# Mathematics and Statistics Courses

(see also **course offerings list by semester**)

**Format: MAT xyz Course Name (credit hours)**, (semesters usually offered)

Description

**MAT 095 Fundamental Mathematics (2)**(fall, spring, summer also online)

Basic operations as they pertain to integers, fractions, decimals, and percentages. Applied problems will include topics in geometry. A developmental and refresher course required for students with math ACT scores of 15 or below. Advanced placement into a higher-level math course is possible through assessment exams such as COMPASS or KYOTE. Credit earned in this course cannot be counted toward graduation requirements and cannot be used to fulfill university studies requirements. Students with credit in a higher-level math course may not schedule this course without instructor permission. Letter-graded course.**MAT 096 (formerly 100) Introductory Algebra (3)**(fall, spring, summer also online)

Introduction to roots, exponents, and polynomials; linear and quadratic equations; factoring; graphing; systems of equations and inequalities with applications using these concepts. A developmental and refresher course required for students with math ACT scores of 16-18. Advanced placement into a higher-level math course is possible through assessment exams such as COMPASS or KYOTE. Credit earned in this course cannot be counted toward graduation requirements and cannot be used to fulfill university studies requirements. Students with credit in a higher-level math course may not schedule this course without instructor permission. Prerequisite: ACT math score of 16-18 or MAT 095.**MAT 097 (formerly 105) Intermediate Algebra (4)**(fall, spring, summer, evening in spring)

Algebraic expressions, exponents, linear and quadratic equations, graphing, systems of equations, inequalities, and mathematical modeling. Students who have received a grade of C or better in any mathematics course numbered MAT 130 or above can not enroll in this course without written permission of the departmental chair. Credit earned in this course cannot be counted toward graduation requirements and cannot be used to fulfill university studies requirements. Required for students with a 19 ACT and degree requirements which include MAT 130, 135, 140, 145, or 150. Prerequisite: ACT math standard score of at least 19 or MAT 096.**MAT 099 Transitions (1)**(fall)

Required for all entering freshmen. Only one freshman orientation course will count toward graduation. Graded pass/fail. (Fall)**MAT 115 Mathematics for Middle and Elementary Teachers I (3)**(fall, spring)

Development of the real number system with arithmetic and basic ideas of algebra. A course specifically designed for the needs of future elementary and middle school teachers. Cannot be used for university studies requirements. Prerequisite: Math ACT score of at least 20 or KYOTE score of at least 22 or a COMPASS algebra score of at least 41 or MAT 097.**MAT 117 Mathematical Concepts (3)**(fall also online, spring also online, summer)

Provides students with problem-solving skills and literacy related to the mathematics which is commonly encountered in our society. Topics can include descriptive statistics, personal finance, voting methods, elementary probability, and graph theory. This course is especially appropriate for students whose degree programs do not otherwise require a course in mathematics. It is not an adequate preparation for any other mathematics course. Prerequisite: ACT math standard score of at least 19 or MAT 096.**MAT 120 College Algebra with Business Applications (4)**(fall, spring)

A study of algebra with motivating examples and applications from various fields of business. Topics include linear, quadratic, rational, exponential and logarithmic equations and functions, systems of linear equations and the mathematics of finance. A student may not receive credit for MAT 120 and MAT 130 or 140 or 150. Prerequisites: ACT Math standard score of at least 21 or MAT 097.**MAT 130 Technical Math I (5)**(fall, spring)

Topics from algebra and trigonometry for the technology student. Restriction: A student may not receive credit for MAT 130 and 140 or 145 or 150. Prerequisite: ACT math standard score of at least 20 or MAT 097.**STA 135 Introduction to Probability and Statistics (4)**(fall, spring, summer)

Elementary probability, the binomial, normal, student's and chi-square distributions, random sampling, regression and correlation. Prerequisite: ACT math standard score of at least 20 or MAT 097.**MAT 140 College Algebra (4)**(fall, spring, summer, evening in fall)

Course develops and extends the student's basic algebra concepts and problem-solving skills in the context of functions, models, and applications. Topics include exponents and radicals, graphing, setting up and solving equations in linear, quadratic, and other forms, systems of equations, and operations on functions. Properties and applications of linear, quadratic, polynomial, rational, exponential, and logarithmic functions are studied. Prerequisite: ACT math standard score of at least 21 or MAT 097. A student may not receive credit for MAT 140 and 130 or 150. (MAT 140 in combination with MAT 145 will substitute for MAT 150.)**MAT 145 Trigonometry (3)**(fall, spring, summer)

Course is a study of plane trigonometry. Topics include angles, right triangle trigonometry, trigonometric functions and their graphs, identities, solving trigonometric equations, and applications of trigonometry. Prerequisite: ACT math standard score of at least 21 or MAT 097. A student may not receive credit for MAT 145 and MAT 130 or 150. (MAT 145 in combination with MAT 140 will substitute for MAT 150.)**MAT 150 Algebra and Trigonometry (5)**(fall, spring)Course is an intensive study of college algebra and trigonometry. A combination of MAT 140 and MAT 145, it is a faster-paced course for students with some familiarity with the subjects. MAT 150 may be used as a "refresher" course to help prepare students for MAT 250. Prerequisite: ACT math standard score of at least 23. Restriction: A student who receives credit for MAT 150 may not receive credit for MAT 130, 140 or 145. (Credit or the combination of MAT 140 and MAT 145 will substitute for MAT 150.)**MAT 215 Mathematics for Middle and Elementary Teachers II (3)**(fall, spring)Geometry, measurements, probability and statistics for elementary and middle school teachers. Cannot be used for university studies requirements. Prerequisite: Math ACT score of at least 20 or KYOTE score of at least 22 or a COMPASS algebra score of at least 41 or MAT 097.**MAT 220 Business Calculus (3)**(fall, spring, sometimes summer, evening in spring)An introduction to calculus and its applications for students in various fields of business. Primary emphasis is on differential calculus. Prerequisite: MAT 120 or 140 or math ACT score of at least 23.**MAT 230 Technical Math II (5)**(fall, spring)

Analytic geometry, differential and integral calculus with applications from technical fields. Prerequisite: MAT 130 or ACT math standard score of at least 24.**MAT 250 Calculus and Analytic Geometry I (5)**(fall, spring)

First course in calculus develops main ideas of differentiation and integration of single-variable functions. Topics include limits, continuity, techniques of differentiation, graphing techniques, definite and indefinite integral, basic integration methods, and applications of the derivative and integral to natural and social sciences. Prerequisites: ACT math standard score of at least 26 or MAT 150 or MAT 140/145.**MAT 305 Intermediate Geometry (3)**(fall, spring in Paducah, Madisonville, Hopkinsville)

Selected elementary topics in Euclidean geometry. Includes studies in parallelism, similarity, congruence, areas, volumes, elementary transformation, and coordinate geometry. Intended for students seeking middle school certification. Prerequisite: MAT 115 or 215.**MAT 308 Calculus and Analytic Geometry II (5)**(fall, spring)A continuation of MAT 250, this course further develops techniques and applications of integration and is an introduction to sequences and series. Topics include integration strategies, computing areas and volumes, arc length, parametric curves, polar coordinates, sequences and series, tests for convergence of series, power series, and Taylor series. Prerequisite: MAT 250.**MAT 309 Calculus and Analytic Geometry III (4)**(fall, spring)

Course develops main ideas of differentiation and integration of functions of several variables and introduces vector calculus. Topics include vectors, analytic geometry of 3-dimensional space, functions of several variables, partial derivatives, directional derivatives, integrals of functions of two and three variables, vector fields, line integrals, Green's theorem, and the divergence theorem. Prerequisite: MAT 308.**MAT 312 Mathematical Reasoning (3)**(fall, spring)Course designed to improve the students understanding of the nature and methods of mathematical proof by means of practice and participation. The content will include mathematical logic, set theory, relations and functions, cardinality, axiomatic structures, techniques of proof, and extensive practice in proof and problem solving. Credit cannot be received for both MAT 312 and 399. The department recommends a student take this course in his/her sophomore year in the program. Prerequisite: MAT 308 or consent of instructor.**MAT 330 Technical Math III (3)**(spring)

Continuation of MAT 230. Includes differentiation and integration of transcendental functions, series expansions of functions, and differential equations. Prerequisite: MAT 230.**MAT 335 Matrix Theory and Linear Algebra (3)**(fall (also in Paducah), spring)

The algebra of matrices and its application to problems in Euclidean spaces and elementary linear transformations. Prerequisite: MAT 308.**MAT 338 (formerly 411) Ordinary Differential Equations (3)**(fall, spring, summer with demand)

First-order differential equations, linear equations with constant coefficients, linear and nonlinear systems of equations. Prerequisite: MAT 308.**MAT 399 Sets, Logic and Functions (3)**(fall in Paducah, Madisonville, Hopkinsville, spring)

An investigation of mathematical reasoning including techniques of mathematical exploration, problem-solving and proof. Intended for students seeking Middle School Certification. Does not count toward a major or minor in mathematics and credit cannot be received for both MAT 299 and MAT 399. Prerequisite: MAT 250 or consent of instructor.**MAT 421 Introductions to Algebraic Structures (3)**An elementary study of the major structures in modern algebra including groups, rings, fields and integral domains. Prerequisite: MAT 308 and 312.**MAT 440 Mathematics Transforms with Applications (3)**Integral and discrete transforms, such as Laplace and Fourier transforms, and the z-transform. Power series solutions and special functions. Prerequisite: MAT 338 or consent of instructor.**MAT 442 Introduction to Numerical Analysis (3)**(spring)

Taylor polynomial approximation, numerical root finding methods and fixed-point iteration, polynomial and spline interpolation, numerical differentiation and integration, and direct methods for the solutions of linear systems. Prerequisite: MAT 308 or consent of instructor.**MAT 450 Introduction to Engineering Statistics (3)**(spring in Paducah)

Probability, population and sample distribution, sampling, hypothesis testing, regression on one variable, and quality control. Prerequisite: MAT 309.**MAT 460 Principles of Biomathematics (3)**The study of biological and mathematical models is united in this research-based course. A variety of quantitative biological models and their underlying mathematics are studied. Students engage in research and communicate their results. Laboratory experiences and short-distance field trips are required. Prerequisites: BIO 216 and MAT 250 or consent of instructor. (Same as BIO 460.)**MAT 488 Cooperative Education/Internship (1-3)**A meaningful, planned, and evaluated work experience related to the career and educational objectives of the student for which he/she may receive academic credit and possible financial remuneration. May be repeated for a maximum of six hours from any 488/489 courses. Graded pass/fail. Prerequisite: permission of chair.**MAT 489 Cooperative Education/Internship (1-3)**A meaningful, planned, and evaluated work experience related to the career and educational objectives of the student for which he/she may receive academic credit and possible financial remuneration. May be repeated for a maximum of six hours from any 488/489 courses. Prerequisite: permission of chair.**MAT 500 Internship (1)**Graded pass/fail.**MAT 506 (formerly 501) Mathematical Modeling I (3)**(fall of odd years)

A study of mathematical models used in the social, life and management sciences and their role in explaining and predicting real world phenomena. The emphasis is on developing skills of model building. Topics include difference equations, perturbation theory and non-dimensional analysis. Prerequisite: MAT 338.**MAT 507 (formerly 502) Mathematical Modeling II (3)**A continuation of topics discussed in MAT 501. A term project consisting of a model of a non-mathematical problem is required. Prerequisite: MAT 501.**MAT 508 Introduction to Combinatorics and Graph Theory (3)**(summer, in rotation)

Selected topics and applications from combinatorics and discrete mathematics, which can include: enumeration, generating functions, recurrence relations, partially ordered sets, Boolean algebras, block designs, coding theory, and topics in graph theory, including trees, networks, optimization, and scheduling. Prerequisites: MAT 308 and either MAT 312 or MAT 335.**MAT 512 Partial Differential Equations (3)**Partial differential equations of first and second order and applications. Prerequisites: MAT 309 and 411.**MAT 513 Modern Algebra I (3)**(fall)

An in-depth study of groups. Topics will include permutation groups, cyclic groups, cosets and factor groups, subgroups and normal groups, and the homomorphism theorems. Some introductory discussions of rings and fields will be included as well. Prerequisites: MAT 308 and 312.**MAT 514 (formerly 521) Modern Algebra II (3)**(spring)

An in-depth study of rings and fields. Topics will include the Isomorphism Theorems, ideals, polynomial rings, integral domains, fields, field extensions. Prerequisite: MAT 421 or consent of instructor.**MAT 515 Theory of Numbers (3)**(spring of odd years)

Divisibility, the Euclidean algorithm, mathematical induction, prime and composite numbers, Diophantine equation, Pythagorean triplets, Fermat's Theorem, congruencies, quadratic residues, continued fractions. Prerequisite: MAT 312.**MAT 516 Introduction to Topology (3)**(fall of odd years)

Set theory, topology of the real line, topological spaces, metric spaces. Prerequisite: MAT 309 and 312.**MAT 517 (formerly 510) Foundations of Geometry (3)**(spring)

Study of postulate systems for geometry, critical examination of Euclid's Elements, introduction to non-Euclidean geometry. Prerequisite: MAT 309 or consent of instructor.**MAT 522 Vector Calculus (3)**Operations with vectors; differentiation and integration of functions of several variables; transformation of coordinates; line and surface integrals; Green's, Stokes', and the divergence theorems. Prerequisite: MAT 309.**MAT 523 (formerly 520) Introduction to Complex Variables (3)**(fall of even years)

Complex numbers, analytic functions, elementary functions, integration, Cauchy theorem, Taylor and Laurent expansions, and applications. Prerequisite: MAT 309.**MAT 524 Boundary Value Problems (3)**(spring)

Analytic and computational techniques for linear first and second order partial differential equations, initial, and boundary value problems. Classification, Fourier series, separation of variables, finite difference and/or finite element methods. Prerequisites: MAT 309, 335 or consent of instructor, and 338.**MAT 525 Advanced Calculus I (3)**(fall)

A rigorous development of one variable calculus including limits, continuity, differentiation, integration and sequences of functions. Prerequisite: MAT 309 and 312.**MAT 526 Advanced Calculus II (3)**(spring)

A continuation of MAT 525 and functions of several variables. Prerequisite: MAT 525.**MAT 528 Introduction to Game Theory (3)**(summer, in rotation)

In this introductory course, we investigate mathematical models of certain conflict and cooperation situations (games), paying attention to applications in biology, philosophy, political science, economics, and social psychology. We study two-person zero-sum games, two-person non-zero-sum games, and/or other multi-player games. We consider pure and mixed strategy solutions, Nash equilibria, and other aspects of such games. Prerequisites: MAT 250 or consent of instructor.**MAT 530 Special Topics in Mathematics I (1-3)**Library investigations of various lengths concerning special topics in mathematics. Periodic conferences will be arranged with the supervising faculty member on an individual basis. May be repeated for credit. Prerequisites: Six hours of mathematics courses numbered 400 and above with a mathematics GPA of at least 3.0; consent of instructor.**MAT 531 Special Topics in Mathematics II (1-3)**Library investigations of various lengths concerning special topics in mathematics. Periodic conferences will be arranged with the supervising faculty member on an individual basis. May be repeated for credit. Prerequisites: Six hours of mathematics courses numbered 400 and above with a mathematics GPA of at least a 3.0; consent of instructor.**MAT 535 Linear Algebra (3)**(spring of even years)

Linear transformations, matrices, quadratic and hermitian forms, eigenvalues and elementary spectral theory. Prerequisite: MAT 335.**MAT 540 Mathematical Statistics I (4)**(fall)

Introduction to probability theory and statistical inference. Combinatorics, conditional probability independence. Discrete and continuous random variables and their distributions. Expected value and moments of distributions. Estimation theory and properties point estimators. Confidence intervals. Basic theory of hypothesis testing. Testing means and proportion. T-tests. Descriptive statistics. Prerequisite: MAT 309 or consent of instructor.**MAT 541 Mathematical Statistics II (3)**(spring)

Additional topics in probability theory and statistical inference. Bayes' Theorem, functions of random variables, order statistics. Bayesian inference, F-tests, chi-square tests, contingency tables, regression and correlation. Prerequisites: MAT 540.**MAT 542 Numerical Analysis (3)**(fall of even years)

Numerical solutions of differential equations, iterative techniques for solving linear systems, discrete least-squares methods, orthogonal polynomials, and approximating eigenvalues. Prerequisites: MAT 338 and either MAT 442 or consent of instructor. Requires knowledge of a scientific programming language.**MAT 543 Financial Matters (3)**Course develops an understanding of the fundamental concepts of financial mathematics. Concepts will be applied in calculating present and accumulated values for various streams of cash flows for future use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and contingencies. An introduction to financial instruments, including derivatives, and concept of nonarbitrage as it relates to financial mathematics may also be provided. Prerequisites: MAT 308 or consent of instructor.**MAT 545 Boolean Algebra with Applications to Digital Computer Design (3)**Boolean algebra is developed as a model to study various physical systems, including the algebra of subsets of a set, propositional logic, and switching circuits. Prerequisite: consent of instructor.**MAT 550 Teaching Mathematics (3)**(fall)

A study of the "whys" of mathematics with the aim of equipping future/current teachers with the ability to explain rather than merely do mathematics. Taught in the context of theories of learning and pedagogy. Involves mathematics content taught at the secondary and community college level. Credit granted toward an undergraduate major or minor in mathematics only for those students following a teacher certification program. Prerequisite: MAT 312 or consent of instructor.**MAT 551 Mathematics for Teachers (3)**(spring)

Explorations of mathematical topics from the viewpoint of future/current secondary and community college teachers of mathematics. Gives credit toward an undergraduate major or minor in mathematics only for those students following a teacher certification program. Can be taken without MAT 550. Prerequisite: MAT 312 or consent of instructor.**MAT 554 (formerly 560) Statistical Methods (3)**(fall)

A survey course in statistical methods for advanced undergraduate students and graduate students with no prior training in statistics. The course covers techniques commonly used for data analysis in many scientific fields. Topics included are probability distributions, sampling, variance, estimation, hypothesis testing, contingency table, regression and analysis of variance. (Does not apply toward any degree in mathematics or a minor in mathematics.)**MAT 565 Applied Statistics I (4)**(spring)

A study of applied statistical techniques including correlation, regression, analysis of variance and non-parametric methods with a view toward applications. A statistical computer package will be used when appropriate, but no computer background is required. Prerequisite: MAT 560 or consent of instructor.**MAT 566 Applied Statistics II (3)**A continuation of MAT 565. Includes further topics in analysis and variance, non-parametrics and multivariate analysis. Prerequisite: MAT 565.**MAT 567 Introduction to Time Series Analysis (3)**An introductory time series analysis course that introduces students to classical and modern time series models. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to forecast future events based on known past events: to predict data points before they are measured. This course serves junior and senior mathematics majors, mathematics minors, and other interested students. A student taking this course should have a background in statistical methods. Prerequisites: MAT 565 or consent of instructor.**MAT 569 Topics in Statistics (3)**Selected topics in probability and statistics. Prerequisite: consent of instructor.**MAT 570 Linear Programming (3)**(summer, in rotation)

Theory and application of linear programming and the role it plays in operations research. Prerequisite: MAT 335.**MAT 606 (formerly 501) Mathematical Modeling I (3)**(taught with 506, fall of odd years)

A study of mathematical models used in the social, life and management sciences and their role in explaining and predicting real world phenomena. The emphasis is on developing skills of model building. Topics include difference equations, perturbation theory and non-dimensional analysis. Prerequisite: MAT 338.**MAT 607 (formerly 502) Mathematical Modeling II (3)**A continuation of topics discussed in MAT 606. A term project consisting of a model of a non-mathematical problem is required. Prerequisite: MAT 506 or 606.**MAT 608 Introduction to Combinatorics and Graph Theory (3)**(taught with 508, summer, in rotation)

Selected topics and applications from combinatorics and discrete mathematics, which can include: enumeration, generating functions, recurrence relations, partially ordered sets, Boolean algebras, block designs, coding theory, and topics in graph theory, including trees, networks, optimization, and scheduling. Prerequisites: MAT 308 and either MAT 312 or MAT 335.**MAT 613 Modern Algebra I (3)**(taught with 513, fall)

An in-depth study of groups. Topics will include permutation groups, cyclic groups, cosets and factor groups, subgroups and normal groups, and the homomorphism theorems. Some introductory discussions of rings and fields will be included as well. Prerequisites: MAT 308 and 312.**MAT 614 (formerly 621) Modern Algebra II (3)**(taught with 514, spring)

An in-depth study of rings and fields. Topics will include the Isomorphism Theorems, ideals, polynomial rings, integral domains, fields, field extensions. Prerequisite: MAT 513, 613, or consent of instructor.**MAT 615 Theory of Numbers (3)**(taught with 515, spring of odd years)

Divisibility, the Euclidean algorithm, mathematical induction, prime and composite numbers, Diophantine equation, Pythagorean triplets, Fermat's Theorem, congruencies, quadratic residues, continued fractions. Prerequisite: MAT 312 or consent of instructor.**MAT 616 Introduction to Topology (3)**(taught with 516, fall of odd years)

Set theory, topology of the real line, topological spaces, metric spaces. Prerequisite: MAT 309 and 312.**MAT 617 (formerly 510) Foundations of Geometry (3)**(taught with 517, spring)

Study of postulate systems for geometry, critical examination of Euclid's Elements, introduction to non-Euclidean geometry. Prerequisite: MAT 309 or consent of instructor.**MAT 623 (formerly 520) Introduction to Complex Variables (3)**(taught with 523, fall of even years)

Complex numbers, analytic functions, elementary functions, integration, Cauchy theorem, Taylor and Laurent expansions, and applications. Prerequisite: MAT 309.**MAT 624 Boundary Value Problems (3)**(taught with 524, spring)

Analytic and computational techniques for linear first and second order partial differential equations, initial, and boundary value problems. Classification, Fourier series, separation of variables, finite difference and/or finite element methods. Prerequisites: MAT 309, 335, or consent of instructor, and 338.**MAT 625 Advanced Calculus I (3)**(taught with 525, fall)

A rigorous development of one variable calculus including limits, continuity, differentiation, integration and sequences of functions. Prerequisite: MAT 309 and 312.**MAT 626 Advanced Calculus II (3)**(taught with 526, spring)

A continuation of MAT 625 and functions of several variables. Prerequisite: MAT 525 or 625.**MAT 628 Introduction to Game Theory (3)**(taught with 528, summer, in rotation)

In this introductory course, we investigate mathematical models of certain conflict and cooperation situations (games), paying attention to applications in biology, philosophy, political science, economics, and social psychology. We study two-person zero-sum games, two-person non-zero-sum games, and/or other multi-player games. We consider pure and mixed strategy solutions, Nash equilibria, and other aspects of such games. Prerequisites: MAT 250 or consent of instructor.**MAT 630 Real Number System I (3)**(Fall, evening only)

Development of the natural numbers and the integers. (This course does not offer graduate credit for those people seeking a master of science degree in mathematics, chemistry or physics, or a master of arts degree in mathematics.) Prerequisite: consent of instructor.**MAT 631 Real Number System II (3)**(Fall, evening only)

A detailed development of the rational and real numbers. (This course does not offer graduate credit for those people seeking a master of science degree in mathematics, chemistry, or physics, or a master of arts degree in mathematics.) Prerequisite: consent of instructor.**MAT 632 Foundations of Analysis (3)**(Fall, evening only)

A study of concepts basic to the elementary calculus, such as limits continuity, the derivative, and the integral. (This course does not offer graduate credit to those people seeking a master of science degree in mathematics, chemistry, or physics, or a master of arts degree in mathematics.) Prerequisites: MAT 309 and consent of instructor.**MAT 633 Probability and Statistics (3)**(Fall, evening only)

An introduction to sample spaces, probabilities, and probability distributions, such as binomial, normal and Poisson. Measure of center, variability and applications. Statistical inference and tests of significance. (This course does not offer graduate credit for those people seeking a master of science degree in mathematics, chemistry, or physics, or a master of arts degree in mathematics.) Prerequisite: consent of instructor.**MAT 635 Linear Algebra (3)**(taught with 535, spring of even years)

Linear transformations, matrices, quadratic and hermitian forms, eigenvalues and elementary spectral theory. Prerequisite: MAT 335.**MAT 640 Mathematical Statistics I (4)**(taught with 540, fall)

Introduction to probability theory and statistical inference. Combinatorics, conditional probability independence. Discrete and continuous random variables and their distributions. Expected value and moments of distributions. Estimation theory and properties point estimators. Confidence intervals. Basic theory of hypothesis testing. Testing means and proportion. T-tests. Descriptive statistics. Prerequisite: MAT 309 or consent of instructor.**MAT 641 Mathematical Statistics II (3)**(taught with 541, spring)

Additional topics in probability theory and statistical inference. Bayes' Theorem, functions of random variables, order statistics. Bayesian inference, F-tests, chi-square tests, contingency tables, regression and correlation. Prerequisites: MAT 540 or 640.**MAT 642 Numerical Analysis (3)**(taught with 542, fall of even years)

Numerical solutions of differential equations, iterative techniques for solving linear systems, discrete least-squares methods, orthogonal polynomials, and approximating eigenvalues. Requires knowledge of a scientific programming language. Prerequisites: MAT 338 and either MAT 442 or consent of instructor.**MAT 643 Financial Mathematics (3)**Course develops an understanding of the fundamental concepts of financial mathematics. Concepts will be applied in calculating present and accumulated values for various streams of cash flows for future use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and contingencies. An introduction to financial instruments, including derivatives, and concept of nonarbitrage as it relates to financial mathematics may also be provided. (Note: Does not apply towards an M.A. in Mathematics degree; may be applied as a mathematics course in the M.A.T. in Mathematics degree. May not be taken as a component of a 700-level mathematics course.) Prerequisites: MAT 308 or consent of instructor.**MAT 644 Graduate Cooperative Education (3)**May be repeated to maximum of six credits. Graded pass/fail.**MAT 645 Boolean Algebra with Applications to Digital Computer Design (3)**Boolean algebra is developed as a model to study various physical systems, including the algebra of subsets of a set, propositional logic, and switching circuits. Prerequisite: consent of instructor.**MAT 650 Teaching Mathematics (3)**(taught with 550, fall)

A study of the "whys" of mathematics with the aim of equipping future/current teachers with the ability to explain rather than merely do mathematics. Taught in the context of theories of learning and pedagogy. Involves mathematics content taught at the secondary and community college level. Prerequisite: MAT 312 or consent of instructor.**MAT 651 Mathematics for Teachers (3)**(taught with 551, spring)

Explorations of mathematical topics from the viewpoint of future/current secondary and community college teachers of mathematics. Can be taken without MAT 650. Prerequisite: MAT 312 or consent of instructor.**MAT 654 (formerly 560) Statistical Methods (3)**(taught with 554, fall)

A survey course in statistical methods for advanced undergraduate students and graduate students with no prior training in statistics. The course covers techniques commonly used for data analysis in many scientific fields. Topics included are probability distributions, sampling, variance, estimation, hypothesis testing, contingency table, regression and analysis of variance. (Does not apply toward any degree in mathematics.)**MAT 660 Biostatistics (4)**(summer, online only)

A study of applied statistical techniques including correlation, regression, analysis of variance, categorical data analysis and non-parametric methods with a view toward applications in clinical research and health related sampling. A statistical computing package will be used when appropriate. A student may not receive credit for both MAT 565 and MAT 660. Prerequisite: MAT 554 or consent of instructor.**MAT 665 Applied Statistics I (4)**(taught with 565, spring)

A study of applied statistical techniques including correlation, regression, analysis of variance and non-parametric methods with a view toward applications. A statistical computer package will be used when appropriate, but no computer background is required. Prerequisite: MAT 554, 654 or consent of instructor.**MAT 666 Applied Statistics II (3)**A continuation of MAT 665. Includes further topics in analysis and variance, non-parametrics and multivariate analysis. Prerequisite: MAT 565 or 665.**MAT 667 Introduction to Time Series Analysis (3)**Linear time series models; moving average, autoregressive and/or ARIMA models; estimation, data analysis and forecasting with time series models; forecast errors and confidence intervals. Prerequisites: MAT 565, MAT 665, or consent of instructor.**MAT 669 Topics in Statistics (3)**Selected topics in probability and statistics. Prerequisite: consent of instructor.**MAT 670 Linear Programming (3)**(taught with 570, summer, in rotation)

Theory and application of linear programming and the role it plays in operations research. Prerequisite: MAT 335.**MAT 690 Selected Topics in Mathematics I (1-3)**Independent work on selected topics. May be repeated for credit. Prerequisite: consent of instructor.**MAT 716 (formerly 620) Selected Topics in Topology (3)**(spring of even years with demand)

An in-depth study of selected topics introduced in MAT 616. Prerequisite: MAT 516 or 616.**MAT 721 Algebra (3)**(fall with demand)

An in-depth study of group theory. Topics will include Lagrange's Theorem, Cauchy's Theorem, the Sylow Theorems, and factor groups. Prerequisite: MAT 514 or 614.**MAT 722 (formerly 610) Selected Topics in Algebra (3)**An in-depth study of selected topics introduced in MAT 521 and 721. Prerequisite: MAT 721.**MAT 723 (formerly 605) Selected Topics in Complex Analysis (3)**(spring of odd years with demand)

An in-depth study of selected topics introduced in MAT 623. Prerequisite: MAT 523 or 623.**MAT 725 (formerly 602) Integration Theory (3)**(fall)

Riemann integrals, continuous functions, functions of bounded variation, Riemann-Stieltjes integrals. Prerequisite: MAT 525 or 625.**MAT 726 (**(spring with demand)**formerly**603) Real Function Theory I (3)

Lebesgue measure and integration theory and related topics. Prerequisite: MAT 526 or 626.**MAT 727 (**Functional analysis, including Classical Banach spaces and Lp spaces. Prerequisite: MAT 726.**formerly**604) Real Function Theory II (3)**MAT 790 - Special Topics in Mathematics I****MAT 791 (**Independent work on selected topics. May be repeated for credit. Prerequisite: consent of instructor.**formerly**691) Selected Topics in Mathematics II (1-3)**MAT 798 (****formerly**698) Research and Thesis (3)**MAT 799 (****formerly**699) Research and Thesis (3)