Department of Mathematical Sciences
Michigan Technological University
Revised November 18, 2025
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The MS degree
MS Degree Plans
There are three different plans under which the master’s of science (MS) degree can
be earned. Regardless of the plan, students must complete the core courses in their
chosen concentration (see below).
Complete 21 credits of approved coursework, complete a research project leading to
a written thesis, and defend the thesis in a public presentation.
A Plan A thesis represents a more substantial body of research than does a Plan B
report. A thesis should represent original, publishable research. It will typically
result in a paper that is submitted to a refereed journal, although submission of
such a paper is not a degree requirement.
Complete 24 credits of approved coursework, complete a research project leading to
a written report, and defend the report in a public presentation.
Plan B reports can vary widely in content. Some possibilities are:
- The student completes a significant programming project in support of a faculty member’s
research.
- The student investigates a topic in detail and presents a high-quality exposition
of some aspect of it.
- The student does some preliminary, original research on a topic, together with
a literature review of known results.
- The student performs consulting duties on a research project, providing mathematical,
statistical, or computational expertise for other researchers (possibly from another
department).
3
Plan C (Coursework plus examination)
Complete 30 credits of approved coursework and pass the departmental qualifying exam. This exam is given twice a year, early in the fall and then in the spring semesters.
It is also a requirement for the PhD degree, although the passing level for PhD students
is higher than for Plan C MS students. MS students are limited to three attempts to
pass the exam.
4
Plan D (Coursework for M.S. in Applied Statistics)
MS Concentrations and core courses
All MS students must choose one of four concentrations and complete the core coursework
in that concentration. Note: It is important to recognize that many of these courses
are offered only in alternate years. Students must plan carefully to complete the
MS degree in the expected two academic years.
MS in Applied Mathematics
Core courses:
MA 5501 - Theoretical Numerical Analysis
Functional analytic basis of modern numerical analysis. Linear spaces, including Sobolev space theory, linear operators, approximation theory, and applications to Fourier analysis, fixed point theorems, iterative methods, finite difference methods, etc.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4330 and MA 4450
MA 5510 - Ordinary Differential Equations
Qualitative theory of solutions of ordinary differential equations, including existence, uniqueness, and continuous dependence; theory of linear equations; solution of constant coefficient systems; phase plane analysis; design and analysis of numerical methods.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4450 and MA 4330
MA 5565 - Partial Differential Equations
Theory of partial differential equations. Covers classification, appropriate boundary conditions and initial conditions, PDEs of mathematical physics, characteristics, Green`s functions, and variational principles.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
- Pre-Requisite(s): MA 5501
MA 5627 - Numerical Linear Algebra
Design and analysis of algorithms for problems in linear algebra. Covers floating point arithmetic, condition numbers, error analysis, solution of linear systems (direct and iterative methods), eigenvalue problems, least squares, and singular value decomposition. Includes the use of appropriate software including high performance computational libraries.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 4330 or MA 4630
MA 5629 - Numerical Partial Differential Equations
Analysis and design of algorithms for the numerical solution of partial differential equations.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4610 or MA 5627 and MA 5501
Elective courses (choose two):
A graduate-level study of the Lebesgue integral including its comparison with the Riemann integral; the Lebesgue measure, measurable functions and measurable sets. Integrable functions, the monotone convergence theorem, the dominated convergence theorem, and Fatou's lemma.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
MA 5630 - Numerical Optimization
Numerical solution of unconstrained and constrained optimization problems and nonlinear equations. Topics include optimality conditions, local convergence of Newton and Quasi-Newton methods, line search and trust region globalization techniques, quadratic penalty and augmented Lagrangian methods for equality-constrained problems, logarithmic barrier method for inequality-constrained problems, and Sequential Quadratic Programming.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in even years
- Pre-Requisite(s): MA 4330 or MA 4610 or MA 4630 or MA 5627
MA 5580 - Topics in Applied Mathematics
Topics will vary with instructor, but will cover areas in applied mathematics.
- Credits:
3.0;
Repeatable to a Max of 48
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
MA 6500 - Advanced Topics in Applied Mathematics
Advanced topics in applied mathematics.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
MA 6600 - Advanced Topics in Computational Mathematics
Advanced topics in computational mathematics.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required;
Must be enrolled in one of the following Level(s): Graduate
MS in Discrete Mathematics
Core courses:
Review of basic graph theory followed by one or more advanced topics which may include topological graph theory, algebraic graph theory, graph decomposition or graph coloring.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in odd years
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
- Pre-Requisite(s): MA 5301 or MA 4209
Methods for the construction of different combilateral structures such as difference sets, symmetric designs, projective geometries, orthogonal latin squares, transversal designs, steiner systems and tournaments.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 4209 and MA 5301
MA 5231 - Error-Correcting Codes
Basic concepts, motivation from information transmission, finite fields, bounds, optimal codes, projective spaces, duality and orthogonal arrays, important families of codes, MacWilliams' identities, applications.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
Theory of finite groups, their actions and applications. Review of basic group theory (Sylow theorems). Simple groups and group actions (transitivity). Symmetric and alternating groups, linear groups and more general classical groups. Applications: finite fields, designs, finite geometries.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
- Pre-Requisite(s): MA 4310
Elective courses (choose two):
MA 5201 - Combinatorial Algorithms
Basic algorithmic and computational methods used in the solution of fundamental combinatorial problems. Topics may include but are not limited to backtracking, hill-climbing, combinatorial optimization, linear and integer programming, and network analysis.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in even years
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
MA 5280 - Topics in Applied Combinatorics
Topics will vary with instructor but will emphasize real world applications of combinatorial methods. Topics include: cryptography, network reliability, operations research or scheduling, among many other possible choices.
- Credits:
3.0;
Repeatable to a Max of 48
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in even years
- Restrictions:
Permission of department required
Introduction to polynomial rings, finite fields and field extensions. Review of basic notions concerning rings, polynomials and power series. General theory of finite and algebraic field extensions. The basics of Galois theory (field extensions and their Galois groups).
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 5301
MA 5320 - Commutative Algebra
Introduction to commutative algebra and combinatorial algebra. A first description of research issues is also given. Topics include: commutative rings (quotients, morphisms; prime, maximal ideals); modules, Noetherian, artinian rings; combinatorial algebra (gradings, monomials, Hilbert functions, resolutions, level, Gorenstein algebras).
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in even years
- Restrictions:
Permission of instructor required
- Pre-Requisite(s): MA 4310
Topics may include, but not limited to, unique factorization, elementary estimates on the distribution of prime numbers, congruences, Chinese remainder theorem, primitive roots, n-th powers modulo an integer, quadratic residues, quadratic reciprocity, quadratic characters, Gauss sums, and finite fields.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
- Restrictions:
Permission of instructor required
- Pre-Requisite(s): MA 4310
MA 6222 - Advanced Topics in Design Theory
Advanced topics in design theory.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 5222
MA 6231 - Advanced Topics in Coding Theory
Advanced topics in coding theory.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 5231
MA 6280 - Advanced Topics in Combinatorics, Algebra, or Number Theory
Advanced topics in combinatorics, algebra, or number theory.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
MA 6300 - Advanced Topics in Algebra
Advanced topics in algebra.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 5302
MS in Pure Mathematics
Core courses:
Review of basic graph theory followed by one or more advanced topics which may include topological graph theory, algebraic graph theory, graph decomposition or graph coloring.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in odd years
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
- Pre-Requisite(s): MA 5301 or MA 4209
Theory of finite groups, their actions and applications. Review of basic group theory (Sylow theorems). Simple groups and group actions (transitivity). Symmetric and alternating groups, linear groups and more general classical groups. Applications: finite fields, designs, finite geometries.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
- Pre-Requisite(s): MA 4310
Additional core courses (choose one):
MA 5510 - Ordinary Differential Equations
Qualitative theory of solutions of ordinary differential equations, including existence, uniqueness, and continuous dependence; theory of linear equations; solution of constant coefficient systems; phase plane analysis; design and analysis of numerical methods.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4450 and MA 4330
MA 5565 - Partial Differential Equations
Theory of partial differential equations. Covers classification, appropriate boundary conditions and initial conditions, PDEs of mathematical physics, characteristics, Green`s functions, and variational principles.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
- Pre-Requisite(s): MA 5501
Elective courses (choose four):
Methods for the construction of different combilateral structures such as difference sets, symmetric designs, projective geometries, orthogonal latin squares, transversal designs, steiner systems and tournaments.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 4209 and MA 5301
MA 5231 - Error-Correcting Codes
Basic concepts, motivation from information transmission, finite fields, bounds, optimal codes, projective spaces, duality and orthogonal arrays, important families of codes, MacWilliams' identities, applications.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
Introduction to polynomial rings, finite fields and field extensions. Review of basic notions concerning rings, polynomials and power series. General theory of finite and algebraic field extensions. The basics of Galois theory (field extensions and their Galois groups).
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 5301
MA 5320 - Commutative Algebra
Introduction to commutative algebra and combinatorial algebra. A first description of research issues is also given. Topics include: commutative rings (quotients, morphisms; prime, maximal ideals); modules, Noetherian, artinian rings; combinatorial algebra (gradings, monomials, Hilbert functions, resolutions, level, Gorenstein algebras).
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in even years
- Restrictions:
Permission of instructor required
- Pre-Requisite(s): MA 4310
Topics may include, but not limited to, unique factorization, elementary estimates on the distribution of prime numbers, congruences, Chinese remainder theorem, primitive roots, n-th powers modulo an integer, quadratic residues, quadratic reciprocity, quadratic characters, Gauss sums, and finite fields.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
- Restrictions:
Permission of instructor required
- Pre-Requisite(s): MA 4310
MA 5501 - Theoretical Numerical Analysis
Functional analytic basis of modern numerical analysis. Linear spaces, including Sobolev space theory, linear operators, approximation theory, and applications to Fourier analysis, fixed point theorems, iterative methods, finite difference methods, etc.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4330 and MA 4450
MA 6222 - Advanced Topics in Design Theory
Advanced topics in design theory.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 5222
MA 6231 - Advanced Topics in Coding Theory
Advanced topics in coding theory.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 5231
MA 6280 - Advanced Topics in Combinatorics, Algebra, or Number Theory
Advanced topics in combinatorics, algebra, or number theory.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
MA 6300 - Advanced Topics in Algebra
Advanced topics in algebra.
- Credits:
3.0;
Repeatable to a Max of 18
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 5302
Review of discrete probability, probability measures, random variables, distribution functions, expectation as a Lebesgue-Stieltjes integral, independence, modes of convergence, laws of large numbers and iterated logarithms, characteristic functions, central limit theorems, conditional expectation, martingales, introduction to stochastic processes.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in odd years
- Pre-Requisite(s): MA 3720 and MA 5401
MS in Statistics
Core courses:
MA 5711 - Mathematical Statistics I
Review of distribution theory and transformation theory of random variables. Topics include sufficiency; exponential and Bayesian models; estimation methods, including optimality theory; basics of confidence procedures and hypothesis testing, including the Neyman-Pearson framework.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4450 and (MA 4770 or MA 4705)
MA 5712 - Mathematical Statistics II
Optimal tests and decision theory. Other topics may include regression and analysis of variance, discrete data analysis, nonparametric models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 5711
A unified development of linear statistical models that includes the following topics: matrices and quadratic forms, normal and chi-square distribution theory, ordinary and generalized least squares modeling, estimability, estimation and tests of hypothesis.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4710 and MA 4720 and MA 4760 and MA 4330
MA 5741 - Multivariate Statistical Methods
Random vectors and matrix algebra. Multivariate Normal distribution. Theory and application of multivariate techniques including discrimination and classification, clustering, principal components, canonical correlation, and factor analysis.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): (MA 4710 or MA 4720) and MA 2320
Elective courses (choose three):
MA 5730 - Nonparametric Statistics
Introduces nonparametric techniques that require less restrictive assumptions on the data. Topics include statistical inference concerning location and dispersion parameters as well as the general distributions. Goodness-of-fit tests for count and ordinal data are also discussed.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in odd years
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715
MA 5732 - Generalized Linear Models
The focus of this course is on generalized linear models (GLM), including the structure of GLM, statistical theory for GLM (maximum-likelihood estimation of GLM and hypothesis tests), and their applications. Also covers generalized linear mixed and random effects models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
- Pre-Requisite(s): (MA 4710 or MA 5731) and (MA 4770 or MA 5712)
MA 5750 - Statistical Genetics
Application of statistical methods to solve problems in genetics such as locating genes. Topics include basic concepts of genetics, linkage analysis and association studies of family data, association tests based on population samples (for both qualitative and quantitative traits), gene mapping methods based on family data and population samples.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
MA 5761 - Computational Statistics
Introduction to computationally intensive statistical methods. Topics include resampling methods, Monte Carlo simulation methods, smoothing technique to estimate functions, and methods to explore data structure. This course will use the statistical software R.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4770(C) or (MA 4700 and MA 5701)
MA 5770 - Bayesian Statistics
The theory of Bayesian inference. Topics include prior specifications, basics of decision theory, Markov chain, Monte Carlo, Bayes factor, linear regression, linear random effects model, hierarchical models, Bayesian hypothesis testing, Bayesian model selection.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in even years
- Pre-Requisite(s): MA 4330 and MA 4710 and MA 4760
MA 5790 - Predictive Modeling
Application, construction, and evaluation of statistical models used for prediction and classification. Topics include data pre-processing, over-fitting and model tuning, linear and nonlinear regression models and linear and nonlinear classification models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, Spring
- Pre-Requisite(s): MA 3740 or MA 4710 or MA 4720 or MA 4780 or (MA 4700 and MA 5701)
MA 5791 - Categorical Data Analysis
Structure of 2-way contingency tables. Goodness-of-fit tests and Fisher's exact test for categorical data. Fitting models, including logistic regression, logit models, probit and extreme value models for binary response variables. Building and applying log linear models for contingency tables.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
MA 6700 - Advanced Topics in Statistics
Topics may include but are not limited to experimental designs, methods of quality improvement, discrete data analysis, regression analysis, sampling theory, multivariate methods, resampling methods, statistical computing, integral and measure theory, stochastic processes, asymptotic methods, optimization, modeling, nonparametric and parametric statistics.
- Credits:
variable to 12.0;
Repeatable to a Max of 18
- Semesters Offered:
Spring, in even years
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
Review of discrete probability, probability measures, random variables, distribution functions, expectation as a Lebesgue-Stieltjes integral, independence, modes of convergence, laws of large numbers and iterated logarithms, characteristic functions, central limit theorems, conditional expectation, martingales, introduction to stochastic processes.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in odd years
- Pre-Requisite(s): MA 3720 and MA 5401
MS in Applied Statistics
Core courses:
MA 4760 - Mathematical Statistics I
Covers joint probability distributions, functions of random variables, sampling and limiting distributions, introduction to parameter estimation.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): (MA 3720 or EE 3180) and MA 3160
MA 4770 - Mathematical Statistics II
Continuation of MA4760. Theory of point and interval estimation; properties of estimators, theory of hypothesis testing, analysis of variance, analysis of categorical data and other topics as time allows
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 4760
MA 5701 - Statistical Methods
Introduction to design, conduct, and analysis of statistical studies, with an introduction to statistical computing and preparation of statistical reports. Topics include design, descriptive, and graphical methods, probability models, parameter estimation and hypothesis testing.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, Spring, Summer
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
MA 5761 - Computational Statistics
Introduction to computationally intensive statistical methods. Topics include resampling methods, Monte Carlo simulation methods, smoothing technique to estimate functions, and methods to explore data structure. This course will use the statistical software R.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4770(C) or (MA 4700 and MA 5701)
MA 5790 - Predictive Modeling
Application, construction, and evaluation of statistical models used for prediction and classification. Topics include data pre-processing, over-fitting and model tuning, linear and nonlinear regression models and linear and nonlinear classification models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, Spring
- Pre-Requisite(s): MA 3740 or MA 4710 or MA 4720 or MA 4780 or (MA 4700 and MA 5701)
Elective courses (choose five):
MA 3740 - Statistical Programming and Analysis
Project-based course enabling students to identify statistical methods and analysis using R. Topics include exploratory data analysis, classical statistical tests, sample size and power considerations, correlation, regression, and design experiments using advanced programming techniques.
- Credits:
3.0
- Lec-Rec-Lab: (0-2-2)
- Semesters Offered:
Fall, Spring
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715
MA 4710 - Regression Analysis
Covers simple, multiple, and polynomial regression; estimation, testing, and prediction; weighted least squares, matrix approach, dummy variables, multicollinearity, model diagnostics and variable selection. A statistical computing package is an integral part of the course. Some prior experience with R is expected.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701
MA 4720 - Design and Analysis of Experiments
Covers construction and analysis of completely randomized, randomized block, incomplete block, Latin squares, factorial, fractional factorial, nested and split-plot designs. Also examines fixed, random and mixed effects models and multiple comparisons and contrasts. The R programming language is an integral part of the course.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701
MA 5711 - Mathematical Statistics I
Review of distribution theory and transformation theory of random variables. Topics include sufficiency; exponential and Bayesian models; estimation methods, including optimality theory; basics of confidence procedures and hypothesis testing, including the Neyman-Pearson framework.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4450 and (MA 4770 or MA 4705)
MA 5712 - Mathematical Statistics II
Optimal tests and decision theory. Other topics may include regression and analysis of variance, discrete data analysis, nonparametric models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 5711
MA 5730 - Nonparametric Statistics
Introduces nonparametric techniques that require less restrictive assumptions on the data. Topics include statistical inference concerning location and dispersion parameters as well as the general distributions. Goodness-of-fit tests for count and ordinal data are also discussed.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in odd years
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715
A unified development of linear statistical models that includes the following topics: matrices and quadratic forms, normal and chi-square distribution theory, ordinary and generalized least squares modeling, estimability, estimation and tests of hypothesis.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4710 and MA 4720 and MA 4760 and MA 4330
MA 5732 - Generalized Linear Models
The focus of this course is on generalized linear models (GLM), including the structure of GLM, statistical theory for GLM (maximum-likelihood estimation of GLM and hypothesis tests), and their applications. Also covers generalized linear mixed and random effects models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
- Pre-Requisite(s): (MA 4710 or MA 5731) and (MA 4770 or MA 5712)
MA 5741 - Multivariate Statistical Methods
Random vectors and matrix algebra. Multivariate Normal distribution. Theory and application of multivariate techniques including discrimination and classification, clustering, principal components, canonical correlation, and factor analysis.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): (MA 4710 or MA 4720) and MA 2320
MA 5750 - Statistical Genetics
Application of statistical methods to solve problems in genetics such as locating genes. Topics include basic concepts of genetics, linkage analysis and association studies of family data, association tests based on population samples (for both qualitative and quantitative traits), gene mapping methods based on family data and population samples.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
MA 5770 - Bayesian Statistics
The theory of Bayesian inference. Topics include prior specifications, basics of decision theory, Markov chain, Monte Carlo, Bayes factor, linear regression, linear random effects model, hierarchical models, Bayesian hypothesis testing, Bayesian model selection.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, in even years
- Pre-Requisite(s): MA 4330 and MA 4710 and MA 4760
MA 5781 - Time Series Analysis and Forecasting
Statistical modeling and inference for analyzing experimental data that have been observed at different points in time. Topics include models for stationary and non stationary time series, model specification, parametric estimation, model diagnostics and forecasting, seasonal models and time series regression models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): (MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701) and (MA 3720 or EE 3180 or MA 4700)
MA 5791 - Categorical Data Analysis
Structure of 2-way contingency tables. Goodness-of-fit tests and Fisher's exact test for categorical data. Fitting models, including logistic regression, logit models, probit and extreme value models for binary response variables. Building and applying log linear models for contingency tables.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
With prior approval of an advisor, related courses (at most two) may also be used
as electives.
MS in Applied Statistics (Online)
Core courses:
MA 4700 - Probability and Statistical Inference I
Introduction to probabilistic methods. Topics include probability laws, counting rules, discrete and continuous random variables, moment generating functions, expectation, joint distributions, and the Central Unit Theorem.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, Spring, Summer
- Pre-Requisite(s): MA 3160 and (MA 2710 or MA 2720 or MA 3710 or MA 3715)
MA 4705 - Probability and Statistical Inference II
Topics include sampling distributions, theory of point and interval estimation, properties of estimators, and theory of hypothesis testing.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Restrictions:
Permission of department required
- Pre-Requisite(s): MA 4700
MA 5701 - Statistical Methods
Introduction to design, conduct, and analysis of statistical studies, with an introduction to statistical computing and preparation of statistical reports. Topics include design, descriptive, and graphical methods, probability models, parameter estimation and hypothesis testing.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, Spring, Summer
- Restrictions:
Must be enrolled in one of the following Level(s): Graduate
MA 5761 - Computational Statistics
Introduction to computationally intensive statistical methods. Topics include resampling methods, Monte Carlo simulation methods, smoothing technique to estimate functions, and methods to explore data structure. This course will use the statistical software R.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 4770(C) or (MA 4700 and MA 5701)
MA 5790 - Predictive Modeling
Application, construction, and evaluation of statistical models used for prediction and classification. Topics include data pre-processing, over-fitting and model tuning, linear and nonlinear regression models and linear and nonlinear classification models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall, Spring
- Pre-Requisite(s): MA 3740 or MA 4710 or MA 4720 or MA 4780 or (MA 4700 and MA 5701)
MA 4710 - Regression Analysis
Covers simple, multiple, and polynomial regression; estimation, testing, and prediction; weighted least squares, matrix approach, dummy variables, multicollinearity, model diagnostics and variable selection. A statistical computing package is an integral part of the course. Some prior experience with R is expected.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701
MA 4720 - Design and Analysis of Experiments
Covers construction and analysis of completely randomized, randomized block, incomplete block, Latin squares, factorial, fractional factorial, nested and split-plot designs. Also examines fixed, random and mixed effects models and multiple comparisons and contrasts. The R programming language is an integral part of the course.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701
MA 5781 - Time Series Analysis and Forecasting
Statistical modeling and inference for analyzing experimental data that have been observed at different points in time. Topics include models for stationary and non stationary time series, model specification, parametric estimation, model diagnostics and forecasting, seasonal models and time series regression models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): (MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701) and (MA 3720 or EE 3180 or MA 4700)
MA 5751 - Statistical Data Mining
Course will cover various topics in statistical data mining, including linear model selection and regularization, regression and smoothing splines, unsupervised learning, resampling methods, tree-based methods, and deep learning. This course will introduce modern statistical data mining techniques and their applications.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring, in odd years
- Pre-Requisite(s): (MA 4700 or MA 4760) and (MA 5701 or MA 4710)
MA 5771 - Applied Generalized Linear Models
Construction, evaluation, and application of generalized linear models to analyze different types of data. Topics include logistic and Poisson regression, multinomial logit models, random effects and mixed effect models, models for repeated measures and longitudinal data. Introduce theory on GLM fitting, hypothesis testing, and diagnostic models.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
On Demand
- Pre-Requisite(s): MA 4710 and (MA 4760 or (MA 4700 and MA 5701))
General advice for MS students
1
Research-based plan (Plan A or Plan B)
You should find an advisor by the end of your first semester if possible, and no later
than the end of your second semester.
2
Coursework-based (Plan C)
You will take the qualifying examination during orientation week. If you do not pass,
you should try to take it again in your second semester. Students are limited to three
attempts to pass the exam.
The graduate school requires MS students to submit certain forms documenting their
progress through the degree requirements (for example, completion of necessary courses,
passage of required exams, scheduling of an oral defense, etc.).
Accelerated MS Programs
- We offer accelerated MS programs in both Applied Statistics and Statistics. The course
requirements are the same as the non-accelerated programs. The accelerated MS in Applied
Statistics is offered as a Plan D option only. The accelerated MS in Statistics is
offered as a Plan A, B or C option.
- The accelerated MS in Applied Statistics is open to undergraduate students of any
major except Statistics.
- The accelerated MS in Statistics is open only to undergraduate Statistics majors.
- Students must be admitted to the accelerated MS according to rules from the graduate
school. The following courses will count toward both the BS and MS in Statistics degrees:
The PhD degree
The PhD degree is offered in the following concentrations:
- Applied Mathematics
- Discrete Mathematics
- Statistics
The requirements are listed below. It is important to note that this list is not chronological;
indeed, not all students will complete the requirements in the same order.
Choose a concentration and complete the core MS coursework in that concentration.
Find an advisor no later than the end of your second regular semester and form a PhD
dissertation committee.
- Complete at least two 6000-level courses in your concentration.
- Students in discrete math and applied and computational math can use MA5980 as a 6000-level
course. MA5980 is repeatable up to 4 times.
Complete the “breadth” requirement by taking two graduate level courses in other concentrations.
Pass the qualifying examination. This is a written exam covering advanced undergraduate material. It must be passed
by the end of the third semester in the PhD program, summer semesters do not count.
Pass the comprehensive examination. This multi-part exam covers graduate coursework. It must be passed by the end of the
sixth semester in the PhD program, summer semesters do not count.
Recommended: Present a dissertation proposal to the satisfaction of your dissertation
committee. Depending on your committee, this proposal may be written or oral. Check with your
advisor.
Write a dissertation detailing the results of a substantial and original research
project.
9
Dissertation Presentation
Defend the dissertation with a public presentation and examination by your committee.
The graduate school requires PhD students to submit certain forms documenting their
progress through the degree requirements (for example, completion of necessary courses,
passage of required exams, scheduling of an oral defense, etc.).
PhD - The qualifying examination
The qualifying examination covers advanced undergraduate material. Each student takes
two 3-hour written examinations, with the subjects determined by the concentration:
- Linear Algebra
- Real Analysis
- Abstract Algebra
- Combinatorics
- Linear Algebra
- Abstract Algebra or Real Analysis
- Linear Algebra
- Mathematical Statistics
The syllabus for each subject and a selection of past exams are archived in a google
folder. Access is obtained by sending a request to the administrative aide. The fall
exam will be given during the orientation week. The spring exam in applied and computational
math and in statistics will be given in week 3, while the exam in discrete math will
be given in week 12.
A PhD student must pass the exam by the end of the third semester in the program,
summer semesters do not count, to continue in the PhD program.
With approval from the graduate committee, a student failing to fulfill this requirement
can still complete an MS degree if he or she has not already done so.
The qualifying examination is graded as “PhD Pass”, “MS Pass”, or “Fail”. PhD students
must pass at the higher level; an MS student who passes at the PhD level may be a
good candidate to continue for the PhD.
Important note: Students must sign up to take the qualifying examination approximately six weeks
before it is given. The deadline will be announced by email by the graduate program
secretary. A student who wishes to withdraw from the exam must inform the graduate
program secretary at least three weeks before the date of the exam; a student who
fails to do so and yet does not show up for the exam will be failed. This rule does
not apply to a student who cannot take the exam due to circumstances beyond his or
her control.
Any incoming student who fails a qualifying exam will be required to take the corresponding
undergraduate courses.
MA 4310 - Abstract Algebra
Detailed study of abstract algebra: elementary number theory (congruences, quadratic residues, arithmetic functions), group theory (monoids, permutation groups, homomorphisms, quotients, Lagrange's theorem, finite abelian groups, Sylow's theorems), ring theory (domains, prime and maximal ideals, quotients, PID's), splitting fields, finite fields.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Spring
- Pre-Requisite(s): MA 3310
MA 4209 - Combinatorics and Graph Theory
An introductory course in combinatorics and graph theory. Topics include designs, enumeration, extremal set theory, finite geometry, graph coloring, inclusion-exclusion, network algorithms, permutations, and trees.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): MA 3210 or CS 3311
A study of fundamental ideas in linear algebra and its applications. Includes review of basic operations, block computations; eigensystems of normal matrices; canonical forms and factorizations; singular value decompositions, pseudo inverses, least-square applications; matrix exponentials and linear systems of ODEs; quadratic forms, extremal properties, and bilinear forms.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): (MA 2320 or MA 2321 or MA 2330) and MA 3160
MA 4760 - Mathematical Statistics I
Covers joint probability distributions, functions of random variables, sampling and limiting distributions, introduction to parameter estimation.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): (MA 3720 or EE 3180) and MA 3160
Real analysis on Euclidean n-space. Topics include real and vector valued functions, metric and normed linear spaces; an introduction to Lebesgue measure and convergence theorems.
- Credits:
3.0
- Lec-Rec-Lab: (0-3-0)
- Semesters Offered:
Fall
- Pre-Requisite(s): (MA 2320 or MA 2321 or MA 2330) and MA 3160 and MA 3450
PhD - The comprehensive examination
The comprehensive examination covers graduate coursework and consists of three parts:
two 3-hour written subject exams, and a specialty exam that can be written or oral.
The subject exams are determined by the area of concentration:
- Any two of
-
- Ordinary Differential Equations,
- Partial Differential Equations
- Numerical Linear Algebra/Numerical Optimization.
- Any two of
-
- Algebra
- Coding Theory
- Design Theory
- Number Theory
- Mathematical statistics
- Linear Models
The syllabus for each subject and a selection of past exams are archived in a Google
Drive folder. Access is obtained by sending a request to the administrative aide.
The fall exam will be given during the orientation week. The spring exam will take
place by the end of week 4.
The specialty exam is intended to make sure the student has the background knowledge
to conduct research in his or her chosen area. The format of the exam (written or
oral) is determined by the student’s advisor.
- The specialty exam must be scheduled so that it and the two written subject exams
are all completed within a 14-day period.
- Students have two attempts to pass the comprehensive exam. If a student fails only
one part of the exam on the first attempt, only that part must be re-taken on the
second try. If a student fails two or all three parts on the first attempt, all three
parts must be re-taken on the second try.
- The comprehensive exam must be passed by the end of the sixth semester in the program
(summer semesters do not count).
Important note: Students must sign up to take the comprehensive examination approximately six weeks
before it is given. The deadline will be announced by email by the graduate program
assistant. A student who wishes to withdraw from the exam must inform the graduate
program assistant at least three weeks before the date of the exam; a student who
fails to do so and yet does not show up for the exam will be failed. This rule does
not apply to a student who cannot take the exam due to circumstances beyond his or
her control.
PhD - Typical milestones
How long should it take you to complete your PhD program? Those who enter the program
with a Master’s may complete the PhD in as little as three years. Others, perhaps
entering with a Bachelor’s, may take four or five years. Durations greater than eight
calendar years require approval from the Graduate School. See table below for typical
timelines:
Table 1. Typical milestones in a PhD program and typical time frames in which they
are completed.
| What: |
When (semesters): |
| Choose a research advisor |
Within 2 |
| Complete required coursework |
5 to 6 |
| Choose a committee |
2 to 4 |
| Pass qualifying exam |
2 to 3 |
| Pass comprehensive exam |
4 to 6 |
| Enter Research Mode / Start writing products to be included in dissertation |
4 to 6 |
| Dissertation Defense / Final Oral Examination |
6 to 10 |
Process for changing your advisor(s)
Before initiating the process to change your graduate advisor, please consider all
the options listed on the Graduate School’s website for Succeeding in Graduate School.
Once you have decided to change your graduate advisor, you must follow the steps listed
below.
- Meet with your Graduate Program Director to initiate the process to change advisor.
If meeting with the Graduate Program Director is not feasible or appropriate, meet
with the Chair of the department.
- Discuss the following with the Graduate Program Director (or Chair) and, if appropriate,
the current advisor:
- Whether additional resources within or outside the department (such as the Ombuds
office) could help resolve the situation.
- The impact of the change of advisor on your time to complete the degree. Coursework,
qualifying exams, and the comprehensive exams are all factors that could be impacted
with a change in advisor.
- Your current and future funding.
- Research already conducted. Whether this will be incorporated into the dissertation,
thesis, or report, and if so, how.
- Impact on immigration status (if any). Consult International Programs and Services
(IPS), if necessary.
- Record the agreement from the discussions in writing, including indications of agreement
from all affected faculty advisors, and provide copies to the student, the Graduate
Program Director, and all affected faculty advisors.
- File an updated Advisor and Committee Recommendation Form for approval by the Graduate School.
- If the student and the Graduate Program Director are unable to reach agreement on
the advisor change, contact the Assistant Dean of the Graduate School to determine
additional steps to resolve the situation.
Required paperwork
The graduate school requires MS and PhD students to submit certain forms documenting
their progress through the degree requirements (for example, completion of necessary
courses, passage of required exams, scheduling of an oral defense, etc.). These forms
can be found at the following web pages:
The graduate program assistant can help students to file these forms; however, it
is the responsibility of each student to file the necessary forms in a timely manner.
Please note that each form has an associated deadline, and that the graduate school
may not accept a form after the deadline.
