DESCRIPTIONS


MAC 3473 Honors Calculus 2. S.
 Credits: 4; Prereq: MAC 3472.
A continuation of MAC 3472. (M)
MAC 3474 Honors Calculus 3. F.
 Credits: 4; Prereq: MAC 3473.
A continuation of MAC 3473. (M)

Mathematics Discrete
MAD 3104 Applications of Discrete Structures. F, S.
 Credits: 3; Prereq: CDA 3101 or consent of instructor.
Sets, relations, functions, and concept of cardinality;
propositional logic and applications; predicate logic,
induction and recursion; finite state machine, gram-
mar, and languages; graphs and trees; elements of*
groups, semigroups, lattices, and Boolean algebra.
This is the same course as COT 3001. (M)
MAD 4203 Introduction to Combinatorics 1. F.
 Credits: 3; Prereq: MAC 3312.
Permutations and combinations, binomial coefficients,
inclusion-exclusion, recurrence relations, Fibonacci
sequences, generating functions, graph theory, block
designs, projective planes. (M)
MAD 4204 Introduction to Combinatorics 2. S.
 Credits: 3
A continuation of MAD 4203. (M)
MAD 4401 Introduction to Numerical Analysis. F, S.
 Credits: 3; Prereq: One of MAS 3114, MAS 4105, and
MAS 3113 and a programming language.
Numeric integration, nonlinear equations, linear and
non-linear systems of equations, differential equations
and interpolation. This is the same course as CNM
4110.
MAD 4504 Theory of Computing. F.
 Credits: 3; Prereq: COP 3530 or consent of instructor.
Finite and infinite state machines; Turing machines,
formal languages and their recognition automata;
recursive functions; decidability and unsolvability;
halting problem; space-time tradeoff. This is the same
course as COT 4125. (M)
MAE 3811 Mathematics for Elementary School
Teachers 2. F, S, SS.
 Credits: 3
Properties and operations of rational numbers, ratio,
proportion, percent, an introduction to real numbers,
elementary algebra, informal geometry and measure-
ment, and an introduction to probability and descrip-
tive statistics.

Mathematics Applied
MAP 3302 Elementary Differential Equations. F, S,
SS.
 Credits: 3; Prereq: MAC 3312.
First order differential equations, theory of linear dif-
ferential equations, solution of linear equations with
constant coefficients, the Laplace transform, solution
of equation by the Laplace transform. (M)
MAP 4101 Probability Theory and Stochastic
Processes 1. F.
 Credits: 3; Prereq: MAC 3313, STA 4321 or consent
of instructor.
Probability spaces, combinatorial analysis, discrete
and continuous random variables, joint distributions,
expectations, conditional densities, the Central Limit
Theorem, laws of large numbers, moment generating
functions, characteristic functions.
MAP 4102 Probability Theory and Stochastic
Processes 2. S.
 Credits: 3; Prereq: MAP 4101.
Random walks and Poisson processes, martingales,
Markov chains, Brownian motion, stochastic integrals
and Ito's formula.


MAP 4305 Introduction to Differential Equations for
Engineers and Physical Scientists. F, S, SS.
 Credits: 3; Prereq: MAP 3302.
Series solutions of differential equations, Sturm-
Liouville Systems.
MAP 4316 Advanced Differential Equations. S.
 Credits: 3; Prereq: MAP 3302 and one of MAS 4105,
MAS 3113, or MAS 3114.
An introduction to the qualitative theory of differential
equations; covers both linear and nonlinear systems.
MAP 4341 Elements of Partial Differential
Equations. S.
 Credits: 3; Prereq: MAP 3302. Recommended MAP
4305.
Origin and solution of partial differential equations by
various methods including Lagrange linear equations;
elementary partial equations of mathematical physics.
MAP 4413 Fourier Series and Transforms 1. F.
 Credits: 3; Prereq: MAP 3302; Recommended MAP
4305.
Introduction to linear systems and transforms,
Laplace, Fourier and Z transforms and their mutual
relationship, convolutions. Operational calculus, com-
putational methods including the fast Fourier trans-
form, second order stationary process, their autocorre-
lation functions, and problems of interpolation,
extrapolation, filtering and smoothing or second order
stationary processes.
MAP 4480 Introductory Mathematics for Biological
Sciences 1. F.
 Credits: 3; Prereq: MAC 3311.
Differential equations, probability theory, matrix theo-
ry, and Markov chains with applications in the biolog-
ical sciences. Among the applications covered are
population dynamics, epidemiology, and genetics.
(M)

Mathematics: Algebraic Structures
MAS 3113 Matrices and Vector Spaces. F, S, SS.
 Credits: 3; Prereq: MAC 3311 or MAC 3233.
Linear equations and matrices, elementary determi-
nants, linear geometry of Euclidean spaces, vector
spaces and linear transformations, eigenvalues. (M)
MAS 3114 Computational Linear Algebra. F, S, SS.
 Credits: 3; Prereq: MAC 3312 and knowledge of a pro-
gramming language.
Linear equations, matrices and determinants. Vector
spaces and linear transformations. Inner products and
eigenvalues. This course emphasizes computational
aspects of linear algebra. (M)
MAS 3203 Introduction to Number Theory. S, SS.
 Credits: 3; Prereq: Two semesters of calculus.
An introduction to elementary number theory and its
applications to computer science and cryptology; divis-
ibility, primes, Euclidean Algorithm, congruences,
Chinese Remainder Theorem, Euler-Fermat Theorem,
primitive roots. Selected applications to decimal frac-
tions, continued fractions, computer file storage and
hashing functions, and public-key cryptography. (M)
MAS 3300 Numbers & Polynomials. F, SS.
 Credits: 3; Prereq: Two semesters of calculus.
Algebraic and order properties of the real numbers,
introduction to number theory, rational numbers and
their decimal expansions, uncountability of the real
numbers, complex numbers, irreducible polynomials
over the integral, rational, real and complex numbers,
elementary theory of equations. This course is particu-
larly useful for prospective secondary school mathe-
matics teachers. (M)
MAS 4105 Linear Algebra 1. F, S, SS.
 Credits: 4; Prereq: MAC 3313.
Linear equations, matrices, vector spaces, linear trans-
formations, determinants, eigenvalues, inner product
spaces.


MAS 4107 Linear Algebra 2. S.
 Credits: 3; Prereq: MAS 4105.
Further topics in linear algebra.
MAS 4124 Introduction to Numerical Linear
Algebra. F.
 Credits: 3; Prereq: MAS 4105 and a high-level com-
puter language, or permission of the instructor.
Topics in linear algebra most useful in applications
with emphasis on the numerical methods involved:
direct and iterative solutions to systems of linear
equations, matrix norms, Householder transforma-
tions, singular value decomposition, least squares and
the generalized inverse, QR method for computing
eigenvalues, condition of linear systems and eigensys-
tems.
MAS 4156 Introduction to Vector Analysis. F, S, SS.
 Credits: 3; Prereq: MAC 3313.
Vector Analysis including the integral theorems;
applications.
MAS 4301 Abstract Algebra 1. F, S.
 Credits: 3; Prereq: MAC 3313 and one of MAS 4105,
MAS 3113, and MAS 3114.
Sets and mappings, groups and subgroups, homomor-
phisms and isomorphisms, permutations, rings and
domains, arithmetic properties of domains, fields. The
course involves learning to prove theorems.
MAS 4302 Abstract Algebra 2. S.
 Credits: 3; Prereq: MAS 4301.
Further topics in abstract algebra.

Mathematics

MAT 4905 Individual Work. F, S, SS.
 Credits: 1 to 3; Maximum of 10 credits; Prereq: MAC
3313 and permission of Chairperson of Department. May
be repeated for credit.
For special topics not obtainable in the regular course
offerings.
MAT 4930 Special Topics in Mathematics. F, S, SS.
 Credits: I to 3; Prereq: Permission of the chairman of
the department's Undergraduate Advisery Panel who
should be consulted well in advance of registration. May be
repeated for credit. Maximum of 16 credits.
MAT 4949 Co-Op Work Experience. F, S, SS.
 Credits: 1; Prereq: MAC 3313 and junior or senior
standing.
Practical co-op work experience as administered
through the Cooperative Education Program of the
Career Resource Center and coordinated by the math-
ematics department Cooperative Education Adviser.

Mathematics: General and Finite

MGF 1202 Fundamental Concepts of Mathematics. F,
S,SS.
 Credits: 3
A General Education course which includes an intro-
duction to logic and set theory, algebra, probability
and statistics, an elementary introduction to linear
programming and game theory, and a review of
geometry and measurement. (M)

Mathematics History and Foundations
MHF 3202 Sets & Logic. F, SS.
 Credits: 3; Prereq: MAC 3311 or consent of instructor.
Examples of sets, operations on sets, set algebra, Venn
diagrams, truth tables, tautologies, applications to
mathematical arguments and mathematical induction.
(M)
MHF 4102 Elements of Set Theory. F.
 Credits: 3; Prereq: A 4000-level mathematics course.
The basic axioms and concepts of set theory. Students
present proofs.


tt Grading is on S-U basis only.