# Mathematics Courses

## Mathematics (MTH) courses

### MTH 101 Intermediate Algebra I

This course is recommended for students who have not mastered algebra concepts needed for college algebra. Topics include linear equations and inequalities, absolute value equations and inequalities, exponents, polynomials, rational expressions, and radicals. 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 102. Cannot be taken Pass/Not Pass.

- Credit hours:
- 2
- Lecture contact hours:
- 1
- Lab contact hours:
- 2

**Typically offered:**Fall, Spring### MTH 102 Intermediate Algebra II

*Prerequisite: "C" grade or better in MTH 101, or appropriate placement score.*This course is a continuation of MTH 101. Topics include quadratic equations and inequalities, lines, systems of equations, parabolas, circles, and functions. Cannot receive credit toward graduation for both MTH 102 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.

- Credit hours:
- 2
- Lecture contact hours:
- 1
- Lab contact hours:
- 2

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 130 Contemporary Mathematics

*Prerequisite: "C" grade or better in MTH 102 or MTH 103 or approved score on a departmental placement test. 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 135 College Algebra

*Prerequisite: "C" grade or better in MTH 102 or MTH 103, or appropriate placement score, Note: MTH 130 does not meet the prerequisite for MTH 135. General Education Course (Focus on Quantitative Literacy).*Contents include the study of linear and quadratic equations; inequalities and their applications; polynomial, rational, exponential and logarithmic functions; and systems of equations. Cannot receive credit toward graduation for both MTH 135 and MTH 138. Cannot count toward a mathematics major or minor. A grade of "C" or better is required in this course in order to take MTH 181, MTH 285, or MTH 287. Cannot be taken Pass/Not Pass.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 138 Pre-Calculus Mathematics

*Prerequisite: "C" grade or better in MTH 102 or MTH 103 (Recommended: "B" grade or better in MTH 102 or MTH 103), or appropriate placement score. General Education Course (Focus on Quantitative Literacy).*Selected topics in algebra and trigonometry to prepare the student for calculus. Cannot receive credit toward graduation for both MTH 138 and MTH 135. Cannot count toward a mathematics major or minor. A grade of "C" or better is required in this course in order to take MTH 261, 287, CSC 125 or 131. Cannot be taken Pass/Not Pass.

- Credit hours:
- 5
- Lecture contact hours:
- 5
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 181 Trigonometry

*Prerequisite: "C" grade or better in MTH 135 or appropriate placement score. General Education Course (Focus on Quantitative Literacy).*Triangle trigonometry and its applications; trigonometric and inverse trigonometric functions; trigonometric identities and equations; Rational, exponential and logarithmic functions. Cannot receive credit toward graduation for both MTH 181 and MTH 138. Cannot count toward a mathematics major or minor. A grade of "C" or better is required in this course in order to take MTH 287. Cannot be taken Pass/Not Pass.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 215 Discrete Mathematics

*Prerequisite: 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 261 Analytic Geometry and Calculus I

*Prerequisite: "C" grade or better in MTH 138 or MTH 181 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.

- Credit hours:
- 5
- Lecture contact hours:
- 5
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 5
- Lecture contact hours:
- 5
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 285 Calculus for Business and the Social Sciences

*Prerequisite: "C" or better in MTH 135, or appropriate placement score.*Short review of algebra; absolute value and inequalities followed by elements of geometry, limits, the derivative, anti-derivative, and their applications. Cannot receive credit toward graduation for both MTH 285 and MTH 261.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 287 Computational Calculus with Analytic Geometry I

*Prerequisite: "C" or better in MTH 135 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. Cannot receive credit for both MTH 287 and MTH 285. 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 1-3
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Upon demand### 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.

- Credit hours:
- 1
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### MTH 302 Multivariate Calculus

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

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 303 Differential Equations

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

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 2
- Lab contact hours:
- 2

**Typically offered:**Fall, Spring### 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, MTH 340, PSY 200, QBA 237, REC 328, SOC 302.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 343 Foundations of Probability and Statistics for Teachers

*Prerequisite: "C" or better in MTH 320.*This course includes the collection, display, analysis, and misuse of data, measures of central tendency and variation; counting techniques including permutations and combinations; elementary probability, and an informal introduction to correlation and regression. Problem solving and communication skills are continuing themes. This is an activity-based course with extensive use of manipulatives, models and technology. It cannot be used as a mathematics elective for a mathematics major or minor.

- Credit hours:
- 3
- Lecture contact hours:
- 2
- Lab contact hours:
- 2

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 2
- Lab contact hours:
- 2

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 2
- Lab contact hours:
- 2

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 2
- Lab contact hours:
- 2

**Typically offered:**Spring### 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 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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 493 Supervised Teaching (Secondary Mathematics)

*Prerequisite: MTH 409; MTH 410; a grade of "C" or better in all professional education courses; current pre-professional liability insurance; and approval for supervised teaching.*Student observes then teaches mathematics classes under the direction of the cooperating teacher and the university supervisor. Student participates in school-related activities appropriate to the assignment and attends all required meetings. In order to receive a grade in this course, the student's professional portfolio must meet or exceed final criteria. Course will not count toward the major GPA. Supplemental course fee. Public Affairs Capstone Experience course.

- Credit hours:
- 5-6
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### MTH 494 Supervised Teaching (Secondary Mathematics)

*Prerequisite: concurrent enrollment in MTH 493.*Student observes then teaches under the direction of the cooperating teacher and the university supervisor. Student participates in school-related activities appropriate to the assignment and attends all required meetings. In order to receive a grade in this course, the student's professional portfolio must meet or exceed final criteria. Course will not count toward the major GPA. Supplemental course fee. Public Affairs Capstone Experience course.

- Credit hours:
- 5-6
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### 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, BSE 499, 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. Supplemental course fee.

- Credit hours:
- 4
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 1
- Lecture contact hours:
- 1
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 532 Introduction to Abstract Algebra

*Prerequisite: MTH 302 and MTH 315.*It is recommended that students not take MTH 532 before taking MTH 533. 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 533 Linear Algebra I

*Prerequisite: MTH 280 and MTH 315.*Vector spaces, linear independence, inner product spaces, linear transformations, Eigenvectors, diagonalization. May be taught concurrently with MTH 633. Cannot receive credit for both MTH 633 and MTH 533.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 534 Linear Algebra II

*Prerequisite: MTH 533.*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 634. Cannot receive credit for both MTH 634 and MTH 534.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 537 Applied Abstract Algebra

*Prerequisite: MTH 532 or MTH 533.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 540 Statistical Theory I

*Prerequisite: MTH 302 and MTH 315.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### MTH 545 Applied Statistics

*Prerequisite: 60 credit 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 580 Applied Mathematics

*Prerequisite: MTH 303 and MTH 533.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 1-3
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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 633 Linear Algebra I

*Prerequisite: MTH 280 and MTH 315.*Vector spaces, linear independence, inner product spaces, linear transformations, Eigenvectors, diagonalization. May be taught concurrently with MTH 533. Cannot receive credit for both MTH 533 and MTH 633.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 634 Linear Algebra II

*Prerequisite: MTH 533 or MTH 633.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 637 Applied Abstract Algebra

*Prerequisite: MTH 532 or MTH 632 or MTH 533 or MTH 633.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 640 Statistical Theory I

*Prerequisite: MTH 302 and MTH 315.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 680 Applied Mathematics

*Prerequisite: MTH 303; and MTH 533 or MTH 633.*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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 1-3
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 710 Contemporary Mathematics for Secondary Teachers

*Prerequisite: MTH 460; and MTH 533 or MTH 633.*Reports, research, and recent trends in secondary mathematics; recently developed programs in algebra and geometry.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 730 Abstract Algebra I

*Prerequisite: MTH 532 or MTH 631; and MTH 533 or MTH 633.*Topics from group theory will include Cayley's Theorem, finite abelian groups, Cauchy's Theorem, the Sylow Theorems, and free groups.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 781 Topology

Point set topology in abstract spaces.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 791 Seminar I

Seminar in Mathematics.

- Credit hours:
- 2
- Lecture contact hours:
- 2
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### MTH 792 Seminar II

Seminar in Mathematics.

- Credit hours:
- 2
- Lecture contact hours:
- 2
- Lab contact hours:
- 0

**Typically offered:**Fall, Spring### 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.

- Credit hours:
- 1-6
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring, Summer### 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.

- Credit hours:
- 3
- Lecture contact hours:
- 3
- Lab contact hours:
- 0

**Typically offered:**Upon demand### MTH 798 Research

Supervised research in special areas of mathematics. May be repeated. Cannot be counted toward the MSEd degree.

- Credit hours:
- 1-6
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring### MTH 799 Projects

Independent research for thesis preparation.

- Credit hours:
- 1-6
- Lecture contact hours:
- Lab contact hours:

**Typically offered:**Fall, Spring