#### MATHEMATICS MA

(With Broad Selection Emphasis,

Mathematics and Computer Science Emphasis, or

Community College Teaching Emphasis)

#### MATHEMATICS AND STATISTICS MS

#### MATHEMATICS EDUCATION MS

(DISCIPLINE-BASED)

*College of Science, Engineering, & Technology
Department of Mathematics and Statistics
273 Wissink Hall • 507-389-1453*

The Department of Mathematics and Statistics offers 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 computer science. The Master of Science programs allow students to specialize in secondary teaching, or mathematics and statistics.

Eighteen graduate faculty support the graduate programs. Faculty specialties include applied computational mathematics, ring theory, combinatorial matrix theory, stochastic differential equations and stochastic processes, partial differential equations and industrial mathematics, topology and dynamical systems, statistics, numerical analysis, probability, algebraic combinatorics and discrete mathematics, complex analysis, real analysis, geometry, optimization, and both elementary and secondary mathematics education.

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. In addition to completing the general admission requirement for the

College of Graduate Studies and Research, applicants with grade point averages below 2.75 may qualify by presenting GRE verbal, quantitative and analytical scores of 500 on any one part or a minimum composite of 1350.

Facilities. The Department of Mathematics and Statistics is housed in Wissink Hall. This building is also home to the Academic Computing Center which houses 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, 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 the library’s collection.

Financial Assistance. Approximately 15 graduate assistantships are available in the department each year. Graduate assistant duties include teaching or research assistantships.

**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.

**Major Common Core**:

At least half of the credits applied to the program must be earned in 600 level courses excluding credit for thesis or alternate plan paper. After completing 16 credits, the student must select an examining committee composed of three graduate faculty and form a plan of study. A student must give an oral defense of the thesis or alternate plan paper. A comprehensive examination covering the required common core is also required.

**Required Common Core: **(6-8 credits)

Two of the following four courses may be counted towards the degree. The other two courses will be regarded as deficiencies.

Math 517 Real Analysis I (3)

Math 547 Linear Algebra (3)

Math 570 Numerical Analysis I (4)

Math 555 Theory of Statistics I (4)

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

Select thesis or alternate plan paper.

MATH 694 Alternate Plan Paper 1

MATH 699 Thesis 1-4

**(Major Emphasis: Broad Selection)**

**Restricted Electives:** (7-8 credits)

Select two of the following courses.

Math 511 Introduction to Complex Variables (4)

Math 518 Real Analysis II (3)

Math 522 Partial Differential Equations (4)

Math 525 Mathematical Modeling (4)

Math 535 Modern Geometry (4)

Math 546 Abstract Algebra II (4)

Math 542 Theory of Numbers (4)

Math 595 Selected Topics (4)

Math 596 Mathematical Logic (3)

**Unrestricted Electives:** (15-20 credits)

Select 500/600 level courses in mathematics or statistics approved by advisor.

Math 511-698 Excluding 517, 547, 555, 570, 694

Stat 550-698 Excluding 555, 694

**(Major Emphasis: Mathematics & Computer Science)**

**Unrestricted Electives:** (9-15 credits)

Select 500/600 level courses in mathematics or statistics approved by advisor.

Math 511-698 Excluding 517, 547, 555, 570, 694

Stat 550-698 Excluding 555, 694

**Computer Science Electives:** (12-14 credits):

Select 500/600 level courses in computer science approved by advisor.

CS 500-662

**(Major Emphasis: Community College Teaching)**

**Restricted Electives:** (7-8 credits)

Select two of the following courses.

Math 511 Introduction to Complex Variables (4)

Math 522 Partial Differential Equations (4)

Math 525 Mathematical Modeling (4)

Math 546 Abstract Algebra II (4)

Math 571 Numerical Analysis II (4)

Math 580 History of Mathematics (3)

Math 595 Selected Topics (4)

**Unrestricted Electives:** (15-21 credits)

Select 12-17 credits of 500/600 level courses in mathematics or statistics approved by advisor, and 3-4 credits of education courses related to higher education approved by advisor.

MATH 511-698 Excluding 517, 547, 555, 570, 694

STAT 550-698 Excluding 555, 694

__Mathematics and Statistics MS Program__

Thesis Plan - 34 credits

Alternate Plan Paper - 34 credits

**Major Common Core**

At least half of the credits applied to the program must be earned in 600 level courses excluding credit for thesis or alternate plan paper. After completing 16 credits, the student must select an examining committee composed of three graduate faculty and form a plan of study. A student must give an oral defense of the thesis or alternate plan paper. A comprehensive examination covering the required common core is also required.

**Required Common Core: **(11-12 credits)

Stat 555 and 556 plus one of the other three courses can be counted towards the degree. The other two courses will be regarded as deficiencies.

Math 517 Real Analysis I (3)

Math 547 Linear Algebra (3)

Math 570 Numerical Analysis I (4)

Stat 555 Theory of Statistics I (4)

Stat 556 Theory of Statistics II (4)

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

Select thesis or alternate plan paper.

Math 694 Alternate Plan Paper (1)

Math 699 Thesis (3)

**Major Restricted Electives:**

Select one of the following two courses.

Stat 550 Regression Analysis (3)

Stat 551 Experimental Design (3)

**Major Unrestricted Electives:** (16-19 credits)

Select 500/600 level courses in mathematics or statistics approved by advisor.

Math 511-698 Excluding 517, 547, 555, 556, 570, 694

Stat 550-698 Excluding 555, 556, 694

**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 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

**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.

**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

**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

**MATH 535 (4) Modern Geometry**

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

Prerequisite: MATH 332 or Con

**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

**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

**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

**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

**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

**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

**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 596 (3) Mathematical Logic**

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

Prerequisite: MATH 345 and PHIL 411

**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 608 (1-4) Seminar in Elementary Mathematics**

An opportunity for a group of elementary teachers to study a mutual problem in mathematics.

**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 (2) Numerical Analysis of Differential Equations **

This course is an in-depth study of solving ordinary differential equations numerically. Both Runge-Kutta methods and general multi-step methods are discussed. Error control and step size changing for both stiff and nonstiff equations are analyzed.

Prerequisite: MATH 315 and 470

**MATH 674 (2) 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) 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 regression, correlation, analysis of variance and covariance.

Prerequisite: MATH/STAT 354 or 455 or con

**STAT 551 (3) Experimental Designs**

Completely randomized, randomized block, fractional factorial, incomplete block, split-plot, Latin squares, expected mean squares, response surfaces, confounding, fixed effects, and random effects models.

Prerequisite: MATH/STAT 354 or 455 or con

**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

**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**

**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

**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

**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

**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 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 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) 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**

Prerequisite: con

**STAT 699 (1-4) Thesis**

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