Mathematics & Statistics

Graduate Programs

Description

The Department of Mathematics and Statistics offers four master’s programs: Mathematics MA, Mathematics and Statistics MS, Applied Statistics MS, and Mathematics Education MS. The Mathematics MA has three emphases: a broad selection of courses in mathematics, mathematics and computer sciences, and mathematics and community college teaching.

The department consists of approximately twenty-four faculty members, including most faculty members with a Ph.D. in mathematics, statistics, or mathematics education. The department supports approximately 30 graduate students per year. Faculty specialties or interests include abstract algebra, applied computational mathematics, combinatorial matrix theory, complex analysis, discrete mathematics and combinatorics, dynamical systems, elementary and secondary mathematics education, differential geometry, symplectic geometry, industrial mathematics, mathematical biology, numerical analysis, optimization, partial differential equations, functional analysis, real analysis, applied statistics, Bayesian analysis, mathematical statistics, time series and survival analysis, stochastic processes, actuarial science, topology, big data, and data analytics.

Graduates of the program have found employment in a variety of fields, including software engineering, graphic design, insurance, community college teaching, secondary mathematics teaching and as statisticians or data scientists. Others have gone on to obtain a Ph.D. in mathematics or statistics.

Facilities. The Department of Mathematics and Statistics is housed in Wissink Hall. This building is also home to the Academic Computing Center which supports over 400 up-to-date workstations on both PC and Macintosh platforms, and a computer-equipped classroom designed for the teaching of mathematics and statistics. The classroom computers are equipped with mathematical and statistical software including Mathematica, Matlab, Maple, SAS, SPSS, Geometer’s Sketchpad, R, Python, and Minitab. Students also have access to Unix mainframe machines and a High Performance Computing (HPC) cluster. The internet is easy to access through the campus-wide wireless network. The library has a wide range of mathematical texts and journals. The library also supports services which provide access to literature not found in our library’s collection.

Majors

 Program Locations Major / Total Credits
Applied Statistics MS MS - Master of Science
  • Mankato
 34 / 34
Mathematics and Statistics MS MS - Master of Science
  • Mankato
 34 / 34
Mathematics Education MS MS - Master of Science
  • Mankato
 34 / 34
Mathematics MA MA - Master of Arts
  • Mankato
 34 / 34

Policies & Faculty

Policies

Admission. Preference will be given to applicants with minimum grade point average of 3.0 and a demonstrated ability to consistently perform at a B or better level in upper division mathematics and/or statistics courses. An applicant must also meet the general admission requirements of the College of Graduate Studies and Research.

Financial Assistance. Approximately 30 graduate assistantships are available in the department each year. Graduate assistant duties include teaching or research.

General Program Requirements. All programs require an alternate plan paper or thesis, a comprehensive exam, and an oral defense of the alternate plan paper or thesis. At least 50% of the course work of each program must be at the 600 level. Alternate plan paper and thesis credit are not counted as course work. After completing 16 credits, the student must select an examining committee composed of a minimum of three graduate faculty members.

Course Application Policy. No course can be used to satisfy more than one program requirement.

Mathematics Education MS

Teaching licensure is a prerequisite to pursuing this degree which is for teachers interested in a graduate program in teaching mathematics. This degree does not lead to initial teaching licensure. Students who desire initial licensure should consult the Master of Arts in Teaching (MAT) program.

  1. At least half of the credits applied to a program must be earned in 600-level courses excluding thesis or Alternate Plan Paper credits.
  2. After completing 16 credits the student must select a three-member examining committee and form a program of study.
  3. A student may choose to write an alternate plan paper or thesis. This program requires a comprehensive exam, and an oral defense of the alternate plan paper or thesis.

Contact Information

273 Wissink Hall

Office 507-389-1453
https://cset.mnsu.edu/departments/mathematics-and-statistics/

Faculty

Chair
  • Ruijun Zhao
Faculty
  • Dat Cao, PhD
  • Jonathan Harper, PhD
  • In-Jae Kim, PhD
  • Wook Kim, PhD
  • Namyong Lee, PhD
  • Hyekyung Min, PhD
  • Galkande Premarathna, PhD
  • Mezbahur Rahman, PhD
  • Brandon Rowekamp, PhD
  • Deepak Sanjel, PhD
  • Soo Yeon Shin, PhD
  • Dan Singer, PhD
  • Yea-Ling Tsao, PhD
  • Han Wu, PhD
  • Hongxia Yin, PhD
  • Ruijun Zhao, PhD
  • Ke Zhu, PhD
  • Mark Zuiker, PhD

500 Level

Credits: 4

An introduction to topological spaces and their fundamental properties such as compactness, connectedness, separation properties and countability properties. Continuous functions between topological spaces and common examples of topological spaces are also discussed.

Prerequisites: MATH 290

Credits: 4

Algebra and geometry of complex numbers, analytic functions, power series, Cauchy's theorem and residue theorem.

Prerequisites: MATH 223 and MATH 290 with “C” (2.0) or better or consent.

Credits: 4

The topology of Euclidean spaces, norms, classical inequalities, local and global properties of continuous functions, preservation of compactness and connectedness, sequences in Euclidean space and sequences of functions.

Prerequisites: MATH 223 and MATH 290 with “C” (2.0) or better or consent.

Credits: 3

A continuation of MATH 4/517. The course may include topics from metric spaces, Riemann-Stieltjes integration, differentiation in Euclidean space, sequences and series of functions, approximation theorems, implicit and inverse function theorems, equicontinuity, and mapping theorems.

Prerequisites: (MATH 417 or MATH 517) with “C” (2.0) or better or consent.

Credits: 4

This course presents the theory, computations, and applications of partial differential equations and Fourier series.

Prerequisites: MATH 223 and MATH 321 with “C” (2.0) or better or consent.

Credits: 4

This course presents topics from mathematical analysis of both discrete and continuous models taken from problems in the natural sciences, economics, and resource management.

Prerequisites: MATH 223 and MATH 247 with “C” (2.0) or better or consent.

Credits: 4

Simplex method and its variants, duality, sensitivity analysis, interior-point methods, quadratic programming and linear complementarity problems. Applications such as classification problems and game theory with linear optimization software.

Prerequisites: MATH 122 and MATH 247

Credits: 4

Geometry of spaces including Euclidean and non-Euclidean and applications of contemporary geometry.

Prerequisites: MATH 247 and MATH 290 with a grade of "C" (2.0) or higher, or consent.

Credits: 4

Euclidean algorithm, primes, composites, number theoretic functions, congruences, Diophantine equations, Euler and Fermat theorems, and algebraic number fields.

Prerequisites: MATH 345 with “C” (2.0) or better or consent.

Credits: 4

A continuation of MATH 345. The course will include topics from groups, rings, and fields.

Prerequisites: MATH 345 with “C” (2.0) or better or consent.

Credits: 3

An in-depth study of linear operators and their related spaces, dimension, rank, matrix representation of linear operators, special matrices, determinants, eigenvectors, and eigenvalues.

Prerequisites: MATH 345 with “C” (2.0) or better or consent.

Credits: 3

Simple and multiple regression, correlation, analysis of variance and covariance.

Prerequisites: MATH 354 or STAT 354 or (MATH 455 or MATH 555) or (STAT 455 or STAT 555) with “C” (2.0) or better or consent.

Credits: 3

Randomized complete block design, Latin squares design, Graco- Latin squares design, balanced incomplete block design, factorial design, fractional factorial design, response surface method, fixed effects and random effects models, nested and split plot design.

Prerequisites: MATH 354 or STAT 354 or (MATH 455 or MATH 555) or (STAT 455 or STAT 555) with “C” (2.0) or better or consent.

Credits: 4

A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications. Includes probability, continuous probability distributions, multivariate distributions, functions of random variables, central limit theorem, and statistical inference. Same as STAT 555

Prerequisites: MATH 223 with “C” (2.0) or better or consent.

Credits: 4

A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications. Includes probability, continuous probability distributions, multivariate distributions, functions of random variables, central limit theorem, and statistical inference. Same as MATH 555.

Prerequisites: MATH 223 with “C” (2.0) or better or consent.

Credits: 4

A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications, including sufficient statistics, additional statistical inference, theory of statistical tests, inferences about normal models, and non-parametric methods. Same as STAT 556.

Prerequisites: (MATH 455 or MATH 555) or (STAT 455 or STAT 555) with “C” (2.0) or better or consent.

Credits: 4

A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications, including sufficient statistics, additional statistical inference, theory of statistical tests, inferences about normal models, and nonparametric methods. Same as MATH 556.

Prerequisites: (MATH 455 or MATH 555) or (STAT 455 or STAT 555) with “C” (2.0) or better or consent.

Credits: 3

Topics include: sampling distributions, means and variances; bias, robustness and efficiency; random sampling; systematic sampling methods including stratified random, cluster and two-state sampling; and ratio, regression, and population size estimation. Suitable software, such as MATLAB, R, SAS, etc., is introduced.

Prerequisites: Either MATH/STAT 354 or both STAT 154 and MATH 121 with “C” (2.0) or better, or consent.

Credits: 3

Topics on multivariate analysis for discrete data, including two/higher dimensional tables; models of independence; log linear models; estimation of expected values; model selection; and logistic models, incompleteness and regression. Suitable statistical software, such as MATLAB, R, SAS, etc., is introduced.

Prerequisites: Either MATH/STAT 354 or both STAT 154 and MATH 121 with “C” (2.0) or better, or consent.

Credits: 3

Topics include derivation and usage of nonparametric methods in univariate, bivariate, and multivariate data; applications in count, score, and rank data; analysis of variance for ranked data; and regression estimation. Suitable software, such as MATLAB, R, SAS, etc., is introduced.

Prerequisites: Either MATH/STAT 354 or both STAT 154 and MATH 121 with “C” (2.0) or better, or consent.

Credits: 3

This course applies probabilistic methods to problems encountered in actuarial science that prepares students for the Society of Actuaries Exam P/1.

Prerequisites: (MATH/STAT 354 and MATH 223) or MATH/STAT 455 or MATH/STAT 555

Credits: 4

This course covers the theory of interest portion of Exam FM/2 of the Society of Actuaries. Topics include time value of money, measurement of interest, annuities certain, arithmetic and geometric annuities, amortization schedules and sinking fund, bonds and other securities, yield rates, and interest rate immunization.

Prerequisites: MATH 223

Credits: 4

This course provides an introduction to techniques and analysis involved with solving mathematical problems using technology. Topics included are errors in computation, solutions of linear and nonlinear equations, numerical differentiation and integration, and interpolation.

Prerequisites: MATH 122 and MATH 247 with “C” (2.0) or better or consent.

Credits: 4

This course is a continuation of MATH 470. Topics included are the algebraic eigenvalue problem, least-squares approximation, solutions of systems of nonlinear equations, and numerical solutions of ordinary differential equations.

Prerequisites: (MATH 470 or MATH 570) and MATH 223 with “C” (2.0) or better or consent.

Credits: 4

Students will learn fundamental concepts of computer programming and write software to implement a variety of mathematical algorithms, manipulate large amounts of data, test conjectures, and make abstract mathematical concepts concrete. Programming concepts include input versus output, data structures, local and global variables, switch statements, iteration, recursion, halting conditions, modularity, debugging, and algorithm analysis. Programming projects may vary with instructor, but could include topics from enumerative combinatorics, graph theory, group theory, linear algebra, and number theory.

Prerequisites: Math 375 and Math 345 with grade of C (2.0) or better in both courses.

Credits: 3

The development of selected topics from before the Hellenistic time period to the late twentieth century. Familiarity with the content of HIST 180 is beneficial.

Prerequisites: MATH 345 with “C” (2.0) or better or consent.

Credits: 3

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Prerequisites: MATH 290 with “C” (2.0) or better or consent.

Credits: 3

This course is designed to inform secondary mathematics teachers about effective utilization of technology in the mathematics curriculum.

Prerequisites: MATH 290 with “C” (2.0) or better or consent.

Credits: 1-3

A course of study in which a group of students study a topic by examining results through reports and discussions. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 1-3

The study of a particular topic primarily based upon recent literature. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 1-4

A short course devoted to a specific mathematical topic. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 1-4

A course designed to upgrade the qualifications of persons on-the-job. May be repeated on each new topic.

Prerequisites: none

Credits: 1-4

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Prerequisites: none

Credits: 1-4

A course in an area of mathematics not regularly offered. May be repeated on each new topic.

Prerequisites: none

Credits: 1-12

Provides a student the opportunity to gain expertise and experience in a special field under the supervision of a qualified person.

Prerequisites: none

Credits: 1-12

Provides a student the opportunity to gain expertise and experience in a special field under the supervision of a qualified person.

Prerequisites: none

600 Level

Credits: 3

Mathematical concepts of graph theory applied to problems that have algorithmic solutions.

Prerequisites: (MATH 417 or MATH 517) and Math 375 and (MATH 447 or MATH 547) or consent.

Credits: 3

Can be used for any graduate level discrete mathematics course not offered as a regular course. Distinct offerings may be repeated for credit.

Prerequisites: MATH 375 and (MATH 447 or MATH 547) or consent.

Credits: 3

Measure theory, integration, metric spaces, and Banach spaces.

Prerequisites: MATH 417 or MATH 517 or consent.

Credits: 3

Can be used for any graduate level analysis course not offered as a regular course. Distinct offerings may be repeated for credit.

Prerequisites: (MATH 417 or MATH 517) or consent.

Credits: 3

An introduction to the basic concepts and principles of functional analysis. Normed spaces, Banach spaces, Hilbert spaces, and approximation theory are studied.

Prerequisites: (MATH 417 or MATH 517) and (MATH 447 or MATH 547) or consent.

Credits: 3

Applications of discrete and continuous mathematics to deterministic problems in the natural sciences, computer science, engineering, and economics. Applied problems will be developed within the mathematical framework of dimensional analysis, asymptotic analysis, perturbation theory, stability, and bifurcation.

Prerequisites: MATH 321 and (MATH 417 or MATH 517) and (MATH 447 or MATH 547) or consent.

Credits: 3

Can be used for any graduate level applied mathematics course not offered as a regular course. Distinct offerings may be repeated for credit.

Prerequisites: (MATH 417 or MATH 517) and (MATH 422 or MATH 522) and (MATH 447 or MATH 547) or consent.

Credits: 3

The theory of functions of one complex variable. Complex numbers, contour integration, analytic functions, residues, and power series.

Prerequisites: (MATH 417 or MATH 517) or consent.

Credits: 3

Optimal conditions for constrained and unconstrained optimization problems, and a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. Large-scale optimization techniques are emphasized in the course.

Prerequisites: MATH 517 and MATH 547

Credits: 3

This course presents selected topics in projective, transformational, and differential geometry.

Prerequisites: Consent

Credits: 3

A rigorous excursion through some of the topics of abstract algebra which are essential components of the background of a masters level graduate student. Abstract topics include groups, rings, fields, and modules. Concrete applications include properties of the integers, polynomial rings, and the symmetric group.

Prerequisites: MATH 345 or consent.

Credits: 3

Bayesian Statistics is an alternative to Frequentist statistics. Bayesian inference uses probability for both hypotheses and data. In Bayesian statistics, population parameters are considered random variables having probability distributions. The probabilities measure a degree of belief in the parameters. Bayes¿ theorem is used to reformulate the beliefs using observed data. This course introduces the Bayesian approach to statistical inference and describes effective approaches to Bayesian modeling and computation.

Prerequisites: MATH/STAT 455/555 and STAT 450/550, or consent

Credits: 3

This course will cover advanced topics such as (but not limited to) free abelian groups, group rings, noetherian/generalized noetherian rings, coherent/generalized coherent rings, homological algebra, homological dimension theory, representation theory of finite fields, galois theory of equations, field theory, valuation theory, and semigroups.

Prerequisites: MATH 641 or consent.

Credits: 3

Most statistical analysis and modeling techniques involve assumptions about the independence of the data. However, many real life data occur in the form of time series where observations are dependent. In this course, we will concentrate on both univariate and multivariate time series analysis and model building strategies with time dependent data. Available software will be used to complete the data analysis projects with a balance between theory and applications.

Prerequisites: MATH/STAT 455/555 and MATH/STAT 450/550, with "C" (2.0) or better, or consent.

Credits: 3

Matrix theory, multivariate normal distribution of quadratic forms, estimation and hypothesis testing in the general linear model, and applications of linear models.

Prerequisites: MATH/STAT 455/555 and STAT 450/550 with “C” (2.0) or higher, or consent.

Credits: 3

Statistical tools used to analyze data in biological and medical research. Topics covered are Statistical Theory, Concepts of Statistical Inference, Regression and Correlation Methods, Analysis of Variance, Survival Analysis and Study Designs. Applications to medical problems.

Prerequisites: STAT 450/550 with “C” (2.0) or higher, or consent.

Credits: 3

This course will cover the basic concepts of big data with an emphasis on the statistical techniques for analyzing structured and unstructured data. Students will learn concepts, techniques and tools that are necessary for working with the various facets of data science practice, including data collection and integration, exploratory data analysis, predictive modeling, descriptive modeling, data product creation, evaluation, and effective communication. The course has applications across many disciplines such as engineering, computer science, statistics, mathematics, economics and management. Prerequisite: MATH 247 and STAT 354 or instructor consent

Prerequisites: STAT 450/550 with “C” (2.0) or higher, or consent.

Credits: 3

Heuristics in mathematical problem solving and mathematical modeling for teachers.

Prerequisites: none

Credits: 3

Algebraic concepts and procedures interpreted and related from the perspectives of abstract algebra, cognitive research on the learning of algebra, and professional curriculum and instruction programs.

Prerequisites: MATH 345 or consent.

Credits: 3

The Van Hiele model of the development of geometric thought and recent developments of geometric theory and applications which are related to the school mathematics curriculum.

Prerequisites: MATH 332 or consent.

Credits: 3

This course is an in-depth study of solving ordinary differential equations and partial differential equations numerically. Runge-Kutta methods and general multi-step methods are developed for ordinary differential equations. Finite Difference Method and Finite Element methods are developed for partial differential equations. Error control and step size changing for both stiff and non-stiff equations are analyzed.

Prerequisites: MATH 321 and (MATH 470 or MATH 570) or consent.

Credits: 3

This course is an in-depth study of solving algebraic eigenvalue problems, least-square problems, direct and iterative methods for solving linear systems, and their applications.

Prerequisites: (MATH 447 or MATH 547) and (MATH 470 or MATH 570) or consent.

Credits: 1-4

Independent individual study under the guidance and direction of a graduate faculty member.

Prerequisites: Consent

Credits: 1-4

Independent individual study under the guidance and direction of a graduate faculty member.

Prerequisites: Consent

Credits: 1-4

A graduate course in an area of mathematics not regularly offered. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 1-4

A graduate course in a particular area of statistics not regularly offered. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 1-3

Independent readings in mathematics under the direction of a graduate faculty member.

Prerequisites: Consent

Credits: 3

Examination of cognitive theories guiding research in mathematics education; analysis and interpretation of research procedures applied in experimental, qualitative, program evaluation, survey, meta-analysis, theory-generating, and action research studies in mathematics education.

Prerequisites: (STAT 450 or STAT 550) or (STAT 451 or STAT 551) or consent.

Credits: 1-4

A course designed to upgrade the qualifications of persons on-the-job. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 3

Topological spaces, continuity, product spaces, connectedness, separation, compactness, and metric spaces.

Prerequisites: MATH 417 or MATH 517 or consent.

Credits: 3

Will cover topics at the discretion of the instructor, such as, but not limited to, those in the following list: algebraic topology, homotopy theory, homology theory, differential topology, topological groups, topological vector spaces, categorical topology, catastrophe theory, lie Groups, algebras of continuous functions, and uniform structures.

Prerequisites: MATH 692 or consent.

Credits: 1-2

Research under the supervision of the student's advisor leading to an alternate plan paper.

Prerequisites: Consent

Credits: 1-2

Research under the supervision of the student's advisor leading to an alternate plan paper.

Prerequisites: Consent

Credits: 1-4

A short course devoted to a specific mathematical topic. May be repeated for credit on each new topic.

Prerequisites: none

Credits: 3

Statistical package programs used in data collection, transformation, organization, summarization, interpretation and reporting, statistical description and hypothesis testing with statistical inference, interpreting outputs, chi-square, correlation, regression, analysis of variance, nonparametrics, and other designs, accessing and using large files (U.S. Census data, National Health Survey, etc.) Same as COMS 696

Prerequisites: STAT 450/550 with “C” (2.0) or higher, or consent.

Credits: 1-12

Provides a student the opportunity to gain expertise and experience in a special field under the supervision of a qualified person.

Prerequisites: none

Credits: 1-12

Provides a student the opportunity to gain expertise and experience in a special field under the supervision of a qualified person.

Prerequisites: Consent

Credits: 1-4

Research under the supervision of the student's advisor leading to a thesis.

Prerequisites: Consent

Credits: 1-4

Research under the supervision of the student's advisor leading to a thesis.

Prerequisites: Consent