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Minnesota State University, Mankato
Minnesota State University, Mankato

Mathematics

Page address: https://grad.mnsu.edu/programs/bulletin/mathematics.html

MATHEMATICS MA

(With Broad Selection Emphasis,
Mathematics and Computer Science Emphasis, or
Community College Teaching Emphasis)

MATHEMATICS AND STATISTICS MS

APPLIED STATISTICS MS

MATHEMATICS EDUCATION MS

(Discipline-Based)

College of Science, Engineering, & Technology
Department of Mathematics and Statistics273

Wissink Hall • 507-389-1453
http://cset.mnsu.edu/mathstat/

The Department of Mathematics and Statistics offers four programs leading to a master’s degree in Mathematics and Statistics. The Master of Arts programs allow students to study pure mathematics, mathematics for community college teaching, or mathematics and information technology. The Master of Science programs allow students to specialize in secondary teaching, or mathematics and statistics.
Nineteen graduate faculty members support the graduate programs. Faculty specialties include algebraic combinatorics, applied computational mathematics, combinatorial matrix theory, complex analysis, discrete mathematics, dynamical systems, elementary and secondary mathematics education, differential geometry, industrial mathematics, mathematical biology, numerical analysis, optimization, partial differential equations, probability, real analysis, ring theory, statistics, stochastic differential equations, stochastic processes, and topology.
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. Others have gone on to obtain a Ph.D. in mathematics or statistics

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.

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.

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 MA Program

Thesis Plan - 34 credits
Alternate Plan Paper - 34 credits

The Master of Arts program allows students to choose a course of studies devoted to one of three different emphases: a broad selection of courses in mathematics, a sequence of courses in both mathematics and computer science, or preparation for community college teaching.

Common Core
(0-15) credits
MATH 517 Real Analysis I 4
MATH 547 Linear Algebra II 3
MATH 555 Theory of Statistics I 4
MATH 570 Numerical Analysis I 4


A Common Core course requirement is waived if credit has been received for an equivalent course with grade of C (2.0) or better at the undergraduate or graduate levels. All Common Core courses, or their equivalents, must be completed before graduation. College of Graduate Study and Research Transfer policy applies.
Emphasis:Broad Selection

A minimum of 15 credits of 600 level courses in mathematics. Advisor approval is required.
Emphasis:Information Technology
A minimum of 6 credits of 600 level courses from mathematics, and a minimum of 9 credits 500/600 level courses from Information Technology (IT). Advisor approval is required.
Emphasis:Community College Teaching
A minimum of 9 credits of 600 level mathematics. Advisor approval required. Choose 6 credits from the course list below.
KSP 676 Adult Development and Learning 3
KSP 680 Developing the Online Learning Environment 3


Math 678 Curriculum Design, Assessment and Evaluation (3) may substitute for KSP 676
Other Graduation Requirements
Thesis or Alternate Plan Paper: (1- 4 credits) MATH 694 Alternate Plan Paper (1-2) or MATH 699 Thesis (1-4)) Comprehensive Exam: The Exam covers courses in the Common Core.

 

Mathematics and Statistics MS Program

Thesis Plan - 34 credits
Alternate Plan Paper - 34 credits

Common Core
(0-16) credits
MATH 517 Real Analysis I 4
MATH 547 Linear Algebra II 3
MATH 570 Numerical Analysis I 4
STAT 550 Regression Analysis 3
STAT 555 Theory of Statistics I 4
STAT 556 Theory of Statistics II 4


A Common Core requirement is waived if credit has been received for an equivalent course with grade of C or better at the undergraduate or graduate levels. Up to, and including, 16 credit hours of Common Core courses taken at the graduate level can be applied to a student’s program. All Common Core courses, or their equivalents, must be completed before graduation. College of Graduate Study and Research Transfer policy applies.
Unrestricted Electives
A minimum of 6 credits of 600 level Mathematics and a minimum of 6 credits of 600 level statistics. Advisor approval is required.
Other Graduation Requirements
Thesis or Alternate Plan Paper: (1-4 credits) Math 694 Alternate Plan Paper (1-2) Math 699 Thesis (1-4) Comprehensive Exam: Four courses, two chosen from MATH 517, MATH 547 and MATH 570, and two chosen from STAT 550, STAT 555, STAT 556. Advisor approval is required.

  

Applied Statistics MS Program

(34 credits)

The graduate program in Applied Statistics is designed to prepare students to join twenty-first century business and industry in their growing needs for statistical analyses. An optimal mix of mathematical and computational background also enables the graduates to contribute effectively in the educational institutions.       

 A Common Core course is waived if credit has been received for an equivalent course with grade of C or better at the undergraduate or graduate levels. All Required Common Core courses, or their equivalents, must be completed before graduation. College of Graduate Study and Research Transfer policy applies.                                                                                                 

Common Core
STAT 550 Regression Analysis 3    
STAT 555 Theory of Statistics I 4    
STAT 556 Theory of Statistics II 4    

Restricted Electives
Applied Statistics Requirement
Choose 6-18 credit(s):
 
STAT 551 Experimental Designs 3    
STAT 557 *Sample Survey, Design and Analysis 3    
STAT 558 *Categorical Data Analysis 3    
STAT 559 *Nonparametric Methods 3    
STAT 653 Linear Models 3    
STAT 654 Statistical Methods in Biostatistics and Survival Analysis 3    
Applied Math Requirement
Choose 3-6 credit(s):
Select at least one of the following:
 
MATH 620 Applied Mathematics 3    
MATH 628 *Numerical Optimization 3    
Thesis or Alternate Plan Paper
Choose 1-3 credit(s):
Select either thesis or APP
 
STAT 694 Alternate Plan Paper 1    
STAT 699 Thesis 1-4    
Unrestricted Electives
Choose (0-12) credits of 500/600 level mathematics or statistics. Advisor approval required.
Other Graduation Requirements
Comprehensive Exam: Four courses chosen from STAT 555, STAT 556, STAT 550, STAT 551, MATH 570, MATH 547, or MATH 517. Advisor approval is required.

 

Mathematics Education MS Program

Thesis Plan - 34 credits
Alternate Plan Paper - 34 credits

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 listed in this bulletin.

At least half of the credits applied to a program must be earned in 600-level courses excluding thesis or Alternate Plan Paper credits. After completing 16 credits the student must select a three-member examining committee and form a program of study. 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.

Required Core: (18 credits)

  • Math 517 Real Analysis I (3)
  • Math 641 Abstract Algebra (3)
  • Math 661 Mathematical Problem Solving and Modeling for Teachers (3)
  • Math 662 Algebraic Structures in School Mathematics (3)
  • Math 663 Geometric Structures in School Mathematics (3)
  • Math 690 Research in Mathematics Education (3)

Required Professional Education Courses: (6 credits)
Any 500/600 level Professional Education courses that must be approved by the student's advisor.

Unrestricted Electives: (7-9 credits)
Any 500/600 level courses must be approved by student's advisor in order to fulfill the total required hours

Required Thesis or Alternate Plan Paper: (1-3 credits)

  • Math 694 Alternate Plan Paper (1)
  • Math 699 Thesis (3)

 

Course Descriptions

MATH 502 (4) Introduction to Topology 

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.

Prereq:  MATH 290 with grade of "C" (2.0) or higher, or instructor consent. 

MATH 511 (4) Introduction to Complex Variables

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

Prerequisite: MATH 223 and 290

(S) Odd years

MATH 517 (4) Real Analysis I

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.

F

MATH 518 (3) Real Analysis II

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.

MATH 522 (4) Partial Differential Equations

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

Prerequisite: MATH 223 and 321

(S) Even years

MATH 525 (4) Mathematical Modeling

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

Prerequisite: MATH 223 and 247

(S) Odd years

MATH 528 (3) Linear Optimization Methods  

Propositional logic, first and second order logic, completeness, consistency, models of theories, and Godel's Incompleteness theorem. 

MATH 535 (4) Modern Geometry

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

Prerequisite: MATH 332 or Con

(F, S, Summer) On demand

MATH 542 (4) Theory of Numbers

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

Prerequisite: MATH 345

MATH 546 (4) Abstract Algebra II

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

Prerequisite: MATH 345

(F, S, Summer) On demand

MATH 547 (3) Linear Algebra II

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

Prerequisite: MATH 345 or Con

S

MATH 555 (4) Theory of Statistics I

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

Prerequisite: MATH 223

F

MATH 556 (4) Theory of Statistics II

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.

Prerequisite: MATH/STAT 555

S

MATH 560 (3) Actuarial Applications in Probability

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

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

F (S, Summer on demand)

MATH 561 (4) Mathematical Theory of Interest

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.

(F, S, Summer) On demand

MATH 570 (4) Numerical Analysis I

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.

Prerequisite: MATH 122, 247

F

MATH 571 (4) Numerical Analysis II

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.

Prerequisite: MATH 470 and 223

MATH 580 (3) History of Mathematics

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.

Prerequisite: MATH 345

(S) Odd years

MATH 583 (3) Viewpoint of 5-8 School Mathematics

MATH 584 (3) Technology in 5-12 School Mathematics

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

Prerequisite: MATH 345 and CI 447

MATH 588 (1-3) Seminar

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.

MATH 590 (1-4) Workshop

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

MATH 591 (1-4) In-Service

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

MATH 595 (1-4) Selected Topics

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

MATH 598 (1-12) Internship

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

MATH 605 (3) Graphs and Algorithms

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

Prerequisite: MATH 417, 375, and 447

MATH 606 (3) Topics in Discrete Mathematics

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

Prerequisite: MATH 375 and 447

MATH 611 (3) Real Analysis

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

Prerequisite: MATH 417

MATH 613 (3) Topics in Analysis

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

Prerequisite: MATH 417, or Con

MATH 618 (3) Functional Analysis

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

Prerequisite: MATH 417 and 447

MATH 620 (3) Applied Mathematics

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.

Prerequisite: MATH 321, 417, and 447

MATH 621 (3) Topics in Applied Mathematics

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

Prerequisite: MATH 417, 422, and 447

MATH 625 (3) Complex Variables

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

Prerequisite: MATH 417

MATH 628 (3) Numerical Optimization

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, MATH 547 (Multivariate Real Analysis, Linear Algebra, and Familiarity with Basic Optimization Theory), or consent of the instructor.

MATH 635 (3) Topics in Geometry

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

Prerequisite: Con

MATH 641 (3) Abstract Algebra

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.

Prerequisite: MATH 345

MATH 645 (3) Topics in Algebra

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.

Prerequisite: MATH 641 or equivalent

MATH 661 (3) Mathematical Problem Solving & Modeling for Teachers

Heuristics in mathematical problem solving and mathematical modeling for teachers.

MATH 662 (3) Algebraic Structures in School Mathematics

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.

Prerequisite: MATH 345, or Con

MATH 663 (3) Geometric Structures in School Mathematics

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.

Prerequisite: MATH 332

MATH 672 (3) Numerical Analysis of Differential Equations

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.

Prerequisite: MATH 321 and 470

MATH 674 (3) Computations in Linear Algebra

This course will be an in-depth study of solving linear systems both directly and iteratively and solving the algebraic eigenvalue problem. Applications may also be included.

Prerequisite: MATH 447 and 470

MATH 677 (1-4) Individual Study

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

Prerequisite: con

MATH 680 (1-4) Topics in Mathematics

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

Prerequisite: will vary with topic

MATH 689 (1-3) Readings in Mathematics

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

Prerequisite: con

MATH 690 (3) Research in Mathematics Education

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.

Prerequisite: STAT 550 or 551 or con

MATH 691 (1-4) In-Service

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

MATH 692 (3) Topology

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

Prerequisite: MATH 417

MATH 693 (3) Topics in Topology

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.

Prerequisite: MATH 692

MATH 694 (1-2) Alternate Plan Paper

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

Prerequisite: con of advisor

MATH 695 (1-4) Workshop

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

MATH 698 (1-12) Internship

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

Prerequisite: con

MATH 699 (1-4) Thesis

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

Prerequisite: con of advisor

Statistics

STAT 550 (3) Regression Analysis

Simple and multiple linear regression, model adequacy checking and validation, identification of outliers, leverage and influence, polynomial regression, variable selection and model building strategies, nonlinear regression, and generalized linear regression.

Prerequisite: MATH/STAT 354 or 455 or con; Spring

STAT 551 (3) Design and Analysis of Experiments

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.

Prerequisite: MATH/STAT 354 or 455 or con; Fall

STAT 555 (4) Theory of Statistics I

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.

Prerequisite: MATH 223

F

STAT 556 (4) Theory of Statistics II

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.

Prerequisite: MATH/STAT 455

S

STAT 557 (3) Sample Survey, Design and Analysis

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

prereq. MATH 354 or STAT 354 or STAT 154

(F) Even years

STAT 558 (3) Categorical Data Analysis

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.

prereq. MATH 354 or STAT 354 or STAT 154; Fall: odd years

STAT 559 (3) Nonparametric Methods

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.

prereq. MATH 354 or STAT 354 or STAT 154; Spring: even years

STAT 588 (1-3) Seminar

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

STAT 591 (1-4) In-Service

STAT 598 (1-12) Internship

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

STAT 650 (3) Time Series Analysis and Forecasting

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. (F,S)

STAT 653 (3) Linear Models

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

Prerequisite: MATH/STAT 455 or con

STAT 654 (3) Statistical Methods in Biostatistics and Survival Analysis

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.

Prerequisite: STAT 354 or MATH 354

STAT 677 (1-4) Individual Study

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

Prerequisite: con

STAT 680 (1-4) Selected Topics

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

Prerequisite: will vary with topic

STAT 694 (1-2) Alternate Plan Paper

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

Prerequisite: con of advisor

STAT 696 (3) Statistical Computing

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

Prerequisite: one statistics course

STAT 698 (1-12) Internship

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

Prerequisite: con

STAT 699 (1-4) Thesis

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