## Mathematics (MTH) courses

### MTH 101 Intermediate Algebra A

This course is recommended for students who have not mastered algebra concepts needed for college algebra. Topics will include linear and quadratic equations, absolute value equations and inequalities, linear and nonlinear inequalities, properties of exponents, rectangular coordinate systems, lines, circles, parabolas, systems of equations, polynomials and rational expressions, and functions. Cannot receive credit toward graduation for both MTH 101 and MTH 103. Cannot count toward a mathematics major or minor. A grade of "C" or better is required in this course in order to take MTH 130, MTH 135, or MTH 138. Cannot be taken Pass/Not Pass.

### MTH 103 Intermediate Algebra

Prerequisite: appropriate placement score.This course is recommended for students who have not mastered algebra concepts needed for college algebra. Topics will include linear and quadratic equations, absolute value equations and inequalities, linear and nonlinear inequalities, properties of exponents, rectangular coordinate systems, lines, circles, parabolas, systems of equations, polynomials and rational expressions, and functions. Cannot receive credit toward graduation for both the MTH 101-102 sequence and MTH 103. Cannot count toward a mathematics major or minor. A grade of "C" or better is required in this course in order to take MTH 130, MTH 135, or MTH 138. Cannot be taken Pass/Not Pass.

### MTH 107 Contemporary Mathematics Corequisite

Prerequisite: concurrent enrollment in MTH 130.The primary objective of the corequisite course is to support student success in MTH 130. Strategies for success and mathematical skills will be emphasized to reinforce the content of MTH 130. Lab activities will solidify understanding of problem solving, geometry, probability, statistics, and personal finance. Cannot be taken Pass/Not Pass.

### MTH 121 Multicultural Views of History and Mathematics

This course explores the impact of major historical events, the mores of various societies, and basic human nature on the development of mathematical knowledge. Parallels will be drawn to events in today's world to determine how each individual can foster the global advancement of knowledge. The level of mathematical and historical knowledge expected on incoming students does not exceed the level of traditional high school courses.

### MTH 130 Contemporary Mathematics

Prerequisite: "C" grade or better in MTH 101 or MTH 103, or approved score on a departmental placement test; Corequisite: Students who do not meet the prerequisite yet have a Math ACT of 19, 20 or 21 (SAT 450 to 509), or a D grade in MTH 101 or MTH 103, or an approved score on the departmental placement exam may enroll in MTH 130 concurrently with MTH 107.General Education Course (Focus on Quantitative Literacy).This is a problem solving and applications of mathematics course. Topics to be studied will include, but not limited to: the art of problem solving, geometry, probability, statistics, and mathematics of finance. Cannot count toward a mathematics major or minor. Cannot be taken Pass/Not Pass. MTH 130 does not meet the prerequisite for MTH 135.

### MTH 134 Algebraic Reasoning and Modeling

Prerequisite: Suitable score on the mathematics placement exam or a grade of C or better in MTH 101 or MTH 103.General Education Course (Focus on Quantitative Literacy).This course focuses on developing and applying concepts of algebra and statistics to real world data and problems. Reasoning skills will be developed as students analyze data sets with descriptive statistics and by creating and analyzing algebraic models to describe the data. The algebraic functions that will be used in modeling include linear, power, exponential and logarithmic. Technology options will be utilized in the analysis of data. Cannot count toward the mathematics major or minor. Cannot be taken Pass/Not Pass.

### MTH 136 Precalculus 1

Prerequisite: Suitable placement score on the mathematics placement exam or a grade of "C" or better in MTH 101 or 103.General Education Course (Focus on Quantitative Literacy).This course is part one of a two course sequence with emphasis on the analytic, graphical, and numerical representations of functions. The focus of the course is on the library of algebraic functions (polynomial, rational, exponential, and logarithmic functions) along with higher algebraic reasoning in preparation for the study of Calculus (MTH 261). Grade of "C" or better required to enroll in MTH 137 or MTH 287. Cannot receive credit for both MTH 136 and MTH 138, or for both MTH 135 and MTH 136. Cannot count toward the mathematics major or minor. Cannot be taken Pass/Not Pass.

### MTH 137 Precalculus 2

Prerequisite: "C" grade or better in MTH 136 or suitable score on the Mathematics placement exam.General Education Course (Focus on quantitative Literacy).This course is part two of a two course sequence with emphasis on the analytic, graphical, and numerical representations of functions. The focus of the course is on the library of trigonometric functions along with higher algebraic and geometric reasoning in preparation for the study of Calculus (MTH 261). Grade of "C" or better required to enroll in MTH 261. Cannot receive credit for both MTH 137 and MTH 138. Cannot count toward the mathematics major or minor. Cannot be taken Pass/Not Pass.

### MTH 138 Pre-Calculus Mathematics

Prerequisite: "C" grade or better in MTH 101 or MTH 103 (Recommended: "B" grade or better in MTH 101 or MTH 103), or appropriate score on the mathematics placement exam.General Education Course (Focus on Quantitative Literacy).The course has emphasis on the analytic, graphical, and numerical representations of functions. The focus is on the library of algebraic functions (polynomial, rational, exponential, and logarithmic functions), the library of trigonometric functions, and a high level of algebraic and geometric reasoning in preparation for the study of Calculus (MTH 261). A grade of "C" or better required to enroll in MTH 261 or MTH 287. Cannot receive credit for both MTH 136 and MTH 138 or for both MTH 137 and MTH 138. Cannot count toward the mathematics major or minor. Cannot be taken Pass/Not Pass.

### MTH 261 Analytic Geometry and Calculus I

Prerequisite: "C" grade or better in MTH 137 or MTH 138 or appropriate placement score.General Education Course (Focus on Quantitative Literacy).Analytic geometry of the plane, limits, continuity, differentiation with applications, introductory integration with applications. A grade of "C" or better is required in this course in order to take MTH 280 or 288. Cannot be taken Pass/Not Pass.

### MTH 280 Analytic Geometry and Calculus II

Prerequisite: "C" or better in MTH 261.Applications of integration, integration techniques, indeterminate forms, improper integrals, sequences, series, conic sections, parametrization, polar coordinates. Cannot be taken Pass/Not Pass.

### MTH 287 Computational Calculus with Analytic Geometry I

Prerequisite: "C" or better in MTH 136 or MTH 138, or an approved score on a department placement test.General Education Course (Focus on Quantitative Literacy).Introduction to the concepts and methods of analytic geometry and differential and integral calculus with emphasis on applications in the natural sciences and technology. Cannot receive credit toward graduation for both MTH 287 and MTH 261. A grade of "C" or better is required in this course in order to take MTH 288. Cannot be taken Pass/Not Pass.

### MTH 288 Computational Calculus II

Prerequisite: "C" grade or better in MTH 261 or MTH 287.Continuation of MTH 287. Cannot receive credit toward graduation for both MTH 288 and MTH 280. Cannot be taken Pass/Not Pass.

### MTH 299 Introductory Topics in Mathematics

Variable content course with topics that can change from semester to semester. Topics will be identified by title in the schedule of classes. The course may be repeated if a different topic is offered. Cannot count toward a mathematics major or minor or General Education requirement.

### MTH 300 Service Learning in Mathematics

Prerequisite: 30 hours and concurrent registration in a Mathematics course designated as a service learning offering.This service component for an existing course incorporates community service with classroom instruction in mathematics to provide an integrative learning experience that addresses the practice of citizenship and promotes an awareness of and participation in public affairs. Includes 40 hours of service that benefits an external community organization, agency, or public service provider. Approved service placements and assignments will vary depending on the course topic and learning objectives; a list of approved placements and assignments is available from the instructor and the Citizenship and Service Learning Office. May be repeated.

### MTH 302 Multivariate Calculus

Prerequisite: MTH 280.Vector algebra and calculus, solid analytic geometry, partial differentiation, multiple integration, vector fields.

### MTH 303 Differential Equations

Prerequisite: MTH 280.Ordinary differential equations; their solutions and applications. Introduction to operators and the Laplace transformation.

### MTH 314 Discrete Mathematics

Prerequisite: MTH 137 or MTH 138 or approved calculus course or appropriate placement score.Topics include: logic, mathematical reasoning, basic counting, discrete probability, matrices, recursion, sets and relations, graphs and trees.

### MTH 315 Algebraic Structures

Prerequisite: MTH 261.Sets, logic, quantifiers, functions, relations, matrices, elementary number theory, induction, recursion, combinatorics, with emphasis on reading and writing proofs and the development of mathematical maturity.

### MTH 320 Foundations of Mathematics for Teachers

Prerequisite: completion of General Education mathematics requirement with grade of "C" or better; MTH 130 recommended.This course centers around the structure and properties of the real number system and its subsets. Numeration systems, patterns of numbers, models and algorithms for operations, number theory, probability, and statistics will be studied. Problem solving and communication are continuing themes of this course. Manipulatives (including Base-10 Blocks, Cuisenaire Rods, Number Cubes, and Colored Counters), calculators, and computer software (including a statistical package, spreadsheet and word processor) are used extensively as tools to develop mathematical concepts. Cannot be used as a mathematics elective for the mathematics major or minor.

### MTH 333 Linear Algebra

Prerequisite: MTH 280.Systems of linear equations, matrices and matrix algebra, determinants, vector spaces, linear independence, inner product spaces, linear transformations, eigenvectors, diagonalization, various applications and computational aspects.

### MTH 340 Statistical Methods

Prerequisite: completion of General Education mathematics requirement or appropriate placement score.Statistics, elementary probability, estimation and tests of simple hypotheses involving both large and small sample methods, linear correlation. Cannot count toward mathematics major or minor. Cannot receive credit toward a degree for more than one of the following courses: AGR 330, IPE 381, MTH 340, PSY 200, QBA 237, REC 328, SOC 302.

### MTH 343 Foundations of Probability and Statistics for Teachers

Prerequisite: "C" or better in MTH 261 or "C" or better in MTH 320.This course includes the collection, display, analysis, and misuse of data. The course is designed to provide preservice teachers with the content and pedagogical tools to effectively teach statistics in a middle school/high school setting. Topics include graphical representations and measures of analysis of univariate data (e.g., mean, MAD, standard deviation, five-number summary) and bivariate data (e.g., two-way tables, independence, correlation, regression). Counting techniques, including permutations and combinations, and elementary probability will also be covered. An informal introduction to inferential statistics topics (e.g. sampling distributions, confidence intervals, and tests of significance) will also be discussed. Problem-solving and communication skills are continuing themes. This is an activity-based course with extensive use of manipulatives, models, and technology (e.g. GeoGebra and CODAP) that have application within middle/secondary mathematics classrooms.

### MTH 345 Statistics for Scientists and Engineers

Prerequisite: MTH 280 or MTH 288.Topics include events, probability, random variables, discrete and continuous density functions, expectations, sampling distributions, central limit theorem, estimation, confidence intervals, tests or hypotheses. Computer statistical packages will be used for simulation study and data analysis.

### MTH 360 Foundations of Geometry for Teachers

Prerequisite: "C" or better in MTH 320.This course includes the study of synthetic, analytic, vector and transformational geometries through properties of geometric figures, measurement, construction, conjecture and proof, and tessellations. Problem solving and communication are continuing themes of this course. Manipulatives (including MIRA, Geoboard, Tangrams, Attribute Blocks and compass), calculators, and computer software (including Logo, Geometer's Sketchpad and a word processor) are used extensively as tools to develop geometric concepts. Cannot be used as a mathematics elective for the mathematics major or minor.

### MTH 377 Mathematical Processes

Prerequisite: MTH 135 or MTH 138; and MTH 340 or MTH 343.This course examines both finite and infinite mathematical processes used when solving problems involving discrete or continuous data. As an activity-base and laboratory-centered course, these processes are to be explored in the context of real-world applications. Communication of mathematical concepts and solutions to problems using technology, as well as paper and pencil procedures, is a continuing theme. This course is for the middle school education major who chooses mathematics as an area of subject matter concentration and elementary education majors with an emphasis area in mathematics. The course connects experiences from the concepts of numbers, algebra, geometry, and data analysis to those of the calculus. This course cannot be used as a mathematics elective for the mathematics major or minor.

### MTH 409 Teaching and Learning of Mathematics I

Prerequisite: SEC 302 and 15 hours of college mathematics, and admission to the Teacher Education Program.Develops foundation for reflective decision-making when teaching algebra to emphasize problem solving, communication, reasoning and proof, connections, and representations. The incorporation of appropriate classroom technology will be stressed. Credited only on the BSEd (Middle School/Secondary). A grade of "C" or better is required in this course in order to take MTH 493. Cannot be taken Pass/Not Pass. Cannot count toward the major GPA.

### MTH 410 Teaching and Learning of Mathematics II, with Practicum

Prerequisite: MTH 409, and admission to the Teacher Education Program.Focus on developing the reflective decisionmaker's appropriate use of current technologies, classroom management techniques and assessment processes in teaching geometry. Some attention devoted to advanced algebra, trigonometry, discrete mathematics and calculus topics. All students will complete a field experience in a mathematics classroom. Credited only on the BSEd (Secondary). A grade of "C" or better is required in this course in order to take MTH 493. Cannot be taken Pass/Not Pass. Cannot count toward the major GPA.

### MTH 411 Teaching and Learning of Mathematics III

Prerequisite: MTH 409; and admission to the Teacher Education Program; and concurrent enrollment in MTH 410 is required.Focus will be on knowledge of students and the learning environment, designing instruction for student learning, and implementing and analyzing instruction to promote student learning. Credited only on the BSEd (secondary). A grade of "C" or better is required in this course to take MTH 493. Cannot be taken Pass/Not Pass. Will not count toward the major GPA.

### MTH 421 Numerical Analysis I

Prerequisite: MTH 280.Recommended Prerequisite: CSC 125 or CSC 130. Solution of systems of linear and nonlinear equations, interpolation, integration, approximation, matrix computations. Problem solution will include the use of software. Identical with CSC 421. Cannot receive credit for both MTH 421 and CSC 421.

### MTH 422 Numerical Analysis II

Prerequisite: MTH 303 and MTH 421.Solution of initial and boundary value problems in ordinary and partial differential equations, simulation, and optimization. Problem solution will include the use of software. Identical with CSC 422. Cannot receive credit for both MTH 422 and CSC 422.

### MTH 450 Theory of Interest

Prerequisite: MTH 280.A thorough treatment of the mathematical theory of interest with some discussion of economic aspects such as inflation, risk and uncertainty, and yield curves. Topics include: Annuities, yield rates, amortization, bonds, and sinking funds.

### MTH 460 College Geometry

Prerequisite: MTH 315.This course examines concepts not usually included in a high school plane geometry course: axiomatic structure, finite geometries; Euclidean geometry axioms, historical development and relationships between various geometries, transformations in two and three dimensions, groups of transformations, convexity, linear programming, geometry of polygons and circles, the nine-point circle, constructions, and an introduction to non-Euclidean geometry. These topics will be developed within a problem solving context and will emphasize construction and communication of mathematical ideas including argument and proof. A dynamic geometry software package, such as Geometer's Sketchpad, will be used as a tool to develop geometric concepts.

### MTH 478 Mathematical Modeling for Teachers

Prerequisite: MTH 343 or MTH 360 or concurrent enrollment.Recommended Prerequisite: 15 hours of elementary or middle school mathematics. This course will focus on topics in upper elementary and middle school mathematics. This includes, within the context of problem solving: algebraic reasoning, proportional reasoning, integer operations, decimal operations, transformational geometry, and coordinate geometry. The course will also focus on integrating mathematical practices and process standards developed by professional organizations in mathematics education. The use of technological tools and manipulatives are embedded in the development of strategies for modeling mathematics. The course also includes school-based experiences for practical implementation.

### MTH 479 Mathematical Tools and Structures

Prerequisite: MTH 343 or MTH 360.Recommended Prerequisite: 15 hours of elementary or middle school mathematics. This course is designed to coordinate, connect and extend the mathematical experiences of the student who is preparing to teach mathematics in the middle school. Specific course content will include all of the following: an in-depth overview of problem solving and the nature of proof in mathematics and the mathematics classroom; history of the development of mathematics; a variety of mathematical topics such as algebraic structures, discrete mathematics, fractals and chaos, etc.; examination and exploration of mathematical topics that are appropriate and necessary for middle school students to ensure their efficient transition into secondary mathematics. A constant awareness of the use and impact of technology upon the mathematician and the mathematics classroom is explored and integrated throughout the course. The course experience is culminated in the final project, which will be an original, independent investigating of some relevant mathematical topic of interest to the student. This course cannot be used as a mathematics elective for the mathematics major or minor.

### MTH 492 Seminar in Supervised Teaching (Secondary Mathematics)

Prerequisite: MTH 409 and MTH 410 and MTH 411; and a grade of "C" or better in all professional education courses; current pre-professional liability insurance; and approval for supervised teaching; and concurrent enrollment in MTH 494.Focus will be on discussion, reflection, and analysis of field experiences during supervised teaching as well as discussion of Missouri Pre-service Teacher Assessment (MoPTA) to be completed while student teaching. Cannot be taken Pass/Not Pass. Course will not count toward the major GPA. Public Affairs Capstone Experience course.

### MTH 493 Supervised Teaching (Secondary Mathematics)

Prerequisite: MTH 409 and MTH 410 and MTH 411; and a grade of "C" or better in all professional education courses; current pre-professional liability insurance; and approval for supervised teaching; and concurrent enrollment in MTH 494.The student observes, then teaches mathematics classes under the direction of the cooperating teacher and the university supervisor. The student also participates in professional activities of a teacher, attends all required university meetings, and completes all required university assignments. Course will not count toward the major GPA. Public Affairs Capstone Experience course.

### MTH 494 Supervised Teaching (Secondary Mathematics)

Prerequisite: concurrent enrollment in MTH 492.The student observes, then teaches mathematics classes under the direction of the cooperating teacher and the university supervisor. The student also participates in professional activities of a teacher, attends all required university meetings, and completes all required university assignments. The student will complete the Missouri Pre-Service Teacher Assessment while student teaching. Cannot be taken Pass/Not Pass. Course will not count toward the major GPA. Public Affairs Capstone Experience course.

### MTH 496 Clinical Experiences in Teaching II

Prerequisite: EDC 199; and admitted to Teacher Education Program; and grades of "C" or better in all professional education courses; and completion of portfolio checkpoints 1 and 2; and current pre-professional liability insurance; and program approval.This course is designed to meet HB 1711 for student's experience as a Teacher's Aide or Assistant Rule (Rule 5 CSR 80-805.040), to that of conventional student teachers within the same program. It is also designed to support completion of additional clinical requirements within that program including: seminars and workshops, required meetings, school related activities appropriate to the assignment, demonstrated mastery of the MoSPE standards and completion and overall assessment of a Professional Preparation Portfolio. This course is credited only on BSEd or appropriate masters-level certification programs. Can only receive credit for one of the following: AGE 499, AGT 499, ART 469, COM 493, ECE 499, ELE 499, ENG 434, FCS 498, HST 499, KIN 498, MCL 491, MID 499, MTH 496, MUS 499, SCI 499, SEC 499, SPE 499, THE 493.

### MTH 497 Topics

Prerequisite: 90 hours.Recommended Prerequisite: completion of or concurrent enrollment in all mathematics courses required for the mathematics major. A written paper on a mathematical topic will be required. The student will be exposed to elementary research topics and to professional opportunities including graduate programs, employment by business, industry and government, and teaching options. Each student will be required to take the mathematics major assessment exam. Public Affairs Capstone Experience course.

### MTH 503 Advanced Calculus I

Prerequisite: MTH 280 and MTH 315.Concepts of limit, continuity, differentiation, Riemann integration, sequences and series, other related topics. May be taught concurrently with MTH 603. Cannot receive credit for both MTH 603 and MTH 503. Public Affairs Capstone Experience course.

### MTH 504 Advanced Calculus II

Prerequisite: MTH 302 and MTH 503.This is a continuation of MTH 503, including sequences and series of functions, uniform convergence, multivariate calculus, and other selected topics. May be taught concurrently with MTH 604. Cannot receive credit for both MTH 604 and MTH 504.

### MTH 506 Theory of Functions of a Complex Variable

Prerequisite: MTH 280 and MTH 315.Theory of elementary functions-polynomial, trigonometric, exponential, hyperbolic, logarithmic-of a complex variable; their derivatives, integrals; power series; other selected topics. May be taught concurrently with MTH 605. Cannot receive credit for both MTH 605 and MTH 506.

### MTH 507 Introduction to Partial Differential Equations

Prerequisite: MTH 302 and MTH 303 and MTH 315.Introduction to linear first and second order partial differential equations, including some formal methods of finding general solutions; the Cauchy problem for such equations, existence theorems, formal methods of finding the solution, and the role of characteristics; the classical boundary and initial value problems for the wave equation, heat equation and the boundary value problems for Laplace's equation. May be taught concurrently with MTH 607. Cannot receive credit for both MTH 607 and MTH 507.

### MTH 510 High School Mathematics from an Advanced Perspective

Prerequisite: permission of instructor.The focus of the course will be on relating what the mathematics students have learned in upper-level courses to what they will be teaching when they are in the high school classroom. The students' ability to reason and problem-solve mathematically and to model real-world problems in a mathematical context will be developed so they will be able to pass these abilities on to their own students. If there is a sufficient demand, an online component may be offered. Credited only on the BSEd (secondary). Cannot be taken Pass/Not Pass. May be taught concurrently with MTH 611. Cannot receive credit for both MTH 510 and MTH 611.

### MTH 532 Introduction to Abstract Algebra

Prerequisite: MTH 302 and MTH 315.It is recommended that students not take MTH 532 before taking MTH 333. Theory of groups, rings, integral domains, fields, polynomials. May be taught concurrently with MTH 631. Cannot receive credit for both MTH 631 and MTH 532. Public Affairs Capstone Experience course.

### MTH 534 Advanced Linear Algebra

Prerequisite: MTH 315 and MTH 333.Topics may include eigenvalue problems; Jordan normal form, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary transformations, Markov processes, and other topics selected by the instructor. May be taught concurrently with MTH 634. Cannot receive credit for both MTH 634 and MTH 534.

### MTH 536 Theory of Numbers

Prerequisite: MTH 302 and MTH 315.Factorization, Euler totient function, congruences, primitive roots, quadratic residues and reciprocity law. May be taught concurrently with MTH 636. Cannot receive credit for both MTH 636 and MTH 536.

### MTH 537 Applied Abstract Algebra

Prerequisite: MTH 333 or MTH 532.Topics typically include finite fields, block designs, error-correcting codes (nonlinear, linear, cyclic, BCH, and Reed-Solomon codes), cryptography, and computer implementation of these applications. May be taught concurrently with MTH 637. Cannot receive credit for both MTH 637 and MTH 537.

### MTH 540 Statistical Theory I

Prerequisite: MTH 302.Random variables, discrete and continuous probability functions, expectation, moment-generating functions, transformation of variables. May be taught concurrently with MTH 640. Cannot receive credit for both MTH 640 and MTH 540. Public Affairs Capstone Experience course.

### MTH 541 Statistical Theory II

Prerequisite: MTH 540 or equivalent.Estimation, complete and sufficient statistics, maximum likelihood estimation, hypothesis testing, nonparametric statistics. May be taught concurrently with MTH 643. Cannot receive credit for both MTH 643 and MTH 541.

### MTH 543 Stochastic Modeling

Prerequisite: MTH 540.This course will study applications of probability and statistics from a modeling point of view. Topics include generating functions, branching processes, discrete time Markov chains, classification of states, estimation of transition probabilities, continuous time Markov Chains, Poisson processes, birth and death processes, renewal theory, queuing systems, Brownian motion, and stationary processes. Computer statistical packages will be used. May be taught concurrently with MTH 653. Cannot receive credit for both MTH 653 and MTH 543.

### MTH 545 Applied Statistics

Prerequisite: 60 hours and completion of General Education Mathematics Requirement.A course on statistical concepts, methods and data analysis with emphasis on assumptions and effects on violating those assumptions. Computer statistical packages will be used. Topics include statistical models, random sampling, normal distribution, estimation, confidence intervals, tests and inferences in single and two populations, and n-way analysis of variance. May be taught concurrently with MTH 645. Cannot receive credit for both MTH 645 and MTH 545.

### MTH 546 Analysis of Variance and Design of Experiments

Prerequisite: MTH 345 or MTH 541 or MTH 545.Topics include analysis of variance, estimation of variance components, randomized incomplete blocks, Latin squares, factorial nested, split-plot designs, fixed, random and mixed models. May be taught concurrently with MTH 646. Cannot receive credit for both MTH 646 and MTH 546.

### MTH 547 Applied Regression Analysis

Prerequisite: MTH 345 or MTH 541 or MTH 545.Topics include fitting a straight line, matrix models, residuals, selecting best equation, multiple regression, and nonlinear estimation. May be taught concurrently with MTH 647. Cannot receive credit for both MTH 647 and MTH 547.

### MTH 548 Applied Time Series Analysis

Prerequisite: MTH 540; and MTH 345 or MTH 541 or MTH 545.This course will study the analysis of data observed at different points of time. Topics include stationary and non-stationary time series models, linear time series models, autoregressive models, autocorrelations, partial autocorrelations, moving average models, ARMA models, ARIMA models, forecasting, prediction limits, model specification, least square estimation, and seasonal time series models. Computer statistical packages will be used. May be taught concurrently with MTH 648. Cannot receive credit for both MTH 648 and MTH 548.

### MTH 567 Introduction to Non-Euclidean Geometry

Prerequisite: MTH 302 and MTH 315.Development of non-Euclidean geometries; intensive study of hyperbolic geometry. May be taught concurrently with MTH 667. Cannot receive credit for both MTH 667 and MTH 567.

### MTH 570 Combinatorial Analysis

Prerequisite: MTH 280 and MTH 315.An introduction to combinatorial analysis including enumeration methods, combinatorial identities with applications to the calculus of finite differences and difference equations. May be taught concurrently with MTH 670. Cannot receive credit for both MTH 670 and MTH 570.

### MTH 575 History of Mathematics

Prerequisite: MTH 302 and MTH 315.Development of mathematics through the calculus; solution of problems of historical interest, problems which use historically significant techniques; problems whose solutions illuminate significant mathematical characteristics of elementary mathematics. May be taught concurrently with MTH 675. Cannot receive credit for both MTH 675 and MTH 575.

### MTH 580 Applied Mathematics

Prerequisite: MTH 303 and MTH 333.An introduction to several areas of applied mathematics including control theory, optimization, modeling of population dynamics, modeling of mathematical economics, minimax and game theory, and calculus of variations. May be taught concurrently with MTH 680. Cannot receive credit for both MTH 680 and MTH 580.

### MTH 582 Introductory Topology

Prerequisite: MTH 302 and MTH 315.Properties of abstract metric and topological spaces; discussion of concepts of compactness and connectedness. May be taught concurrently with MTH 682. Cannot receive credit for both MTH 682 and MTH 582.

### MTH 596 Readings

Prerequisite: permission of department head.Periodic conferences with an advisor are required. May be repeated to a total of 6 hours. May be taught concurrently with MTH 696. Cannot receive credit for both MTH 696 and MTH 596.

### MTH 603 Advanced Calculus I

Prerequisite: MTH 280 and MTH 315.Concepts of limit, continuity, differentiation, Riemann integration, sequences and series, other related topics. May be taught concurrently with MTH 503. Cannot receive credit for both MTH 503 and MTH 603.

### MTH 604 Advanced Calculus II

Prerequisite: MTH 302; and MTH 503 or MTH 603.This is a continuation of MTH 603, including sequences and series of functions, uniform convergence, multivariate calculus, and other selected topics. May be taught concurrently with MTH 504. Cannot receive credit for both MTH 504 and MTH 604.

### MTH 605 Theory of Functions of a Complex Variable

Prerequisite: MTH 280 and MTH 315.Theory of elementary functions-polynomial, trigonometric, exponential, hyperbolic, logarithmic-of a complex variable; their derivatives, integrals; power series; other selected topics. May be taught concurrently with MTH 506. Cannot receive credit for both MTH 506 and MTH 605.

### MTH 607 Introduction to Partial Differential Equations

Prerequisite: MTH 302 and MTH 303 and MTH 315.Introduction to linear first and second order partial differential equations, including some formal methods of finding general solutions; the Cauchy problem for such equations, existence theorems, formal methods of finding the solution, and the role of characteristics; the classical boundary and initial value problems for the wave equation, heat equation and the boundary value problems for Laplace's equation. May be taught concurrently with MTH 507. Cannot receive credit for both MTH 507 and MTH 607.

### MTH 611 High School Mathematics from an Advanced Perspective

Prerequisite: permission of instructor.The focus of the course will be on relating what the mathematics students have learned in upper-level courses to what they will be teaching when they are in the high school classroom. The students' ability to reason and problem-solve mathematically and to model real-world problems in a mathematical context will be developed so they will be able to pass these abilities on to their own students. If there is a sufficient demand, an online component may be offered. May be taught concurrently with MTH 510. Cannot receive credit for both MTH 611 and MTH 510.

### MTH 631 Introduction to Abstract Algebra

Prerequisite: MTH 302 and MTH 315.Theory of groups, rings, integral domains, fields, polynomials. May be taught concurrently with MTH 532. Cannot receive credit for both MTH 532 and MTH 631.

### MTH 634 Linear Algebra II

Prerequisite: MTH 333.Topics include eigenvalue problems; Jordan normal form, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary transformations, Markov processes, and other topics selected by the instructor. May be taught concurrently with MTH 534. Cannot receive credit for both MTH 534 and MTH 634.

### MTH 636 Theory of Numbers

Prerequisite: MTH 302 and MTH 315.Factorization, Euler totient function, congruences, primitive roots, quadratic residues and reciprocity law. May be taught concurrently with MTH 536. Cannot receive credit for both MTH 536 and MTH 636.

### MTH 637 Applied Abstract Algebra

Prerequisite: MTH 333 or MTH 532 or MTH 632.Topics typically include finite fields, block designs, error-correcting codes (nonlinear, linear, cyclic, BCH, and Reed-Solomon codes), cryptography, and computer implementation of these applications. May be taught concurrently with MTH 537. Cannot receive credit for both MTH 537 and MTH 637.

### MTH 640 Statistical Theory I

Prerequisite: MTH 302.Random variables, discrete and continuous probability functions, expectation, moment-generating functions, transformation of variables. May be taught concurrently with MTH 540. Cannot receive credit for both MTH 540 and MTH 640.

### MTH 643 Statistical Theory II

Prerequisite: MTH 540 or MTH 640 or equivalent.Estimation, complete and sufficient statistics, maximum likelihood estimation, hypothesis testing, nonparametric statistics. May be taught concurrently with MTH 541. Cannot receive credit for both MTH 541 and MTH 643.

### MTH 645 Applied Statistics

A course on statistical concepts, methods and data analysis with emphasis on assumptions and effects on violating those assumptions. Computer statistical packages will be used. Topics include statistical models, random sampling, normal distribution, estimation, confidence intervals, tests and inferences in single and two populations, and n-way analysis of variance. May be taught concurrently with MTH 545. Cannot receive credit for both MTH 545 and MTH 645.

### MTH 646 Analysis of Variance and Design of Experiments

Prerequisite: MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645.Topics include analysis of variance, estimation of variance components, randomized incomplete blocks, Latin squares, factorial nested, split-plot designs, fixed, random and mixed models. May be taught concurrently with MTH 546. Cannot receive credit for both MTH 546 and MTH 646.

### MTH 647 Applied Regression Analysis

Prerequisite: MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645.Topics include fitting a straight line, matrix models, residuals, selecting best equation, multiple regression, and nonlinear estimation. May be taught concurrently with MTH 547. Cannot receive credit for both MTH 547 and MTH 647.

### MTH 648 Applied Time Series Analysis

Prerequisite: MTH 540 or MTH 640; and MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645.This course will study the analysis of data observed at different points of time. Topics include stationary and non-stationary time series models, linear time series models, autoregressive models, autocorrelations, partial autocorrelations, moving average models, ARMA models, ARIMA models, forecasting, prediction limits, model specification, least square estimation, and seasonal time series models. Computer statistical packages will be used. May be taught concurrently with MTH 548. Cannot receive credit for both MTH 548 and MTH 648.

### MTH 653 Stochastic Modeling

Prerequisite: MTH 540 or MTH 640.This course will study applications of probability and statistics from a modeling point of view. Topics include generating functions, branching processes, discrete time Markov chains, classification of states, estimation of transition probabilities, continuous time Markov Chains, Poisson processes, birth and death processes, renewal theory, queuing systems, Brownian motion, and stationary processes. Computer statistical packages will be used. May be taught concurrently with MTH 543. Cannot receive credit for both MTH 543 and MTH 653.

### MTH 667 Introduction to Non-Euclidean Geometry

Prerequisite: MTH 302 and MTH 315.Development of non-Euclidean geometries; intensive study of hyperbolic geometry. May be taught concurrently with MTH 567. Cannot receive credit for both MTH 567 and MTH 667.

### MTH 670 Combinatorial Analysis

Prerequisite: MTH 280 and MTH 315.An introduction to combinatorial analysis including enumeration methods, combinatorial identities with applications to the calculus of finite differences and difference equations. May be taught concurrently with MTH 570. Cannot receive credit for both MTH 570 and MTH 670.

### MTH 675 History of Mathematics

Prerequisite: MTH 302 and MTH 315.Development of mathematics through the calculus; solution of problems of historical interest, problems which use historically significant techniques; problems whose solutions illuminate significant mathematical characteristics of elementary mathematics. May be taught concurrently with MTH 575. Cannot receive credit for both MTH 575 and MTH 675.

### MTH 680 Applied Mathematics

Prerequisite: MTH 303 and MTH 333.An introduction to several areas of applied mathematics including control theory, optimization, modeling of population dynamics, modeling of mathematical economics, minimax and game theory, and calculus of variations. May be taught concurrently with MTH 580. Cannot receive credit for both MTH 580 and MTH 680.

### MTH 682 Introductory Topology

Prerequisite: MTH 302 and MTH 315.Properties of abstract metric and topological spaces; discussion of concepts of compactness and connectedness. May be taught concurrently with MTH 582. Cannot receive credit for both MTH 582 and MTH 682.

### MTH 696 Readings

Prerequisite: permission of department head.Periodic conferences with an advisor are required. May be repeated to a total of 6 hours. May be taught concurrently with MTH 596. Cannot receive credit for both MTH 596 and MTH 696.

### MTH 701 Real Analysis

Prerequisite: MTH 503 or MTH 603.Topics include countable and uncountable sets, convergence, Lebesgue measure on the real line, the development of the Lebesgue integral, the fundamental theorem of calculus and Lp spaces.

### MTH 702 Real and Abstract Analysis

Prerequisite: MTH 701.A study of the theory of abstract measures and integration, and an introduction to functional analysis.

### MTH 706 Complex Analysis

Prerequisite: MTH 503 or MTH 603.Analytic functions, power series, Cauchy's theorem and its applications, residues. Selected topics from conformal mapping, analytic continuation, harmonic functions, Fourier series, and Dirichlet problems.

### MTH 710 Contemporary Mathematics for Secondary Teachers

Prerequisite: MTH 460 and MTH 333.Reports, research, and recent trends in secondary mathematics; recently developed programs in algebra and geometry.

### MTH 721 Theory of Ordinary Differential Equations I

Prerequisite: MTH 303; and MTH 503 or MTH 603.Existence and uniqueness theorems for first order differential equations; system of linear and nonlinear differential equations; continuous dependence of solutions on initial conditions and parameters; behavior of solutions of equations with constant coefficients, study of Lyapunov's theorems on stability; introduction to boundary value problems.

### MTH 722 Theory of Ordinary Differential Equations II

Prerequisite: MTH 721.Theory and application of boundary value problems; periodic solutions; linear systems with periodic coefficients (Floquet theory); two dimensional (autonomous) systems limit cycles. Differential equations under Caratheodory conditions; theory of differential and integral inequalities and other selected topics, if time permits.

### MTH 730 Abstract Algebra I

Prerequisite: MTH 532 or MTH 631; and MTH 333.Topics from group theory will include Cayley's Theorem, finite abelian groups, Cauchy's Theorem, the Sylow Theorems, and free groups.

### MTH 732 Abstract Algebra II

Prerequisite: MTH 730.Topics from ring theory will include the Chinese Remainder Theorem, Euclidean domains, rings of fractions, PID's and UFD's, and polynomial rings. Topics from field theory will include splitting fields, Galois Theory, separability, normality, and finite fields.

### MTH 741 Statistical Inference I

Prerequisite: MTH 540 or MTH 640 or equivalent.Formulation of statistical models, sufficiency and exponential families, methods of estimation, optimality theory. Uniformly minimum variance unbiased estimators, Fisher information, Cramer/Rao inequality, large sample theory, Bayes procedures and minimax procedures.

### MTH 742 Statistical Inference II

Prerequisite: MTH 741.Confidence intervals and regions, hypothesis testing, the Neyman-Pearson framework, uniformly most powerful tests, likelihood ratio criteria, power functions, similar regions, invariant tests, distribution free tests.

### MTH 750 Number and Operations for Elementary Mathematics Specialists

Prerequisite: Two years teaching experience and permission of program coordinator; and concurrently enrollment in ELE 730.This course is designed to develop an understanding of the learning and teaching of pre-number concepts, counting and cardinality, and numbers and operations in base ten. Emphasis will be given to how children think about and learn these concepts and how they fit into the elementary school curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 752 Rational Numbers and Proportional Thinking for Elementary Mathematics Specialists

Prerequisite: MTH 750 and permission of program coordinator; and concurrent enrollment in ELE 732.This course is designed to develop an understanding of the learning and teaching of rational numbers and ratio and proportional relationships. Emphasis will be given to how children think about and learn these concepts and how they fit into the elementary school curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 754 Algebraic Reasoning for Elementary Mathematics Specialist

Prerequisite: two years teaching experience and permission of program coordinator; and concurrently enrollment in ELE 734.This course will focus on the content and complexities of teaching and assessing algebraic reasoning in grade 1-6 settings. Course content will include examination of representation and analysis of mathematical situations and structures. Attention will be given to patterns, functions, and the transition from arithmetic to algebra. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 758 Data and Probability for Elementary Mathematics Specialist

Prerequisite: two years teaching experience and permission of program coordinator.This course is designed to develop understanding of probabilistic reasoning and the collection, exploration, and analysis of data. Emphasis will be given to how children think and learn about these concepts and how they fit into the elementary school curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 760 Geometry and Measurement for Elementary Mathematics Specialist

Prerequisite: two years teaching experience and permission of program coordinator; and concurrently enrollment in ELE 738.This course is designed to develop an understanding of the teaching and learning of geometry and measurement. Emphasis will be given to how children think about and learn these concepts and how they fit into an elementary curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 781 Topology

Point set topology in abstract spaces.

### MTH 791 Seminar I

Seminar in Mathematics.

### MTH 792 Seminar II

Seminar in Mathematics.

### MTH 796 Science Internship

Completion of an internship project (at least 80 hours per credit hour) at a discipline-related business, nonprofit organization, or government agency, approved and supervised by both the departmental and internship advisors. Includes a formal report in the appropriate professional format, and an oral presentation at an approved venue. Graded Pass/Not Pass only. No more than 6 hours may count toward a masters degree. This course may only be counted toward the PSM designation of the MNAS degree.

### MTH 797 Topics

Prerequisite: permission of department head.Material covered determined by the interests and backgrounds of the students. May be repeated for a maximum of 6 hours.

### MTH 798 Research

Supervised research in mathematics or mathematics education. May be repeated.

### MTH 799 Projects

Independent research for thesis preparation.