__Mathematics
MATH__

*General education courses
are marked with stars ()*.

*No student may receive
more than nine semester hours of credit in mathematics courses numbered below
1550, with the exception of students who are pursuing the elementary education
degree and following the 12-hour sequence specified in that curriculum. No student
who has already received credit for a mathematics course numbered 1550 or above
may be registered in a mathematics course numbered below 1550, unless given
special permission by the Department of Mathematics*.

**0091 Preparation
for College Mathematics I (4)** *Prereq: placement by department.
3 hrs. lecture; 1 hr. recitation/lab. For students not prepared to take MATH
0092. Not for degree credit; 4 sem. hrs. will be added to the degree program
of any student taking this course. No student who has received credit for a
mathematics course numbered 1000 or above may register for this course*.
Real numbers; elementary equations and inequalities; polynomials and basic factoring;
algebraic fractions; graphing linear equations.

**0092 Preparation
for College Mathematics II (4)** *Prereq: MATH 0091 or placement by
department. 3 hrs. lecture; 1 hr. recitation/lab. For students not prepared
to take MATH 1009, 1015, or 1021. Not for degree credit; 4 sem. hrs. will
be added to the degree program of any student taking this course. No student
who has received credit for a mathematics course numbered 1000 or above may
register for this course*. Linear equations and inequalities, polynomials
and factoring, algebraic fractions, operations on radical expressions, rational
exponents, quadratic equations, graphing.

**1009 Mathematics
for Prospective Elementary School Teachers I (3) V** *Prereq: MATH
0092 or placement by department. Offered by correspondence only*. Logic;
counting numbers, integers, rational numbers, real numbers; emphasis on field
properties; set nomenclature and some number theory; units of measurement.

**1010 Mathematics
for Prospective Elementary School Teachers II (3) V** *Prereq: MATH
1009. Offered by correspondence only. Continuation of MATH 1009*. Measurement,
informal geometry, systems of equations, introduction to probability and statistics.

**1015 Basic Mathematics
and Applications (3) V** *Prereq: MATH 0092 or placement by department.
This course does not serve as a prerequisite for calculus. Credit will not be
given for both this course and MATH 1021, 1022, or 1023. Offered by correspondence
only*. Basic mathematical skills of graphing, formulas for geometric measurement,
systems of linear equations and inequalities, review of quadratic equations,
logarithms and application to exponential growth and decay, triangle trigonometry
and its application to geometry and measurements.

** 1021 College Algebra
(3) F,S,Su** *Prereq: MATH 0092 or placement by department. Credit
will not be given for both this course and MATH 1015 or 1023*. Quadratic
equations, systems of linear equations, inequalities, functions, graphs, exponential
and logarithmic functions, complex numbers, theory of equations.

** 1022 Plane Trigonometry
(3) F,S,Su** *Prereq: MATH 1021 or placement by department. Credit
will not be given for both this course and MATH 1015 or 1023*. Trigonometric
functions and identities, inverse trigonometric functions, graphs, solving triangles
and equations, complex numbers, polar coordinates.

** 1023 College Algebra
and Trigonometry (5) F,S,Su** *Prereq: placement by department or
grade of "A" in MATH 0092. Credit will not be given for both this course and
MATH 1015, 1021, or 1022. For qualified students, a replacement for MATH 1021
and 1022 as preparation for calculus*.

**1025 Mathematics
of Commerce (3) F,S** *Prereq: MATH 1015 or 1021*. Interest, discount,
annuities, depreciation, and insurance.

** 1029 Introduction
to Contemporary Mathematics (3)** *Prereq: MATH 0092 or placement
by department. Primarily for students in liberal arts and social sciences. 2
hrs. lecture; 2 hrs. lab*. Mathematical approaches to contemporary problems
of growth, size, and measurement, handling of data, and optimization using basic
concepts from algebra, geometry, and discrete mathematics.

** 1100 The Nature
of Mathematics (3) F,S,Su** *Prereq: MATH 1021 or 1029 or consent
of department. Not for science, engineering, or mathematics majors. For students
who desire an exposure to mathematics as part of a liberal education. An honors
course, MATH 1101, is also available*. Logic; the algebra of logic, computers,
and number systems; networks and combinatorics; probability and statistics.

** 1101 HONORS: The
Nature of Mathematics (3) V** *Prereq: a grade of "A" in MATH 1021
or consent of department. Same as MATH 1100, with special honors emphasis for
qualified students*. Logic; the algebra of sets, logic, and networks; probability
and statistics; game theory; infinities; famous impossibilities and unsolved
problems.

**1201 Number Sense
and Open-Ended Problem Solving (3) F,S,Su** *Prereq: MATH 1021. Primarily
for students in the elementary education curriculum*. Cardinality and integers;
decimal representation and the number line; exploratory data analysis; number
sense; open-ended problem solving strategies; written communication of mathematics.

**1202 Geometry, Reasoning,
and Measurement (3) F,S,Su** *Prereq: MATH 1201. Primarily for students
in the elementary education Holmes curriculum*. Synthetic and coordinate
geometry in two and three dimensions; spatial visualization and counting procedures;
symmetries and tilings; history of geometry; written communication of mathematics.

** 1431 Calculus with
Business and Economic Applications (3) F,S,Su** *Prereq: MATH 1021
or equivalent. Credit will be given for only one of the following: MATH 1431,
1441, 1550*. Differential and integral calculus of algebraic, logarithmic,
and exponential functions; applications to business and economics, such as maximum-minimum
problems, marginal analysis, and exponential growth models.

** 1435 Mathematics
for Business Analysis (3) F,S,Su** *Prereq: MATH 1431 or equivalent*.
Sets and counting; probability, including conditional probability, discrete
and continuous random variables, variance, and normal distributions; matrices
and echelon method for solving systems of equations; functions of several variables
and partial derivatives.

** 1441 Calculus with
Application to Technology (3) F,S** *Prereq: MATH 1021 and 1022; or
1023; or consent of department. Credit will be given for only one of the following:
MATH 1431, 1441, 1550*. Differentiation and integration of algebraic and
trigonometric functions; application to technology.

** 1550 Analytic Geometry
and Calculus I (5) F,S,Su** *Prereq: MATH 1022 or 1023 or consent
of department. An honors course, MATH 1551, is also available. Credit will be
given for only one of the following: MATH 1431, 1441, 1550*. Analytic geometry,
limits, derivatives, integrals.

** 1551 HONORS: Analytic
Geometry and Calculus I (5) F** *Same as MATH 1550, with special honors
emphasis for qualified students*.

** 1552 Analytic Geometry
and Calculus II (4) F,S,Su** *Prereq: MATH 1550. An honors course,
MATH 1553, is also available*. Techniques of integration, parameter equations,
polar coordinates, infinite series, vectors in low dimensions; introduction
to differential equations and partial derivatives.

** 1553 HONORS: Analytic
Geometry and Calculus II (4) S** *Same as MATH 1552 with special honors
emphasis for qualified students*.

**1635 Further Calculus
for Quantitative Analysis (5)** *Prereq: MATH 1435 or 1550. Credit
will not be given for this course and either MATH 1552 or 2057*. Selected
topics in single-variable calculus, including related rates, Riemann sums, Newton's
method, elementary differential equations, infinite sequences and series; functions
of several variables, including partial derivatives, least squares regression,
Lagrange multipliers, double integrals; vectors in two and three dimensions.

**2020 Solving Discrete
Problems (3) F,S** *Prereq.: MATH 1550*. Logic, counting, discrete
probability, graph theory, and number theory.

**2025 Integral Transforms
and Their Applications (3) F,S** *Prereq.: MATH 1552*. Introduction
to mathematical proofs and structures using selected topics from analysis; series
of functions, Fourier series, Fourier integrals, and introduction to wavelets;
applications in differential equations and signal processing.

**2030 Discrete Dynamical
Systems (3) F,S** *Prereq.: MATH 1552 or permission of instructor*.
Dynamical systems with discrete time and in one spatial dimension; hyperbolicity;
quadratic maps; chaos; structural stability; bifurcation theory; and higher
dimensional systems.

**2040 Fundamentals
of Mathematics (3) F,S** *Prereq: MATH 1550*. Introduction to
techniques of mathematical proofs; sets, logic, relations and functions, induction,
cardinality, and properties of real numbers.

**2057 Multidimensional
Calculus (3) F,S,Su** *Prereq: MATH 1552. An honors course, MATH 2058,
is also available*. Three-dimensional analytic geometry, partial derivatives,
multiple integrals.

**2058 HONORS: Multidimensional
Calculus (3) F** *Same as MATH 2057, with special honors emphasis
for qualified students*.

**2060 Technology
Lab (1) F,S,Su** *Prereq.: Credit or concurrent enrollment in MATH
2057. Students are encouraged to enroll in MATH 2057 and 2060 concurrently*.
Use of computers for investigating, solving, and documenting mathematical problems;
numerical, symbolic, and graphical manipulation of mathematical constructs discussed
in MATH 1550, 1552, and 2057

**2065 Elementary
Differential Equations (3) F,S** *Prereq: MATH 1552. Credit will be
given for only one of the following: MATH 2065, 2070, 2090*. Ordinary differential
equations; emphasis on solving linear differential equations.

**2070 Mathematical
Methods in Engineering (4) F,S** *Prereq: MATH 1552. Credit will be
given for only one of the following: MATH 2065, 2070, 2090. *Ordinary differential
equations, Laplace transforms, linear algebra, and Fourier series; physical
applications stressed.

**2085 Linear Algebra
(3) F,S,Su** *Prereq: MATH 1552, 1635 or 2040, or equivalent. An honors
course, MATH 2086, is also available. Credit will not be given for both this
course and MATH 2090*. Systems of linear equations, vector spaces, linear
transformations, matrices, determinants.

**2086 HONORS: Linear
Algebra (3) V** *Same as MATH 2085, with special honors emphasis for
qualified students*.

**2090 Elementary
Differential Equations and Linear Algebra (4) F,S,Su** *Prereq: MATH
1552. Credit will be given for only one of the following: MATH 2065, 2070, 2090.
Credit will not be given for both this course and MATH 2085*. Introduction
to first order differential equations, linear differential equations with constant
coefficients, and systems of differential equations; vector spaces, linear transformations,
matrices, determinants, linear dependence, bases, systems of equations, eigenvalues,
eigenvectors, Laplace transforms, and Fourier series.

**3903 Methods of
Problem Solving (1) F** *Prereq: MATH 1552 and MATH 2070, 2085, or
2090. May be taken for a max. of 3 hrs. of credit when topics vary. Pass-fail
grading*. Instruction and practice in solving a wide variety of mathematical
and logical problems, and participation in the Putnam competition.

**3998 Undergraduate
Major Seminar (1) V** *May be taken for a max. of 4 hrs. of credit.
Pass-fail grading*. Topics of current interest.

**4005 Geometry (3)
S** *Prereq: MATH 2040*. The foundations of geometry, including
work in Euclidean and non-Euclidean geometries.

**4020 Capstone Course
(3) S** *Prereq.: Students should be within two semesters of completing
the requirements for a mathematics major*. Provides opportunities for students
to consolidate their mathematical knowledge, and to obtain a

perspective on the meaning and significance of that knowledge. Course work will emphasize communication skills, including reading, writing, and speaking mathematics.

**4023 Applied Algebra
(3) S** *Prereq: MATH 2085 or equivalent. Credit will not be given
for both this course and MATH 4200*. Finite algebraic structures relevant
to computers: groups, graphs, groups and computer design, group codes, semigroups,
finite-state machines.

**4024 Mathematical
Models (3) S** *Prereq: MATH 1552 and credit or registration in MATH
2085; or equivalents*. Construction, development, and study of mathematical
models for real situations; basic examples, model construction, Markov chain
models, models for linear optimization, selected case studies.

**4025 Optimization
Theory and Applications (3) F** *Prereq: MATH 2057 and credit or registration
in MATH 2085; or equivalent*. Basic methods and techniques for solving optimization
problems; n-dimensional geometry and convex sets; classical and search optimization
of functions of one and several variables; linear, nonlinear, and integer programming.

**4027 Differential
Equations (3) Su** *Prereq: MATH 2057 and 2085*. Ordinary differential
equations, with attention to theory.

**4031 Advanced Calculus
I (3) F** *Prereq: MATH 2057 and 2085; or equivalent*. Differential
and integral calculus of real and vector-valued functions of several real variables.

**4032 Advanced Calculus
II (3) S** *Prereq: MATH 4031 or equivalent*. Vector integral
calculus, Stokes's theorem, series, orthogonal functions, selected related topics.

**4036 Complex Variables
(3) F,S,Su** *Prereq: MATH 2057*. Analytic functions, integration,
power series, residues, and conformal mapping.

**4038 Mathematical
Methods in Engineering (3) F,S,Su** *Prereq: MATH 2065 or 2070 or
2090. Also offered as ME 4563*. Vector analysis; solution of partial differential
equations by the method of separation of variables; introduction to orthogonal
functions including Bessel functions.

**4039 Introduction
to Topology (3) V** *Prereq: MATH 4031 or equivalent*. Examples
and classification of two-dimensional manifolds, covering spaces, the Brouwer
theorem, and other selected topics.

**4050 Interest Theory
(3) F,S** *Prereq.: MATH 1550 and EXST 4001*. Measurement of interest
(including accumulated and present value factors), annuities certain, yield
rates, amortization schedules and sinking funds, and bonds and related securities.

**4055 Introduction
to Probability (3) F** *Prereq: MATH 2057. Suggested for preparation
for actuarial exams*. Introduction to probability, emphasizing concrete
problems and applications; combinatorial analysis, random variables, conditional
probability, special distributions, law of large numbers, central limit theorem,
and Markov chains.

**4056 Mathematical
Statistics (3) S** *Prereq: MATH 4055. Suggested for preparation for
actuarial exams*. Experimental design, sampling methods, nonparametric methods,
hypothesis testing, and regression.

**4060 Preparation
for Actuarial Examinations (3) S** *Prereq.: MATH 1552, 2085 or 2090
and 4055 or 4056 or 4065*. Concentrated preparation for Actuarial Examinations;
focus on areas in mathematics treated in actuarial examinations on calculus,
linear algebra, probability, statistics, and numerical methods.

**4065 Numerical Analysis
I (3) F** *Prereq: MATH 2057; basic programming ability in Fortran,
Pascal, or C*. Newton's method, Lagrange interpolation, least-squares approximation,
orthogonal polynomials, numerical differentiation and integration, Gaussian
elimination.

**4066 Numerical Analysis
II (3) S** *Prereq: MATH 4065 and one of the following: MATH 2065,
2070, 2090, 4027*. Numerical solutions of initial value problems and boundary
value problems for ordinary and partial differential equations.

**4153 Finite Dimensional
Vector Spaces (3) S** *Prereq: MATH 2057 or 2085*. Vector spaces,
linear transformations, determinants, eigenvalues and vectors, and topics such
as inner product space and canonical forms.

**4158 Foundations
of Mathematics (3) V** *Prereq: MATH 2057 or equivalent*. Real
number systems, sets, relations, product spaces, order, and cardinality.

**4171 Theory of Graphs
(3) S** *Prereq: MATH 2085 or equivalent*. Fundamental concepts
of undirected and directed graphs, trees, connectivity and traversability, planarity,
colorability, network flows, matching theory, and applications.

**4172 Combinatorics
(3) F** *Prereq: MATH 2085 or equivalent*. Topics selected from
permutations and combinations, generating functions, principle of inclusion
and exclusion, configurations and designs, matching theory, existence problems,
applications.

**4181 Elementary
Number Theory (3) F** *Prereq: MATH 2057 or 2085*. Divisibility,
Euclidean algorithm, prime numbers, congruences, and topics such as Chinese
remainder theorem and sums of integral squares.

**4200 Abstract Algebra
I (3) F** *Prereq: MATH 2085 or equivalent. Credit will not be given
for both this course and MATH 4023*. Elementary properties of sets, relations,
mappings, integers; groups, subgroups, normal subgroups, quotient groups, homomorphisms,
automorphisms, and permutation groups; elementary properties of rings.

**4201 Abstract Algebra
II (3) S** *Prereq: MATH 4200 or equivalent*. Ideals in rings,
factorization in polynomial rings; unique factorization and Euclidean domains,
field extensions, splitting fields, finite fields, Galois theory.

**4325 Fourier Transforms
(3) V** *Prereq: MATH 1552 and at least one from MATH 2057, 2065,
2070, 2085, 2090. For students majoring in mathematics, physics, and engineering*.
Fourier analysis on the real line, the integers, and finite cyclic groups; the
fast Fourier transform; generalized functions; attention to modern applications
and computational methods.

**4340 Partial Differential
Equations (3) V** *Prereq: either MATH 2057, 2090, and knowledge of
Laplace transforms; or MATH 2057, 2065, or 2070 and 2085*. First-order partial
differential equations and systems, canonical second-order linear equations,
Green's functions, method of characteristics, properties of solutions, and applications.

**4345 Special Functions
(3) V** *Prereq: either MATH 2057 and 2090; or MATH 2057, 2065 or
2070 and 2085*. Sturm-Liouville problems, orthogonal functions (Bessel,
Laguerre, Legendre, Hermite), orthogonal expansions including Fourier series,
recurrence relations and generating functions, gamma and beta functions, Chebychev
polynomials, and other topics.

**4470 Error-Correcting
Codes (3) V** *Prereq: MATH 2085 or 2090 or equivalent knowledge of
linear algebra*. Vector spaces over finite fields, basic properties of codes,
examples of important codes and decoding schemes, bounds on sizes and rates
of codes, the weight enumerator polynomial, perfect codes, and other topics.

**4700 History of
Mathematics (3) V** *Prereq.: MATH 2040, 2057, and 2085; students
entering the course should have a firm sense of what constitutes a proof*.
This course will have substantial mathematical content; topics such as early
Greek mathematics, from Euclid to Archimedes; algebra and number theory from
Diophantus to the present; the calculus of Newton and Leibniz; the renewed emphasis
on rigor and axiomatic foundations in the 19^{th} and 20^{th}
centuries; interactions of mathematics with technology and the natural sciences;
biographies of significant mathematicians.

**4998 Senior Seminar
for Mathematics Majors (3) S** *Prereq: the student should be within
two semesters of completion of requirements for a mathematics major; for undergraduate
credit only; under guidance of professor teaching the course, student will undertake
several independent reading projects and write expository papers; oral presentations
will follow preparation of written papers*.

**4999 Selected Readings
in Mathematics (1-3)** *Prereq: consent of department. May be taken
for a max. of 9 sem. hrs. credit*.

**6300 Topics in Mathematics
for Secondary Teachers (1-3) V** *Prereq: 6 sem. hrs. of mathematics
at or above the level of 2040 or equivalent. May be taken for a max. of 6 sem.
hrs. credit when topics vary. May be taken by M.N.S. students in mathematics
with departmental approval*. Areas of current interest to teachers of secondary
school mathematics.

**7200 Geometric and
Abstract Algebra (3)** *Prereq: MATH 2085 or equivalent*. Linear
algebra, rings, finite fields, groups, multilinear algebra, other topics.

**7210, 7211 Algebra
I, II (3,3) 7210 offered S; 7211 offered F** *Prereq: MATH 7200 or
equivalent*. Groups: Sylow Theorems, finitely generated abelian groups;
rings and modules: exact sequences, projective modules; fields: algebraic, transcendental,
normal, separable field extensions; Galois theory, valuation theory, Noetherian
and Dedekind domains, topics from commutative rings.

**7280 Seminar in
Commutative Algebra (1-3) V** *Prereq: consent of department. May
be repeated for credit with consent of department*. Advanced topics such
as commutative rings, homological algebra, algebraic curves, or algebraic geometry.

**7290 Seminar in
Algebra and Number Theory (1-3) V** *Prereq: consent of department.
May be repeated for credit with the consent of the department*. Advanced
topics such as algebraic number theory, algebraic semigroups, quadratic forms,
or algebraic K-theory.

**7311 Real Analysis
I (3)** *Prereq: MATH 4032 or equivalent*. Axiom of choice, Lebesgue
measure and integration, convergence theorems, bounded variation and absolute
continuity, differentiation, Minkowski-Holder inequalities, Riesz-Fischer theorem.

**7312 Real Analysis
II (3)** *Prereq: MATH 7311 or equivalent*. Ascoli theorem, Stone-Weierstrass
theorem, Hahn-Banach theorem, uniform boundedness theorem, Hilbert spaces, weak
topologies, general measure and integration, Riesz representation theorem, other
related topics.

**7320 Ordinary Differential
Equations (3) S** *Prereq: MATH 2085 and 4031; or equivalent*.
Existence and uniqueness theorems, approximation methods, linear equations,
linear systems, stability theory; other topics such as boundary value problems.

**7330 Functional
Analysis (3) V** *Prereq: MATH 7312 or equivalent*. Banach spaces
and their generalizations; Baire category, Banach-Steinhaus, open mapping, closed
graph, and Hahn-Banach theorems; duality in Banach spaces, weak topologies;
other topics such as commutative Banach algebras, spectral theory, distributions,
and Fourier transforms.

**7350 Complex Analysis
(3) V** *Prereq: MATH 7311 or equivalent*. Theory of holomorphic
functions of one complex variable; path integrals, power series, singularities,
mapping properties, normal families, other topics.

**7360 Probability
Theory (3) F** *Prereq: MATH 7311 or equivalent*. Probability
spaces, random variables and expectations, independence, convergence concepts,
laws of large numbers, convergence of series, law of iterated logarithm, characteristic
functions, central limit theorem, limiting distributions, martingales.

**7370 Lie Groups
and Representation Theory (3) V** *Prereq: MATH 7312, 7200, and 7510
or equivalent*. Lie groups, Lie algebras, subgroups, homomorphisms, the
exponential map. Also topics in finite and infinite dimensional representation
theory.

**7380 Seminar in
Functional Analysis (1-3) V** *Prereq: consent of department. May
be repeated for credit with consent of department*. Advanced topics such
as topological vector spaces, Banach algebras, operator theory, or nonlinear
functional analysis.

**7390 Seminar in
Analysis (1-3) V** *Prereq: consent of department. May be repeated
for credit with consent of department*. Advanced topics such as harmonic
analysis, partial differential equations, Lie group representation theory, several
complex variables, or probability theory.

**7400 Combinatorial
Theory (3) S** *Prereq: MATH 7200 or equivalent*. Problems of
existence and enumeration in the study of arrangements of elements into sets;
combinations and permutations; other topics such as generating functions, recurrence
relations, inclusion-exclusion, Polya's theorem, graphs and digraphs, combinatorial
designs, incidence matrices, partially ordered sets, matroids, finite geometries,
Latin squares, difference sets, matching theory.

**7490 Seminar in
Combinatorics, Graph Theory, and Discrete Structures (1-3) V** *Prereq:
consent of department. May be repeated for credit with consent of department*.
Advanced topics such as combinatorics, graph theory, automata theory, or optimization.

**7510 Topology I
(3)** *Prereq: MATH 2057 or equivalent*. Basic notions of general
topology, with emphasis on Euclidean and metric spaces, continuous and differentiable
functions, inverse function theorem and its consequences.

**7512 Topology II
(3)** *Prereq: MATH 7510*. Theory of the fundamental group and
covering spaces including the Seifert-Van Kampen theorem; universal covering
space; classification of covering spaces; selected areas from algebraic or general
topology.

**7520 Algebraic Topology
(3) S** *Prereq: MATH 7200 and 7510; or equivalent*. Basic concepts
of homology, cohomology, and homotopy theory.

**7550 Differential
Geometry and Topology (3) F** *Prereq: MATH 7200 and 7510; or equivalent*.
Manifolds, vector fields, vector bundles, transversality, Riemannian geometry,
other topics.

**7590 Seminar in
Geometry and Algebraic Topology (1-3) V** *Prereq: consent of department.
May be repeated for credit with consent of department*. Advanced topics
such as advanced algebraic topology, transformation groups, surgery theory,
sheaf theory, or fiber bundles.

**7690 Seminar in
Topological Algebra (1-3) V** *Prereq: consent of department. May
be repeated for credit with consent of department*. Advanced topics such
as topological groups, topological semigroups, or topological lattices.

**7999 Selected Readings
in Mathematics (1-3)** *Prereq: consent of department. May be repeated
for credit with consent of department*.

**8000 Thesis Research
(1-12 per sem.)** *"S"/"U" grading*.

**9000 Dissertation
Research (1-12 per sem.)** *"S"/"U" grading*.