional thesis credits at the committee chair's discretion. In the rare case when a student has not previously enrolled in thesis and plans to work on and complete the thesis in one term, the student will enroll in both 5399A and 5399B.

The only grades assigned for thesis courses are PR (progress), CR (credit), W (withdrew), and F (failing). If acceptable progress is not being made in a thesis course, the instructor may issue a grade of F. If the student is making acceptable progress, a grade of PR is assigned until the thesis is completed. The minimum number of hours of thesis credit (“CR”) will be awarded only after the thesis has been both approved by The Graduate College and released to Alkek Library.

A student who has selected the thesis option must be registered for the thesis course during the term or Summer I (during the summer, the thesis course runs ten weeks for both sessions) in which the degree will be conferred.

Thesis Deadlines and Approval Process

Thesis deadlines are posted on  The Graduate College  website under "Current Students." The completed thesis must be submitted to the chair of the thesis committee on or before the deadlines listed on The Graduate College website.

The following must be submitted to The Graduate College by the thesis deadline listed on The Graduate College website:

After the dean of The Graduate College approves the thesis, Alkek Library will harvest the document from the Vireo submission system for publishing in the Digital Collections database (according to the student's embargo selection).  NOTE: MFA Creative Writing theses will have a permanent embargo and will never be published to Digital Collections.  

While original (wet) signatures are preferred, there may be situations as determined by the chair of the committee in which obtaining original signatures is inefficient or has the potential to delay the student's progress. In those situations, the following methods of signing are acceptable:

If this process results in more than one document with signatures, all documents need to be submitted to The Graduate College together.

No copies are required to be submitted to Alkek Library. However, the library will bind copies submitted that the student wants bound for personal use. Personal copies are not required to be printed on archival quality paper. The student will take the personal copies to Alkek Library and pay the binding fee for personal copies.

Master's level courses in Mathematics:  MATH ,  MTE

Courses Offered

Mathematics (math).

MATH 5111. Graduate Assistant Training.

This course is concerned with techniques used in the teaching of mathematics. This course is required as a condition of employment for graduate teaching and instructional assistants. This course does not earn graduate degree credit. Repeatable with different emphasis.

MATH 5199B. Thesis.

This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding.

MATH 5299B. Thesis.

MATH 5301. Partial Differential Equations.

Theory and application of partial differential equations; derivation of the differential equation; use of vector and Tensor methods; equations of the first order; wave equations; vibrations and normal functions; Fourier series and integral; Cauchy’s methods, initial data; methods of Green; potentials; boundary problems; methods of Riemann-Volterra; characteristics. Prerequisites: MATH 3323 and consent of the instructor.

MATH 5303. History of Mathematics.

A study of the development of mathematics and of the accomplishments of men and women who contributed to its progress. Cannot be used on a degree plan for M.S. degree. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5304. Topics in Mathematics for the Secondary Teacher.

A study of the current trends and topics found in the secondary school mathematics curriculum with the goal of improving the mathematical background of the secondary teacher. Course content will be flexible and topics will be selected on the basis of student needs and interests. Cannot be used on degree plan for M.S. degree. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5305. Advanced Course in Probability and Statistics.

Advanced topics in probability and statistics. May be repeated once with different emphasis for additional credit. Prerequisite: MATH 3305 .

MATH 5307. Modern Algebra.

Topics in modern algebra. Material will be adapted to the needs of the class. Prerequisite: MATH 4307 with a grade of "C" or better, or MATH 5384 with a grade of "B" or better.

MATH 5311. Foundations of Differential Equations.

A critical study of the foundations of derivation equations, operator spaces, and such basic topics. Recent developments in this field will be investigated and independent investigation will be encouraged. Prerequisite: MATH 2393 and [ MATH 3380 or MATH 5382 ] both with grades of "C" or better.

MATH 5312. Functions of a Complex Variable.

Modern developments in the field of a complex variable. Prerequisite: MATH 2393 and MATH 4315 and [ MATH 3380 or MATH 5382 ] all with grades of "C" or better or departmental approval.

MATH 5313. Field Theory.

Topics in field theory, separable extensions, and Galois Theory. Prerequisite: MATH 4307 with a grade of "C" or better, or MATH 5384 with a grade of "B" or better.

MATH 5314. Number Theory.

Topics in algebra selected from quadratic forms, elementary number theory, algebraic or analytic number theory, with material adapted to the needs of the class. Prerequisite: MATH 4307 with a grade of "C" or better, or MATH 5384 with a grade of "B" or better.

MATH 5315. Mathematical Statistics.

This course discusses theoretical aspects of estimation theory and hypothesis testing procedures, with some of their important applications. The main topics include convergence of random variables, parameter estimation, properties of estimators, interval estimation, sufficiency and applications to the exponential family, hypothesis testing, decision theory, and Bayesian inference. Prerequisite: Instructor approval.

MATH 5317. Problems in Advanced Mathematics.

Open to graduate students on an individual basis by arrangement with the mathematics department. A considerable degree of mathematical maturity is required. May be repeated with different emphasis. This course does not earn graduate degree credit.

MATH 5319. The Theory of Integration.

A course in the theory of integration with special emphasis on the Lebesgue integrals. A course in the theory of real variables, with a knowledge of point set theory, is desirable as a background for this course. A considerable amount of mathematical maturity is required. Prerequisite: MATH 4315 with a grade of "C" or better, or departmental approval.

MATH 5329. General Topology.

Point-set topology with an emphasis on general topological spaces; separation axioms, connectivity, the metrization theorem, and the C-W complexes. Prerequisite: MATH 4330 with a grade of "C" or better, or departmental approval.

MATH 5331. Metric Spaces.

Point-set topology with an emphasis on metric spaces and compactness but including a brief introduction to general topological spaces. Prerequisite: MATH 4330 with a grade of "C" or better, or departmental approval.

MATH 5335. Survival Analysis.

This course introduces concepts and methods in the analysis of survival data. Topics include characteristics of survival data; basic functions; parametric models for survival time; maximum likelihood estimation of survival functions; two-sample test techniques; regression analysis with parametric and semi-parametric models; and mathematical and graphical methods for model checking. Prerequisite: Math 5305 with a grade of "B" or better or instructor approval.

MATH 5336. Studies in Applied Mathematics.

Topics selected from optimization and control theory, numerical analysis, calculus of variations, boundary value problems, special functions, or tensor analysis. May be repeated with different emphasis for additional credit. Prerequisites: Six hours of advanced mathematics pertinent to topic and consent of the instructor.

MATH 5340. Scientific Computation.

This course will involve the analysis of algorithms from science and mathematics, and the implementation of these algorithms using a computer algebra system. Symbolic numerical and graphical techniques will be studied. Applications will be drawn from science, engineering, and mathematics. A knowledge of differential equations is expected. Prerequisite: Consent of instructor.

MATH 5345. Regression Analysis.

This course introduces formulation and statistical methodologies for simple and multiple regression, assessment of model fit, model design, and criteria for selection of optimal regression models. Students will develop skills with the use of statistical packages and the writing of reports analyzing a variety of real-world data. Prerequisite: MATH 2472 .

MATH 5350. Combinatorics.

This course, covers permutations, combinations, Stirling numbers, chromatic numbers, Ramsey numbers, generating functions, Polya theory, Latin squares and random block design. Prerequisite: MATH 3398 or consent of instructor.

MATH 5355. Applied and Algorithmic Graph Theory.

This course is designed to emphasize the close tie between the theoretical and algorithmic aspects. The topics may include basic concepts such as connectivity, trees, planarity, coloring of graphs, matchings, and networks. It also covers many algorithms such as Max-flow Min-cut algorithm, maximum matching algorithm, and optimization algorithms for facility location problems in networks. Prerequisite: MATH 5388 or MATH 3398 .

MATH 5358. Applied Discrete Mathematics.

Boolean algebra, counting techniques, discrete probability, graph theory, and related discrete mathematical structures that are commonly encountered in computer science. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5360. Mathematical Modeling.

This course introduces the process and techniques of mathematical modeling. It covers a variety of application areas from the natural sciences. Emphasis is placed on deterministic systems, stochastic models, and diffusion. Prerequisite: [ MATH 2393 and MATH 3323 both with grades of "D" or better and MATH 5301 with a grade of "C" or better] or instructor approval.

MATH 5373. Theory of Functions of Real Variables.

This course will discuss those topics that will enable the student to obtain a better grasp of the fundamental concepts of the calculus of real variables and the more recent developments of this analysis. Prerequisite: MATH 4315 with a grade of "C" or better, or departmental approval.

MATH 5374. Numerical Linear Algebra.

This course introduces tools that mathematical scientists use with vectors and matrices. Applications include least squares and eigenvalue problems, and systems of equations from applied mathematics. The stability of algorithms to perturbations are considered. Theory is balanced with numerically implementing algorithms, in particular for iterative methods for large, sparse systems. Prerequisite: MATH 3377 with a "C" or better.

MATH 5376A. Design and Analysis of Experiments.

This course introduces fundamental concepts in the design of experiments, justification of linear models, randomization and principles of blocking. It also discusses the construction and analysis of basic designs including fractional replication, composite designs, factorial designs, and incomplete block designs. Prerequisite: Approval of instructor.

MATH 5376B. Analysis of Variance.

This course introduces basic methods, one-way, two-way ANOVA procedures, and multifactor ANOVA designs. Prerequisite: Approval of instructor.

MATH 5376D. Statistical Applications in Genetics and Bioinformatics.

The statistical concepts and methods to be covered include important probability distributions, analysis of variance, regression analysis, hidden Markov model, and Markov Chain Monte Carlo methods. These methods will be used to address important and challenging questions arising in the analysis of large genetic and bioinformatic datasets. Prerequisite: Math4305 or equivalent.

MATH 5376E. Introduction to Data Science.

This course introduces basic concepts and methods in the field of data science. Topics include data wrangling, data exploration and visualization, optimization, deep learning, supervised learning subjects such as nearest-neighbor techniques, regression, Lasso, linear discriminant analysis, logistic regression, tree-based models, neural networks, as well as unsupervised learning subjects such as market basket analysis and cluster analysis, and random forests. The material will be approached with a blend of theory and application, and will include programming in Python, R, or another modern, popular language of the instructor's choice.

MATH 5376F. Introduction to Probability Theory and Models.

This course covers the definitions, constructions, theorems, and techniques to build and analyze probability models. The emphasis of this class is the active construction and analysis of probability models. However, we will develop a rigorous treatment of the requisite abstract theory in service of this goal. Topics include conditional expectation, the convergence of random variables, weak and strong law of large numbers, central limit theorem, random walk, Martingales, and Brownian motion.

MATH 5381. Foundations of Set Theory.

A formal study of the theory of sets, relations, functions, finite and infinite sets, set operations and other selected topics. This course will also train the student in the understanding of mathematical logic and the writing of proofs. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5382. Foundation of Real Analysis.

A course covering the foundations of mathematical analysis. Topics include: real numbers, sequences, series, and limits and continuity of functions. Prerequisite: MATH 5381 .

MATH 5384. Geometric Approach to Abstract Algebra.

Definitions and elementary properties of groups, rings, integral domains, fields and vector spaces with great emphasis on the rings of integers, rational numbers, complex numbers, polynomials, and the interplay between algebra and geometry. Prerequisite: MATH 5381 .

MATH 5386. Knots and Surfaces, An Introduction to Low-Dimensional Topology.

Knot polynomials and other knot invariants. The topological classification of surfaces and topological invariants of surfaces. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5388. Discrete Mathematics.

This course covers topics from: basic and advanced techniques of counting, recurrence relations, discrete probability and statistics, and applications of graph theory. Prerequisites: MATH 2472 with a grade of "C" or better.

MATH 5390. Statistics.

This course will cover not only some of the basic statistical ideas and techniques but also the mathematical and probabilistic underpinnings of these techniques with an emphasis on simulations and modeling. The planning, conducting, analysis, and reporting of experimental data will also be covered. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5392. Survey of Geometries.

A study of topics in geometry including geometrical transformations, the geometry fractals, projective geometry, Euclidean geometry, and non-Euclidean geometry. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 5393. Numerical Optimization.

This course focuses on optimization methods for a broad range of applications, such as engineering and applied sciences. Subjects are the basic theory of optimization, numerical algorithms to locate points satisfying optimality conditions and to analyze the convergence properties. Prerequisites: MATH 2472 and MATH 3377 and MATH 3383 , all with a grade of “C” or better.

MATH 5399A. Thesis.

This course represents a student’s initial thesis enrollment. No thesis credit is awarded until student has completed the thesis in Mathematics 5399B.

MATH 5399B. Thesis.

MATH 5599B. Thesis.

MATH 5999B. Thesis.

Mathematics for Teacher Education (MTE)

MTE 5301E. Visual Models for Middle School Mathematics.

This course uses visual models to motivate understanding of the fundamental concepts underlying middle school mathematics. Pedagogical techniques to engage middle school students will also be addressed including inquiry-based instructional methods utilizing these visual models.

MTE 5301F. Implementing New Mathematics Curriculum.

In this course we will investigate the keys to successfully implementing new curriculum. Two main aspects considered are: 1) the mathematical content knowledge required for a new curriculum and 2) how to build a community of practice which provides support during the implementation process.

MTE 5301G. Mathematics for Teaching.

A study of the current trends and topics found in the secondary school mathematics curriculum taught from an advance perspective. Course context will be flexible and topics will be selected on the basis of student needs and interests.

MTE 5302A. Quantitative Reasoning.

This course covers current pedagogy, curriculum, and methods related specifically to the teaching of middle school mathematics. Some of the topics explored are curriculum theory, instructional theory, learning theory, problem solving, national and state standards and assessment, discovery learning, assessment methods, manipulative, and technology in the classroom.

MTE 5313. Geometry and Measurement.

This course will focus on using spatial reasoning to investigate the concepts of direction, orientation, shape and structure; using mathematical reasoning to develop and prove geometric relationships; using logical reasoning and proof in relation to the axiomatic structure of geometry; using measurement of geometry concepts to solve real-world problems. 5315 Algebraic Reasoning. (3-0) This course will focus on using algebraic reasoning to.

MTE 5315. Algebraic Reasoning.

This course will focus on using algebraic reasoning to investigate patterns, make generalizations, formulate mathematical models, and make predications; using properties, graphs, and applications of relations and function to analyze, model and solve problems; and making connections among geometric, graphic, numeric and symbolic representation of functions and relations.

MTE 5321. Probability and Statistics.

This course will deal with using graphical and numerical techniques to explore date, characterize patterns, and describe departures from patterns; designing experiments to solve problems; understanding the theory of probability and its relationship to sampling and statistical inference and its use in making and evaluating predication. Prerequisite: MTE 5315 with a grade of "C" or better.

MTE 5323. Logic and Foundations of Mathematics.

This course will consist of an introduction to fundamental mathematical structures and techniques of proof. Topics will include: logic, set theory, number theory, relations, and functions. Emphasis will be placed on communication about mathematics and construction of well-reasoned explanations. Prerequisite: MTE 5313 and MTE 5319 both with grades of "C" or better.

2022-2023 Catalogs

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