# Mathematics Courses (MATH)

TO MEET ANY COURSE PREREQUISITE, GRADE OF C- OR HIGHER IS REQUIRED IN THE PREREQUISITE COURSE.

### Courses

**MATH 100. Intermediate Algebra — 3 hrs.**

Fundamental mathematical concepts; functions and graphs; solutions of equations; systems of equations and inequalities; matrices and determinants. Does not count toward minimum hours required for baccalaureate degree. (Fall)

**MATH 1000. Exploring Social Justice Issues through Mathematics — 3 hrs.**

Exploration of a number of social justice issues through the lens of mathematics. Students will explore, understand, and respond to local and global social justice issues using mathematical concepts and ideas including geometry, statistics, and algebra. (Spring)

**MATH 1100. Mathematics in Decision Making — 3 hrs.**

Selection of mathematical topics and their applications with an emphasis on mathematical reasoning. Topics include probability and statistics. (Fall, Spring, Summer)

**MATH 1110. Analysis for Business Students — 3 hrs.**

Analysis and interpretation of data using numerical, graphical, and functional viewpoints; linear and exponential functions; modeling data using functions. No credit for students with credit in MATH 1140 or MATH 1120. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)

**MATH 1120. Mathematics for Biological Sciences — 3 hrs.**

Proportional reasoning, linear functions and linear regression, exponential functions, and logarithmic functions with scientific applications. No credit for students with credit in MATH 1110 or MATH 1140. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)

**MATH 1130. Trigonometry — 2 hrs.**

Trigonometric functions, solution of triangles and applications of simple harmonic motion, polar coordinates, and vectors. No credit for students with credit in MATH 1140. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)

**MATH 1140. Precalculus — 4 hrs.**

Pre-calculus mathematics; equations and inequalities; logarithms, exponential and circular functions; analytic trigonometry, analytic geometry, mathematical induction; applications. Credit reduced to 1 hour for students with credit in MATH 1110 or MATH 1120, and to 2 hours for students with credit in MATH 1130. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)

**MATH 1150. Calculus for Technology — 4 hrs.**

Survey of analytic geometry and elementary calculus with emphasis on applications. May not be applied to Mathematics major or minor. Prerequisite(s): Satisfactory score on ALEKS exam. (Spring)

**MATH 1160. Calling Hogwash: Mathematics for Critical Thinking — 3 hrs.**

This course will discuss how mathematics, statistics, and "mathematics" are used to persuade people, and to spread hogwash with a veneer of scientific credibility. Example topics include uses and abuses of data visualization, choices in measures of center and spread, selective use of percentages, truncating axes, the relationship between correlation and causation, forms of bias, and abuses of Big Data. There will be discussions, videos, readings, and examples from current traditional and social media. There will be at least one project where students will apply these techniques to attempt to persuade their classmates of something important to them. (Fall)

**MATH 1204. Mathematical Reasoning — 3 hrs.**

Mathematics as problem solving, communication, connections, and reasoning. Includes whole numbers, rational number concepts, operations, and connections to algebraic thinking. (Fall and Spring)

**MATH 1310. Technology for Secondary Mathematics Teachers — 3 hrs.**

Introduction to technologies (calculators, spreadsheets, and dynamic geometric and statistical programs) used in mathematics classrooms (5-12). Activities to develop facility with the technologies while addressing mathematics and pedagogical implications. Prerequisite(s) or corequisite(s): MATH 1420. (Fall)

**MATH 1420. Calculus I — 4 hrs.**

Limits, differentiation, introduction to integration including the fundamental theorem of calculus. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)

**MATH 1421. Calculus II — 4 hrs.**

Integration techniques, sequences and series, applications. Prerequisite(s): C- or better in MATH 1420. (Fall and Spring)

**MATH 1900. Mathematical Problem Solving — 1 hr.**

Basic techniques used to solve challenging mathematics problems. Problems considered will come from a broad range of courses. Prepares students to take the William Lowell Putnam Examination and the Iowa Collegiate Mathematics Competition. May be repeated. (Fall and Spring)

**MATH 2204. Mathematical Reasoning for Elementary Teachers II — 3 hrs.**

Mathematics as problem solving, communication, connections, and reasoning. Includes data analysis, probability, and algebraic reasoning. Activities connected to elementary school mathematics. Designed for elementary education majors. Prerequisite(s): MATH 1204. (Fall and Spring)

**MATH 2303. Introduction to Teaching Secondary Mathematics — 3 hrs.**

Students will be introduced to National Council of Teachers of Mathematics Principles and Standards and research-based methods of teaching secondary mathematics while learning ways to teach proportional reasoning and rational numbers. A grade of C or better is required for MATH 3304. Prerequisite(s): admitted to Teacher Education. (Spring)

**MATH 2422. Calculus III — 4 hrs.**

The derivatives and integrals of multi-variable functions and their applications; Gauss', Green's, and Stokes' theorems. Prerequisite(s): for Mathematics majors and minors: C- or better in MATH 1421 and MATH 2500. Prerequisites for non-Mathematics majors and minors: C- or better in MATH 1421; MATH 2500 or consent of department. (Fall and Spring)

**MATH 2500. Linear Algebra for Applications — 3 hrs.**

Gaussian elimination; matrix algebra; vector spaces, kernels, and other subspaces; orthogonal projection; eigenvalues and eigenvectors. Prerequisite(s): MATH 1420. (Fall and Spring)

**MATH 2900. Discrete and Argumentative Mathematics — 3 hrs.**

Logical argument techniques. The writing process in a mathematical context. Theory of sets, functions, and relations. Elements of graph theory. Prerequisite(s): MATH 1420. (Fall)

**MATH 3203. Teaching Mathematics in the Elementary School — 3 hrs.**

Effective instructional models and strategies for teaching elementary school mathematics; involves selecting and designing mathematical tasks, creating an environment, and orchestrating discourse. Using and supplementing mathematics materials within a sound psychological framework for making instructional decisions. Prerequisite(s): MATH 3204; UNI and cumulative GPA of 2.50 or better; full admission to teacher education is required. (Fall, Spring, Summer)

**MATH 3204. Mathematical Reasoning for Elementary Teachers III — 3 hrs.**

Mathematics as problem solving, communication, connections, and reasoning. Includes geometry, measurement, and proportionality. Activities connected to elementary school mathematics. Designed for elementary education majors. Prerequisite(s): MATH 2204; UNI and cumulative GPA of 2.50 or better; junior standing or consent of department. (Fall and Spring)

**MATH 3211. Introduction to Algebraic Thinking for Elementary Teachers — 3 hrs.**

Investigation of problems involving patterns, variables, relations, functions, and their graphs. Exploration and representation of these problems using physical models and technology. Prerequisite(s): MATH 2204. (Fall and Spring)

**MATH 3212/5212. Introduction to Geometry and Measurement for Elementary Teachers — 3 hrs.**

Van Hiele levels of thinking. Investigation of two- and three-dimensional concepts, rigid transformations, symmetry, and spatial sense. Prerequisite(s): MATH 3204; junior standing. (Fall and Spring)

**MATH 3213/5213. Topics in Mathematics for Grades K-8 — 3 hrs.**

Investigation of number theory, extending ratio, proportion and probability with connections to rational numbers, algebra and geometry. Reasoning about topics in the context of the K-8 mathematics curriculum. Prerequisite(s): CS ED 1310; MATH 3204; junior standing. (Fall and Spring)

**MATH 3214/5214. Problem Solving in Mathematics for Elementary Teachers — 3 hrs.**

Strategies for constructing and communicating a mathematics problem-solving process. Analysis of resources and strategies to generate mathematics tasks and to create an effective problem-solving environment. Problem solving as a means of constructing mathematics knowledge. Prerequisite(s): MATH 3203; at least one of MATH 3211, MATH 3212/5212, MATH 3213/5213; junior standing. (Fall and Spring)

**MATH 3215. Mathematics for Elementary Students with Special Needs — 1 hr.**

Assessing, designing, and providing appropriate mathematical tasks for students with special needs. Prerequisite(s): MATH 3203 or MATH 3304; junior standing. Prerequisite(s) or corequisite(s): MATH 3214/5214. (Variable)

**MATH 3302. Field Experience in Teaching Secondary Mathematics — 1 hr.**

Field experience in which students are actively involved in preparing and teaching lessons in 6-12 mathematics classrooms. Teacher candidates will spend a minimum of 30 hours in math classrooms. In preparing, teaching and reflecting on their lessons, teacher candidates will be expected to draw on theory and research related to teaching and learning processes, motivation, and classroom management and to discuss these theory/practice connections in required written assignments. Offered on credit/no credit basis only. Prerequisite(s): TEACHING 3128; EDPSYCH 3148; MEASRES 3150; MATH 3600/5600; MATH 4500/5500. Corequisite(s): MATH 3304. (Fall)

**MATH 3304. The Teaching of Secondary Mathematics — 3 hrs.**

Mathematics teaching strategies for grades 5-12; roles of content and methods; addressing the needs of diverse learners in secondary mathematics classes; assessing teaching and learning of secondary mathematics. A grade of C or better is required to be eligible for student teaching. Prerequisite(s): TEACHING 3128; EDPSYCH 3148; MEASRES 3150; MATH 4500/5500; MATH 3610/5610 or MATH 3600/5600; a grade of C or better in MATH 2303. (Fall)

**MATH 3305. Connections: University Mathematics and the Secondary Curriculum — 3 hrs.**

Connections between the undergraduate mathematics major and the secondary mathematics curriculum. Consideration of modern algebra, modern geometry, probability and statistics, calculus and number theory in the context of the secondary mathematics curriculum. Prerequisite(s): 6 hours of 100/3000/4000-level courses in mathematics. Corequisite(s): EDPSYCH 3148; MEASRES 3150. Prerequisite(s) or corequisite(s): EDPSYCH 2030; TEACHING 2017; TEACHING 3128; MATH 2303. (Spring)

**MATH 3313. Topics in Secondary Mathematics — 3 hrs.**

Investigation of selected topics from algebra, geometry and data analysis. Reasoning about topics in the context of the secondary mathematics curriculum. Prerequisite(s): TEACHING 2017; EDPSYCH 2030. (Spring)

**MATH 3410/5410. Dynamical Systems: Chaos Theory and Fractals — 3 hrs.**

Historical background, including examples of dynamical systems; orbits, fixed points, and periodic points; one-dimensional and two-dimensional chaos; fractals: Julia sets, the Mandelbrot set, and fractal dimension; computer programs and dynamical systems. Prerequisite(s): MATH 1421; MATH 2500; junior standing. (Even Springs)

**MATH 3425/5425. Differential Equations — 3 hrs.**

Elementary theory and applications of first order differential equations; introduction to numerical techniques of solving differential equations; solutions of nth order linear differential equations with constant coefficients. Prerequisite(s): MATH 2422; MATH 2500; junior standing. (Odd Springs)

**MATH 3430/5430. Partial Differential Equations — 3 hrs.**

Study of applied partial differential equations using heat, wave, and potential equations as basis; Fourier series and integrals; Laplace transformations. Prerequisite(s): MATH 3425/5425; junior standing. (Even Springs)

**MATH 3440/5440. Numerical Analysis — 3 hrs.**

Theory and application of standard numerical techniques dealing with nonlinear equations, systems of linear equations, interpolation and approximation, numerical differentiation and integration. Prerequisite(s): MATH 1421; MATH 2500; CS 1130 or CS 1160 or CS 1510 or equivalent; junior standing. (Odd Falls)

**MATH 3530/5530. Combinatorics — 3 hrs.**

Various ways to enumerate elements of a set and graph theory. Appropriate for mathematics, mathematics education, computer science, and actuarial science students. Prerequisite(s): MATH 1420 or CS 1800; junior standing. (Fall and Spring)

**MATH 3600/5600. Euclidean Geometry — 3 hrs.**

Topics of plane geometry beyond a first course; compass and straightedge constructions, the nine-point circle, Ceva's and Menelaus' theorems, triangle centers, conics, and tessellations. Prerequisite(s): MATH 1420 or equivalent; junior standing. (Fall)

**MATH 3610/5610. Modern Geometries — 3 hrs.**

Euclid's postulates serve as a model for studying various axiomatic systems defining incidence geometries. Geometries include finite geometries, plane geometry, neutral geometry, taxicab geometry, spherical geometry, and hyperbolic geometry. Prerequisite(s): MATH 2900 or MATH 3600/5600; junior standing. (Even Springs)

**MATH 3630/5630. Differential Geometry — 3 hrs.**

Analytic study of curves and surfaces in three-dimensional Euclidean space. Prerequisite(s): MATH 2422; MATH 2500; junior standing. (Odd Springs)

**MATH 3640/5640. History of Mathematics — 3 hrs.**

Survey of mathematical activities of humankind in numeration and number systems, algebra, number theory, and calculus from pre-history through the present day. Motives, influences, and methods affecting development of these mathematical topics in Mesopotamian, Egyptian, Greek, Islamic, Indian, Chinese, Native American, and Western civilizations. Ethnomathematics as related to these topics. Prerequisite(s): junior standing. (Variable)

**MATH 3751. Probability and Statistics — 3 hrs.**

Descriptive statistics and graphical representations, basic concepts of probability and distributions, random variables, expectations, sampling theory, tests of statistical significance. Calculus is employed in developing and applying these ideas. Specific attention devoted to the use of technology in motivating and explaining concepts and techniques. No credit with credit in STAT 3770, credit reduced to 1 hour for students with credit in STAT 1772. Prerequisite(s): MATH 1421. (Same as STAT 3751) (Variable)

**MATH 3752/5752. Introduction to Probability — 3 hrs.**

Axioms of probability, sample spaces having equally likely outcomes, conditional probability and independence, random variables, expectation, moment generating functions, jointly distributed random variables, weak law of large numbers, central limit theorem. Prerequisite(s): MATH 1421; junior standing. (Same as STAT 3752/5752) (Fall and Spring)

**MATH 3780/5780. Mathematics of Finance — 3 hrs.**

Measurement of interest, annuities, yield rates, amortization and sinking funds, bonds, term structure of interest rates, interest rate sensitivity, stocks and derivatives, elements of risk management. Prerequisite(s): MATH 1420; junior standing. (Same as ACT SCI 3780/5780) (Spring)

**MATH 4198. Independent Study.**

(Variable)

**MATH 4420/5420. Advanced Calculus I — 3 hrs.**

Algebraic and topological structure of the reals; limits and continuity; theory of differentiability of functions of a single real variable. Prerequisite(s): MATH 2422; MATH 2500; MATH 2900 or consent of the instructor; junior standing. (Fall)

**MATH 4421/5421. Advanced Calculus II — 3 hrs.**

Riemann integration; sequences and series of functions; introduction to Lebesgue integration. Prerequisite(s): MATH 4420/5420; junior standing. (Spring)

**MATH 4460/5460. Introduction to Complex Analysis — 3 hrs.**

Algebraic and geometric structure of of complex number system; elementary functions and mappings; differentiation and integration of functions of a single complex variable; analytic and harmonic functions. Prerequisite(s): MATH 2422; junior standing. (Odd Springs)

**MATH 4500/5500. Modern Algebra I — 3 hrs.**

Basic properties of rings, integral domains, and fields. Polynomials over fields. Ideals and quotient rings. Introduction to groups. Prerequisite(s): MATH 2500; MATH 2900; junior standing. (Fall)

**MATH 4501/5501. Modern Algebra II — 3 hrs.**

Groups, homomorphisms, and quotient groups. Field extensions, straightedge and compass constructions. Additional topics from group theory and field theory. Prerequisite(s): MATH 4500/5500; junior standing. (Spring)

**MATH 4510/5510. Elementary Number Theory — 3 hrs.**

Topics from properties of integers, prime numbers, congruences, cryptography, Pythagorean triples, Diophantine equations, Fermat's last theorem, Fibonacci numbers, and the golden rectangle. Also, number theoretic connections to abstract algebra. Prerequisite(s): MATH 2900; junior standing. (Falls and Even Springs)

**MATH 4615/5615. Geometric Transformations — 3 hrs.**

Isometries of the plane in context of Klein's definition of a geometry as a group acting on a set of points. Rotations, reflections, and translations are used to study congruence, similarity, and symmetry and to solve problems that would otherwise be difficult using analytic geometry and calculus. Prerequisite(s): MATH 2500; MATH 3610/5610 or MATH 3600/5600; junior standing. (Fall)

**MATH 4641/5641. Topology I — 3 hrs.**

Introductory study of metric spaces, completeness, topological spaces, continuous functions, compactness, connectedness, separability, product, and quotient spaces. Prerequisite(s): MATH 2422; MATH 2500; junior standing. (Odd Springs)

**MATH 4900. Senior Mathematics Seminar — 1 hr.**

Researching and writing a paper exploring specific theme, topic, or problem in mathematics, culminating with oral presentation to the class. Prerequisite(s): senior mathematics major. (Fall and Spring)

**MATH 4990. Undergraduate Research in Mathematics — 3 hrs.**

Research on selected topic in mathematics with faculty supervision. Presentation of written paper at departmental seminar. Prerequisite(s): completion of the major core with minimum GPA of 3.00. (Fall and Spring)

**MATH 6201. Foundations of Mathematics Education — 3 hrs.**

Introduces current recommendations and policies regarding mathematics goals, content, frameworks, instructional strategies, and curricula. Investigates topics and documents with a focus on application and impact to classrooms. (Variable)

**MATH 6203. Contemporary Assessment in Mathematics Education I — 2 hrs.**

Study of strategies and practices for assessing students' thinking and performance. Multiple forms of quality assessment with an emphasis on formative assessment, aligning assessment to instruction, and interpreting evidence. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6204. Contemporary Mathematics Curricula — 2 hrs.**

Study and evaluation of innovative curriculum materials. Focus on application to classroom practice and planning for change for a selected topic. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6205. Teaching Rational Numbers and Proportionality — 3 hrs.**

Examination of literature, problems, and issues related to teaching fractions, decimals, ratios, proportion, and percent. Exploration of innovative strategies for developing concepts, skills, and proportional reasoning. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6207. Mathematics Literacy in an Information Age — 2 hrs.**

Examination of applications and contributions of mathematics to other disciplines, the workplace, personal lives, and society. Investigation of shifting conceptions of mathematics and mathematics literacy in today's world. Diverse uses of mathematics illustrated. Prerequisite(s): MATH 6201; MATH 6224; MATH 6226. (Variable)

**MATH 6208. Contemporary Assessment in Mathematics Education II — 1 hr.**

Focus on assessment design for classroom use and development of an assessment scheme. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6209. Mathematics Curriculum and Assessment — 3 hrs.**

In this course, students will explore various curricula and strategies and practices for assessing students' thinking and performance. Multiple curricula and forms of quality assessment will be considered, with an emphasis on formative assessment, aligning assessment to instruction, and interpreting evidence. (Even Falls)

**MATH 6210. Technology in Middle Grades Mathematics — 1 hr.**

Uses of technology in teaching and learning mathematics. Examination of research related to incorporating technology in the teaching of mathematics. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6212. Foundations of Algebraic Reasoning — 3 hrs.**

Examination of algebraic standards, content, instructional strategies and curricula. Focus on application and impact on classroom practice, planning, and assessment in algebra. Focus on change in one's teaching and curriculum. (Summer)

**MATH 6215. Foundations of Geometric Reasoning — 3 hrs.**

Examine geometric standards, content, methods and curricula. Analyze student thinking, examine van Hiele levels and expand conceptions of proof. Focus on impact on one's own practice, planning and assessment. (Variable)

**MATH 6216. Number and Operations — 3 hrs.**

Examination of literature, problems, and issues related to the teaching of number and operations, with emphasis on whole numbers, decimals, and fractions. Reasoning about topics in the context and pedagogy of the K-8 mathematics curriculum and exploration of innovative problem solving strategies. (Even Summers)

**MATH 6224. Mathematics for the Middle Grades Teachers I — 3 hrs.**

Integrated, historical, and cultural study of development and structure of quantity, data, and chance. Focus on mathematical ways of knowing and verification. (Variable)

**MATH 6225. Teaching and Learning Mathematics — 3 hrs.**

Exploration of instructional strategies to support mathematical learning of K-16 students with focus on your own practice. This includes establishing mathematical goals for learning, selecting appropriate tasks, facilitating classroom discourse, building conceptual understanding from procedural fluency, and using technology to enhance instruction. (Even Springs)

**MATH 6226. Mathematics for the Middle Grades Teacher II — 3 hrs.**

Integrated, historical, and cultural study of development and structure of patterns, functions, relationships, and shapes. Focus on ways of knowing and verification. Prerequisite(s): MATH 6224. (Variable)

**MATH 6227. Data Analysis, Probability, and Discrete Mathematical Reasoning — 3 hrs.**

In this course, students will explore data collection, display, and interpretation methods including measures of central tendency; theoretical and empirical probability of single- and multi-stage events; and apportionment, fair division, and counting. Concepts will be explored through and connected to best mathematical teaching practices. (Odd Falls)

**MATH 6230. Reflective Teaching-Cognitive Demand of Mathematical Tasks — 1 hr.**

Students will critically reflect on classroom practice with the focus on cognitive demand of mathematical tasks. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6231. Reflective Teaching-Classroom Discourse — 1 hr.**

Students will critically reflect on classroom practice with the focus on classroom discourse. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6232. Reflective Teaching: Meaningful Distributed Instruction — 1 hr.**

Students will critically reflect on classroom practice with the focus on meaningful distributed instruction. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6234. Reflective Teaching: Leadership — 1 hr.**

Students will critically reflect on classroom practice with the focus on leadership in mathematics education. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6235. Reflective Teaching: Investigation of Classroom Practice — 1 hr.**

Students will critically reflect on classroom practice with the focus on instruction. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6236. Equity and Mathematics Education — 3 hrs.**

Examines theories of race, gender, social class, and sexuality and how these theories play out in K-16 mathematics classrooms. Exploration of historical, political, and pedagogical issues within mathematics education. Includes history of treatment of minorities in mathematics education, teaching mathematics for social justice, culturally relevant mathematics pedagogy, and other pedagogies and theories related to teaching socioculturally diverse students. (Odd Springs)

**MATH 6299. Research.**

Prerequisite(s): consent of department. (Variable)

**MATH 6370. Applied Linear Statistical Methods — 3 hrs.**

Elements of experimental design. Statistical inferential processes, confidence intervals and hypothesis tests, for comparing means, medians and proportions from multiple groups. Prerequisite(s): STAT 1772, MATH 3751 or consent of instructor. (Fall and Spring)

**MATH 6371. Probability and Statistical Inference — 3 hrs.**

Discrete and continuous random variables, central limit theorem, regression, correlation, analysis of covariance and categorical data analysis. Multiple regression, ANOVA and categorical data analysis will provide students with tools to analyze real data sets. Prerequisite(s): STAT 1772 or MATH 3751 or consent of instructor. (Variable)

**MATH 6380. Mathematics at the Secondary Level — 1-3 hrs.**

History of secondary mathematics in the U.S. Overview of the most recent reform movement in mathematics education; its effect on the teaching and learning of high school mathematics. May be repeated on different topics for up to 3 hours of credit. Prerequisite(s): graduate standing in mathematics. (Variable)

**MATH 6381. Current Research in Mathematics Education — 3 hrs.**

Understand purposes and methods of research in mathematics education with a focus on action research. Review mathematics education research and its implications for instruction. Conduct a classroom-based action research project. Prerequisite(s): MATH 6201 or consent of department. (Variable)

**MATH 6410. Foundations of Calculus — 3 hrs.**

Fundamentals of Calculus from the viewpoint of exploring reasons for the details that support Differential and Integral Calculus. Emphases on examples and proving justifications for a variety of mathematical statements. (Variable)

**MATH 6420. Mathematical Analysis I — 3 hrs.**

Set theory; the real number system; Lebesque measure; Lebesque integral. Prerequisite(s): MATH 4420/5420. Corequisite(s): MATH 4421/5421 or consent of instructor. (Odd Springs)

**MATH 6421. Mathematical Analysis II — 3 hrs.**

Differentiation and integration; classical Banach spaces; metric spaces; general measure and integration theory. Prerequisite(s): MATH 6420. (Spring)

**MATH 6460. Complex Analysis I — 3 hrs.**

Analyticity; differentiation and integration of functions of one complex variable; power series, Laurent series; calculus of residues. Prerequisite(s): MATH 4420/5420; MATH 4460/5460; or consent of instructor. (Spring)

**MATH 6461. Complex Analysis II — 3 hrs.**

Analytic continuation; harmonic functions; entire functions; conformal mapping; selected applications. Prerequisite(s): MATH 6460. (Variable)

**MATH 6500. Abstract Algebra I — 3 hrs.**

Groups: quotient groups, isomorphism theorems, products of groups, group actions, Sylow theorems, solvable and nilpotent groups. Rings and fields: quotient rings, rings of polynomials, integral domains, fields of fractions. Prerequisite(s): MATH 4500/5500. Corequisite(s): MATH 4501/5501 or consent of instructor. (Fall)

**MATH 6501. Abstract Algebra II — 3 hrs.**

Rings: arithmetic properties, prime and maximal ideals, Noetherian rings. Modules and vector spaces: linear transformations, free modules, finitely generated modules over PIDs, canonical forms. Fields: field extensions, Galois theory, solvability by radicals. Prerequisite(s): MATH 6500. (Spring)

**MATH 6504. Advanced Linear Algebra — 3 hrs.**

Vector spaces, linear transformations, matrices, eigenvalues and eigenvectors, canonical forms, bilinear and quadratic forms. Prerequisite(s): MATH 2500 or consent of instructor. (Odd Summers)

**MATH 6510. Theory of Numbers — 3 hrs.**

Mathematical study of integers: induction, divisibility, prime numbers, congruences, quadratic reciprocity, multiplicative functions. (Variable)

**MATH 6530. Topics in Discrete Mathematics — 3 hrs.**

Topics from combinatorics, graph theory, analysis and application of algorithms, recurrence relations, difference equations, linear programming, and mathematical induction. Applications of these topics in the secondary curriculum. Prerequisite(s): MATH 3530/5530 or MATH 4500/5500. (Variable)

**MATH 6640. Topics in the History of Mathematics — 3 hrs.**

Topics from history of algebra, analysis, arithmetic, geometry, number theory, probability, and topology as they appear in the development of Mesopotamian, Greek, Islamic, Indian, Chinese, and Western civilizations. May be repeated on different topic with consent of instructor. Prerequisite(s): MATH 3640/5640. (Variable)

**MATH 6650. Topics in Mathematical Logic and Set Theory — 3 hrs.**

Topics from the predicate calculus and first-order mathematical theories; the Godel completeness and incompleteness theorems; algebraic and many-valued logic; Boolean algebras, lattices, representation theorems, and models in set theory and mathematical logic; independence of the axioms of set theory (including the axiom of choice and the continuum hypothesis). May be repeated on different topic with consent of instructor. (Variable)

**MATH 6670. Non-Euclidean Geometry — 3 hrs.**

Historical development of geometry models that do not assume Euclid's fifth postulate. Emphasis on Poincare's disc and upper half-plane models, distance and area in the hyperbolic plane, and Mobius transformations. Prerequisite(s): MATH 2500; MATH 4500/5500; MATH 3610/5610 or MATH 3600/5600. (Variable)

**MATH 6745. Deterministic Operations Research — 3 hrs.**

Overview of optimization models, mathematical programming (linear, integer, goal), optimization software LINGO, transportation and assignment problems, network models (shortest-path, maximum-flow), multi-period planning problems. Prerequisite(s): MATH 2422; MATH 2500. (Fall and Spring)

**MATH 6746. Probabilistic Operations Research — 3 hrs.**

Decision making under uncertainty, Markov chains, deterministic and probabilistic dynamic programming, inventory control, production scheduling, supply chain management, portfolio optimizations. Prerequisite(s): MATH 2422; MATH 2500, MATH 3752/5752. (Same as STAT 6746) (Fall and Spring)

**MATH 6747. Discrete-Event System Simulation — 3 hrs.**

Discrete-event systems simulation theory including input analysis, output analysis; applications of simulation software ARENA to studying performances of systems such as bank services, call centers, material-handling systems, and computer networks. Prerequisite(s): MATH 2422; STAT 1772. (Same as STAT 6747) (Fall and Spring)

**MATH 6748. Modeling Industrial Systems Using Queueing Networks — 3 hrs.**

Queueing networks, applications to modeling and evaluating industrial systems such as flexible manufacturing systems, pull-type production systems, polling systems in computer networks, handoff schemes in cellular mobile networks; computational package MATLAB. Prerequisite(s): MATH 2422; MATH 2500; MATH 3752/5752. (Same as STAT 6748) (Fall and Spring)

**MATH 6779. Topics in Probability and Statistics — 3 hrs.**

Topics from correlation and regression analysis, analysis of variance and co-variance, non-parametric methods, order statistics. May be repeated on different topic with consent of instructor. Prerequisite(s): consent of instructor. (Same as STAT 6779) (Variable)

**MATH 6795. Industrial Internship/Project — 6 hrs.**

Mathematical analysis of industrial problems. Features work on a project of interest to a cooperating company. Oral and written reports required on the project. Prerequisite(s): approval of graduate coordinator and admittance to the P.S.M. program. (Variable)

**MATH 6796. PSM Capstone Project — 3 hrs.**

Mathematical/statistical modeling and analysis of a problem arising in industrial applications. Oral and written reports required on the project. Prerequisite(s): Approval of PSM-Industrial Mathematics coordinator and admittance to the PSM program in Industrial Mathematics. Completion of at least 9 hours in the PSM-Industrial Mathematics program. (Variable)