# Mathematics and Statistics Courses

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

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

Description

### Mathematics Courses

**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 100T Transitions (1)** (fall)

Course is designed to assist students in their transition to Murray State University.
Content includes orientation to the specific area or major(s) and minor(s) within
the academic program; university procedures, policies, and resources; strategies for
personal and academic success, and extracurricular opportunities. Only one transitions
course will count toward graduation. Required for all entering freshmen. 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 21 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 for 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 permission
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 312 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 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, with an emphaisis on population dynamics and evolutionary biology. Students
engage in research and communicate thier results. Laboratory experiences and short-distance
field trips are required. Only one of MAT 460 and 461 may count as a limited elective
for the mathematics major. Prerequisites: BIO 216 and MAT 250 or consent of instructor.
(Same as BIO 460.)

**MAT 461 Biomathematics in the Biomedical Sciences (3)**

A variety of quantitative biological models and their underlying mathematics are studied,
with an emphasis on epidemiology, genetics, and physiology. Students engage in research
and communicate their results. Laboratory experiences and short-distance field trips
are required. Only one of MAT 460 or MAT 461 may count as a limited elective for the
mathematics major. Prerequisites: MAT 250 and BIO 216 or consent of instructor. (Same
as BIO 461.)

**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 338.

**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 513 or permission 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, and 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,
and introduction to non-Euclidean geometry. Prerequisite: MAT 309 or permission 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 permission 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. Prerequisites: 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.
Prerequisite: 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 as different topics are offered. 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 as different topics are offered. Prerequisites:
Six hours of mathematics courses numbered 400 and above with a mathematics GPA of
at least 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 538 Ordinary Differential Equations II (3)**

Systems of differential equations (including matrix based solutions), higher order
differential equations, series solutions to differential equations, numerical applications,
and stability analysis. Prerequisites: MAT 335 and MAT 338.

**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 permission of instructor.
Requires knowledge of a scientific programming language.

**MAT 543 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. Prerequisites: MAT 308 or permission
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:
permission 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 permission of instructor.

**MAT 555 Probability in the Actuarial Sciences (3)**

Course develops knowledge of the fundamental probability tools for quantitatively
assessing risk. The application of these tools to problems encountered in actuarial
science is emphasized. Prerequisites: MAT 309 and STA 540 or 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 permission 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 permission of instructor.

**MAT 616 Introduction to Topology (3)** (taught with 516, fall of odd years)

Set theory, topology of the real line, topological spaces, and 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,
and introduction to non-Euclidean geometry. Prerequisite: MAT 309 or permission 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, MAT 335, and MAT 338 or permission of instructor.

**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 permission 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: permission
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: permission
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 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 638 Ordinary Differential Equations II (3)**Systems of differential equations (including matrix based solutions), higher order
differential equations, series solutions to differential equations, numerical applications,
and stability analysis. Prerequisites: MAT 335 and 338.

**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 permission 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 be applied as a 600-level course in an allied field for
the M.S. in Mathematics degree. May not be taken as a component of a 700-level mathematics
course.) Prerequisites: MAT 308 or permission 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:
permission 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 permission 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 permission of instructor.

**MAT 655 Probability in the Actuarial Sciences (3)**

Course develops knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. Does not count towards an M.A. in Mathematics degree. Prerequisite: STA 540 or 640 and MAT 309 or 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: permission
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 614 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, and Riemann-Stieltjes
integrals. Prerequisite: MAT 526 or 626 or consent of instructor.

**MAT 726 ( formerly 603) Real Function Theory I (3)** (spring with demand)

Lebesgue measure and integration theory and related topics. Prerequisite: MAT 725 or consent of instructor.

**MAT 727 ( formerly 604) Real Function Theory II (3)**

Functional analysis, including Classical Banach spaces and Lp spaces. Prerequisite: MAT 726.

**MAT 738 Advanced Ordinary Differential Equations (3)**Existence and uniqueness of first-order initial value problems. Linear systems of
differential equations. Boundary value problems. Stability of dynamical systems. Lyapunov’s
method. Periodicity of planar systems. Prerequisite: MAT 625 and MAT 638.

**MAT 742 Numerical Linear Algebra (3)**

Consideration of topics in numerical linear algebra: the Singular Value Decomposition,
QR Factorization, Conditioning and Stability, Advanced Iterative Methods. Prerequisite:
MAT 642.

**MAT 790 - Special Topics in Mathematics I**

Independent work on selected topics. May be repeated for credit. Prerequisite: permission
of instructor.

**MAT 791 ( formerly 691) Selected Topics in Mathematics II (1-3)**

Independent work on selected topics. May be repeated for credit. Prerequisite: permission of instructor.

**MAT 798 ( formerly 698) Research and Thesis (3)**

**MAT 799 ( formerly 699) Research and Thesis (3) **

### Statistics Courses

**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.

**STA 235 Introduction to Probability and Statistics II (3)**A study of applied statistical techniques, including re-expressing data, categorical
data analysis, regression inference, analysis of variance, multiple and non-linear
regression, and nonparametric analysis, from a conceptual standpoint. Prerequisite:
STA 135 or consent of instructor.

**STA (MAT) 450 Introduction to Engineering Statistics (3)**

Probability, population and sample distribution, sampling, hypothesis testing, regression
on one variable, and quality control. Prerequisite: MAT 309.

**STA 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 308 or permission
of instructor.

**STA 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: STA 540.

**STA 554 (formerly 560) Statistical Methods (3)** (fall)

A survey course in statistical methods for advanced undergraduate 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.)

**STA 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: STA 554 or permission of instructor.

**STA 566 Applied Statistics II (3)**

A continuation of STA 565. Includes further topics in analysis and variance, non-parametrics
and multivariate analysis. Prerequisite: STA 565.

**STA 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: STA 565 or permission of instructor.

**STA 568 Bayesian Methods (3)**

A study of Bayesian data analysis methods including Bayesian inference, hierarchical
modeling, model checking, model building, Bayesian computation, and convergence monitoring
and diagnostics. A Bayesian statistical computing package will be used when appropriate.
Prerequisites: STA 540 or 565 or consent of instructor.

**MAT 569 Topics in Statistics (3)**

Selected topics in probability and statistics. Prerequisite: permission of instructor.

**STA 633 Probability and Statistics (3)** (Fall, evening only)

An exploration of topics in probability and statistics from the viewpoint of future/current
secondary and community college teachers of mathematics and statistics. Such topics
include descriptive statistics, correlation and regression, uses and abuses of statistics
in real life, traditional and simulation-based approaches to teaching statistical
inference, common misconceptions in probability, and the AP Statistics curriculum.
(This course does not offer graduate credit for those people seeking a master of science
degree in mathematics or chemistry or a master of arts degree in mathematics.) Prerequisite:
permission of instructor.

**STA 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 308 or permission
of instructor.

**STA 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: STA 540 or 640.

**STA 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.)

**STA 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 STA
565 and 660 or STA 665 and 660. This course does not offer graduate credit for students
seeking a Master of Science in mathematics or chemistry, or a Master of Arts in mathematics.
Prerequisite: STA 554 or 654 or permission of instructor.

**STA 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: STA 554 or 654 or permission of instructor.

**STA 666 Applied Statistics II (3)**

A continuation of STA 665. Includes further topics in analysis and variance, non-parametrics
and multivariate analysis. Prerequisite: STA 565 or 665.

**STA 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: STA 565, STA 665, or consent of instructor.

**STA 668 Bayesian Methods (3)**

A study of Bayesian data analysis methods including Bayesian inference, Hierarchical
modeling, model checking, model building, Bayesian computation, and convergence monitoring
and diagnostics. A Bayesian statistical computing package will be used when appropriate.
Does not count towards a M.A. in Mathematics degree. Prerequisite: STA 565 or 665
or STA 540 or 640 or consent of instructor.

**MAT 669 Topics in Statistics (3)**Selected topics in probability and statistics. Prerequisite: consent of instructor.