Mathematics (Comprehensive)

1. General Education (see General Education section of catalog)

2. Major Requirements (56 hours)

   1. MTH 261(5), 280(5), 302(3), 303(3), 315(3), 497(1), 503(3), 532(3), 533(3), 540(3); MTH 421(3) or 541(3)

   2. Select an additional 18 hours from mathematics courses numbered 400 or above. The comprehensive major is individualized. Selection of courses for the additional 18 hours shall be made in conference with the advisor and is subject to approval by the department head. Students are encouraged to elect courses from other disciplines to enhance the comprehensive major. Minimum for major is 53 hours.

   3. Courses required from related areas: CSC 125(3) or 131(4); PHY 203(5) (PHY 203 may partially fulfill the natural world general education requirement.)

3. General Baccalaureate Degree Requirements (see “Academic Programs and Requirements” section of catalog)

Mathematics (Non-Comprehensive)

1. General Education (see General Education section of catalog)

2. Major Requirements (34 hours)

   1. MTH 261(5), 280(5), 302(3), 315(3), 497(1), 503(3), 532(3), 533(3), 540(3)

   2. Select an additional course from: MTH 303(3), 575(3), 421(3) or from mathematics courses numbered 400 or above. Minimum for major is 34 hours.

   3. Course required from related area: CSC 121(3) or 125(3) or 131(4)

3. Minor Required

4. Specific Requirements for Bachelor of Arts Degree (see “Academic Programs and Requirements” section of catalog)

5. General Baccalaureate Degree Requirements (see “Academic Programs and Requirements” section of catalog)

Mathematics (Non-Comprehensive)

1. General Education (see General Education section of catalog)

2. Major Requirements

   1. MTH 261(5), 280(5), 302(3), 303(3), 315(3), 497(1), 503(3), 532(3), 533(3), 540(3)

   2. Select one of the following options:

      1. Actuarial Mathematics:

         1. MTH 450(3), 541(3)

         2. Select an additional six hours from the following courses: MTH 543(3), 546(3), 547(3), 548(3)

         3. A minor in Insurance is recommended

      2. Applied Mathematics:

         1. MTH 421(3), 580(3)

         2. Select an additional six hours from the following courses: MTH 422(3), 507(3), 537(3), 543(3), 570(3)

      3. General Mathematics:

         1. MTH 421(3) or 541(3)

         2. Select an additional nine hours from mathematics courses numbered 400 or above

      4. Statistics:

         1. MTH 541(3)

         2. Select an additional nine hours from the following courses: MTH 543(3), 545(3), 546(3), 547(3), 548(3)

   3. Courses required from related areas: CSC 125(3) or 131(4); PHY 203(5) (PHY 203 may partially fulfill the natural science general education requirement.)

3. Minor Required

4. General Baccalaureate Degree Requirements (see “Academic Programs and Requirements” section of catalog)

Mathematics

1. General Education (see General Education section of catalog)

2. Major Requirements

   1. MTH 261(5), 280(5), 302(3), 315(3), 345(3), 460(3), 497(1), 532(3), 533(3), 575(3)

   2. Select two courses from: MTH 503(3), 536(3), 540(3), 567(3)

   3. Courses required from related areas: CSC 121(3) or 125(3) or 131(4); PHY 123(4) or 203(5)

3. Professional Education Requirements: MTH 409(3), 410(3), 493(5-6), 494(5-6); and the Professional Education Required Core and Competencies (see "Teacher Certification, Teacher Education Program and Secondary Education Requirements" section of catalog).

4. General Baccalaureate Degree Requirements (see “Academic Programs and Requirements” section of catalog

5. In order to meet Missouri state teacher certification requirements, candidates for the Bachelor of Science in Education degree are required to meet the following grade point average requirements: at least a 2.50 GPA on all course work attempted at all colleges attended; at least a 2.50 GPA in the certificate subject area (major field of study) which includes all courses listed under C; at least a 2.50 GPA in any additional certificate subject area; at least a 2.50 GPA in the professional education courses; and no grade lower than a “C” in all professional education courses. All GPA requirements include both Missouri State and transfer grades.

Mathematics

1. MTH 261(5), 280(5), 215(3) or 315(3)

2. Additional mathematics courses numbered 300 or above, other than MTH 315, to total at least 15 hours.

Mathematics

1. MTH 261(5), 280(5), 315(3), 575(3)

2. Select one course from: CSC 121(3), 125(3), 131(4)

3. Select one course from: MTH 460(3), 567(3)

4. Select additional mathematics courses numbered 300 or above to total at least 24 hours.

Mathematics Courses

MTH 101 Intermediate Algebra I 2(1-2), F,S

Prerequisite: appropriate placement score. 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. A student who takes MTH 103 and MTH 101 receives credit toward graduation for only one of these courses. This course will not count toward a mathematics major or minor. A grade of "C" or better is required in this course to take MTH 102. This course may not be taken Pass/Not Pass.

MTH 102 Intermediate Algebra II 2(1-2), F,S

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. A student who takes MTH 103 and MTH 102 receives credit toward graduation for only one of these courses. This course will not count toward a mathematics major or minor. A grade of "C'' or better is required in this course to take MTH 130, MTH 135, or MTH 138. This course may not be taken Pass/Not Pass.

MTH 103 (003) Intermediate Algebra 3(3-0), F,S

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. A student cannot receive credit toward graduation for both MTH 103 and either of MTH 101 and 102. This course will not 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. This course may not be taken Pass/Not Pass. Assignment to the 3(3-0) version of the course is in summer only.

MTH 130 (145) Contemporary Mathematics 3(3-0), F,S

Prerequisite: "C" grade or better in MTH 102 or MTH 103 or appropriate placement score. This is a problem solving course. Topics will include: patterns, set theory, algebra applications, number theory, geometry, probability, statistics, and mathematics of finance. This course will not count towards a mathematics major or minor. This course may not be taken Pass/Not Pass.

MTH 135 College Algebra 3(3-0), F,S

Prerequisite: "C" grade or better in MTH 102 or MTH 103, or appropriate placement score. Contents include the study of linear and quadratic equations; inequalities and their applications; polynomial, rational, exponential and logarithmic functions; and systems of equations. A student who takes MTH 135 and MTH 138 receives credit toward graduation for MTH 138 only. This course will not count toward a mathematics major or minor. Assignment to the 3(3-0) version of the course is in the summer session only. A grade of "C" or better is required in this course to take MTH 181, MTH 285, or MTH 287. This course may not be taken Pass/Not Pass.

MTH 138 Pre-Calculus Mathematics 5(5-0), F,S

Prerequisite: "C" grade or better in MTH 102 or MTH 103 or appropriate placement score. Selected topics in algebra and trigonometry to prepare the student for calculus. A student who takes MTH 135 and 138 receives credit toward graduation only for one of the courses. Will not count toward 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. This course may not be taken Pass/Not Pass.

MTH 181 Trigonometry 3(3-0), F,S

Prerequisite: "C" grade or better in MTH 135, or appropriate placement score. Triangle trigonometry and its applications; trigonometric and inverse trigonometric functions; trigonometric identities and equations; Rational, exponential and logarithmic functions. A student may not receive credit for more than one of MTH 138 and 181. Will not count toward mathematics major or minor. A grade of "C" or better is required in this course in order to take MTH 287. This course may not be taken Pass/Not Pass.

MTH 215 Discrete Mathematics 3(3-0), F,S

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

MTH 261 Analytic Geometry and Calculus I 5(5-0), F,S

Prerequisite: "C" grade or better in MTH 138 or appropriate placement score or permission of department head. 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, 288. This course may not be taken Pass/Not Pass.

MTH 280 Analytic Geometry and Calculus II 5(5-0), F,S

Prerequisite: "C" or better in MTH 261, or permission of department head. Applications of integration, integration techniques, indeterminate forms, improper integrals, sequences, series, conic sections, parametrization, polar coordinates. This course may not be taken Pass/Not Pass.

MTH 285 Calculus for Business and the Social Sciences 3(3-0), F,S

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. Student taking MTH 285 and 261 receives credit only for 261.

MTH 287 Computational Calculus with Analytic Geometry I 3(3-0), F

Prerequisite: "C" or better in MTH 138, or "C" or better in both MTH 135 and MTH 181, or appropriate placement score. Introduction to the concepts and methods of analytic geometry and differential and integral calculus with emphasis on applications in the natural sciences and technology. Students taking MTH 287 and MTH 261 receive credit only for MTH 261. A student can receive credit for only one of the courses MTH 285 or MTH 287. A grade of "C" or better is required in this course in order to take MTH 288. This course may not be taken Pass/Not Pass.

MTH 288 Computational Calculus II 3(3-0), S

Prerequisite: "C" grade or better in MTH 261 or MTH 287. Continuation of MTH 287. Students taking both MTH 288 and MTH 280 receive credit only for MTH 280. This course may not be taken Pass/Not Pass.

MTH 299 Introductory Topics in Mathematics 1-3, D

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. Will not count toward a mathematics major or minor, nor will it satisfy the general education basic skills requirement in mathematics.

MTH 300 Service Learning in Mathematics 1, F,S

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 but no more than two hours of service learning credit may count toward graduation.

MTH 302 Multivariate Calculus 3(3-0), F,S

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

MTH 303 Differential Equations 3(3-0), F,S

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

MTH 315 Algebraic Structures 3(3-0), F,S

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 3(2-2), F,S

Prerequisite: completion of math general education 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 340 Statistical Methods 3(3-0), F,S

Prerequisite: MTH 135 or appropriate placement score. Statistics, elementary probability, estimation and tests of simple hypotheses involving both large and small sample methods, linear correlation. Will not count toward mathematics major or minor. A student may not receive credit toward a degree for more than one of the following courses: AGR 330, ECO 308, MTH 340, PSY 200, QBA 237, REC 331, SOC 302.

MTH 343 Foundations of Probability and Statistics for Teachers 3(2-2), F,S

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.

MTH 345 Statistics for Scientists and Engineers 3(3-0), F,S

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 3(2-2), F,S

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 3(2-2), S

Prerequisite: MTH 135 and 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 (SEC) Teaching and Learning of Mathematics I 3(2-2), S

Prerequisite: SEC 302 and 15 hours of college mathematics. 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 B.S. in Education (Middle/Secondary). A grade of "C" or better is required in this course in order to take MTH 493. This course may not be taken Pass/Not Pass. This course will not count toward the major GPA.

MTH 410 Teaching and Learning of Mathematics II, with Practicum 3(2-2), F

Prerequisite: MTH 409. Focus on developing the reflective decision-maker'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 B.S. in Education (Secondary). A grade of "C" or better is required in this course in order to take MTH 493. This course may not be taken Pass/Not Pass. This course will not count toward the major GPA.

MTH 421 Numerical Analysis I 3(3-0), D

Prerequisite: MTH 280. Recommended: CSC 125 or CSC 131. 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 3(3-0), D

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 3(3-0), S

Prerequisite: MTH 302 and MTH 315. 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 3(3-0), F,S

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 none-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 479 Mathematical Tools and Structures 3(2-2), F

Prerequisite: MTH 343 or MTH 360. Recommended: 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) 5-6, F,S

Prerequisite: MTH 409; MTH 410; a grade of "C" or better in all professional education courses; a passing score on the appropriate Mathematics PRAXIS II examination; 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.

MTH 494 Supervised Teaching (Secondary Mathematics) 5-6, F,S

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.

MTH 496 Clinical Experiences in Teaching II 4, F,S

Prerequisite: EDC 199 and admitted to Teacher Education Program and grades of "C" or better in all professional education courses and passing the appropriate PRAXIS exam and completion of portfolio checkpoints 1 and 2. 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 MOSTEP quality indicators and completion and overall assessment of a Professional Preparation Portfolio. This course is credited only on B.S. in Education or appropriate master's-level certification programs. Can only receive credit for one of the following: AGE 499, AGT 499, ART 469, BSE 499, CFS 498, COM 493, ECE 499, ELE 499, ENG 434, HST 499, MCL 491, MID 499, MTH 496, MUS 499, PED 498, SCI 499, SEC 499, SPE 499, THE 493.

MTH 497 (490) Topics 1(1-0), F,S

Prerequisite: 90 credit hours. Recommended: 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.

MTH 503 Advanced Calculus I 3(3-0), F,S

Prerequisite: MTH 302 and MTH 315. Concepts of limit, continuity, differentiation, Riemann integration, sequences and series, other related topics.

MTH 504 Advanced Calculus II 3(3-0), D

Prerequisite: MTH 503. This is a continuation of MTH 503, including sequences and series of functions, uniform convergence, multivariate calculus, and other selected topics.

MTH 506 Theory of Functions of a Complex Variable 3(3-0), D

Prerequisite: MTH 302 and MTH 315. Theory of elementary functions-polynomial, trigonometric, exponential, hyperbolic, logarithmic-of a complex variable; their derivatives, integrals; power series; other selected topics.

MTH 507 Introduction to Partial Differential Equations 3(3-0), D

Prerequisite: 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.

MTH 532 Introduction to Abstract Algebra 3(3-0), F

Prerequisite: MTH 302 and MTH 315. Theory of groups, rings, integral domains, fields, polynomials.

MTH 533 Linear Algebra I 3(3-0), F,S

Prerequisite: MTH 302 and MTH 315. Vector spaces, linear independence, inner product spaces, linear transformations, Eigenvectors, diagonalization.

MTH 534 Linear Algebra II 3(3-0), D

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.

MTH 536 Theory of Numbers 3(3-0), D

Prerequisite: MTH 302 and MTH 315. Factorization, Euler totient function, congruences, primitive roots, quadratic residues and reciprocity law.

MTH 537 Applied Abstract Algebra 3(3-0), D

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.

MTH 540 (440) Statistical Theory I 3(3-0), F

Prerequisite: MTH 302 and MTH 315. Random variables, discrete and continuous probability functions, expectation, moment-generating functions, transformation of variables.

MTH 541 Statistical Theory II 3(3-0), S

Prerequisite: MTH 540. Estimation, complete and sufficient statistics, maximum likelihood estimation, hypothesis testing, nonparametric statistics.

MTH 543 Stochastic Modeling 3(3-0), S

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.

MTH 545 Applied Statistics 3(3-0), F

Prerequisite: 60 credit hours and either MTH 135 or MTH 138. 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.

MTH 546 Analysis of Variance and Design of Experiments 3(3-0), D

Prerequisite: MTH 345 or MTH 541 or MTH 545 or permission of the department head. Topics include analysis of variance, estimation of variance components, randomized incomplete blocks, Latin squares, factorial nested, split-plot designs, fixed, random and mixed models.

MTH 547 Applied Regression Analysis 3(3-0), D

Prerequisite: MTH 345 or MTH 541 or MTH 545 or permission of the department head. Topics include fitting a straight line, matrix models, residuals, selecting best equation, multiple regression, and nonlinear estimation.

MTH 548 Applied Time Series Analysis 3(3-0), F

Prerequisite: MTH 345 or MTH 541 or MTH 545 or permission of the department head. 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.

MTH 567 Introduction to Non-Euclidean Geometry 3(3-0), S

Prerequisite: MTH 302 and MTH 315. Development of non-Euclidean geometries; intensive study of hyperbolic geometry.

MTH 570 Combinatorial Analysis 3(3-0), D

Prerequisite: MTH 280. An introduction to combinatorial analysis including enumeration methods, combinatorial identities with applications to the calculus of finite differences and difference equations.

MTH 575 (370) History of Mathematics 3(3-0), F,S

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.

MTH 580 Applied Mathematics 3(3-0), D

Prerequisite: MTH 303 and MTH 533 or permission of the department head. 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.

MTH 582 Introductory Topology 3(3-0), D

Prerequisite: MTH 302 and MTH 315. Properties of abstract metric and topological spaces; discussion of concepts of compactness and connectedness.

MTH 596 (554) Readings 1-3, F,S

Prerequisite: permission of the department head. Periodic conferences with an advisor are required. May be repeated to a total of 6 hours.

MTH 601 Real Analysis 3(3-0), D

Prerequisite: MTH 503. 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 602 Real and Abstract Analysis 3(3-0), D

Prerequisite: MTH 601. A study of the theory of abstract measures and integration, and an introduction to functional analysis.

MTH 606 Complex Analysis 3(3-0), D

Prerequisite: MTH 503. 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 610 Contemporary Mathematics for Secondary Teachers 3(3-0), D

Prerequisite: either MTH 532 or MTH 533 and; either MTH 460 or MTH 567. Reports, research, and recent trends in secondary mathematics; recently developed programs in algebra and geometry.

MTH 621 Theory of Ordinary Differential Equations I 3(3-0), D

Prerequisite: MTH 303 and MTH 503. 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 622 Theory of Ordinary Differential Equations II 3(3-0), D

Prerequisite: MTH 621. 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 630 Abstract Algebra I 3(3-0), D

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

MTH 632 Abstract Algebra II 3(3-0), D

Prerequisite: MTH 630. 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 641 Statistical Inference I 3(3-0), D

Prerequisite: MTH 541. 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 642 Statistical Inference II 3(3-0), D

Prerequisite: MTH 641. 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 681 Topology 3(3-0), D

Prerequisite: MTH 503 or MTH 582. Point set topology in abstract spaces.

MTH 691 Seminar I 2(2-0), F,S

Seminar in Mathematics

MTH 692 Seminar II 2(2-0), F,S

Seminar in Mathematics.

MTH 697 (655) Topics 3(3-0), D

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 698 Research 1-6, F,S

Supervised research in special areas of mathematics. May be repeated. May not be counted toward the Master of Science in Education degree.

MTH 699 (694) Projects 1-6, F,S

Independent research for thesis preparation.