MATHEMATICS (MA) 

MA
110 
Finite
Mathematics 
3
cr 

This course is intended to give
an overview of topics in finite mathematics together with their
applications. The course includes logic, sets, counting, permutations,
combinations, basic probability, descriptive statistics, and their
applications. Students are required to have a scientific calculator.
Prerequisite: Mathematics placement
test score of 35 or more or C or better in DS 90.
Core
Course. 
Note: May be offered for Honors
Credit. 

NOTE: MA
110 is not a prerequisite for nor is it intended to be preparatory for
any course listed below. Students who do not have the
prerequisites for MA 110 or MA 112 should contact Developmental Studies. 

MA
112 
Precalculus
Algebra 
3
cr 

Study of use of variable
quantities to interpret information about relationships that can be
expressed in mathematical terms. Linear, polynomial, absolute value,
rational, exponential and logarithmic functions with emphasis on
numerical, graphical and algebraic properties and applications and use
in modeling real world situations. Systems of linear equations. Credit
for both MA 112 and MA 115 not allowed. Prerequisite: C or better in DS 090
or mathematics
placement test score of 65 or more. Core
Course. 

MA
113 
Precalculus
Trigonometry 
3
cr 

Continuation of MA 112.
Numerical, graphical and algebraic properties of polynomial, rational
and trigonometric functions. Parametric equations, right angle
trigonometry, inverse trigonometric functions. Polar coordinates. Conic
sections. Development and use of mathematical models to solve problems
which concern realworld situations emphasized. Credit for both MA 113
and MA 115 not allowed. Prerequisite: C or
better in MA 112 or mathematics
placement test score of 75 or more. Core
Course. 

MA
115 
Precalculus
Algebra and Trigonometry 
4
cr 

Study of elementary functions,
their graphs and applications, including polynomial, rational,
algebraic, exponential, logarithmic, and trigonometric functions. This
fastpaced course is designed as a review of the algebra and
trigonometry needed in calculus. Prerequisite:
Mathematics placement test score of 75 or more. Core Course. 

MA
120 
Calculus
and Its Applications 
3
cr 

Introduction to calculus with an
emphasis on problem solving and applications. Key concepts are
presented graphically, numerically and algebraically, although the
stress is on a clear understanding of graphs and tabular data. The
course covers: algebraic, exponential and logarithmic functions, their
properties and their use in modeling; the concepts of derivative and
definite integral and their applications to marginal analysis,
optimization and probability; examples of multivariable functions,
partial derivatives and applications to optimization problems. Students
are encouraged to have a graphing
calculator. Credit for both MA 120 and MA 125 not allowed.
Prerequisite: C or better in MA 112 or mathematics
placement test score of 75 or
more. MA 120 is not a prerequisite
for subsequent calculus courses. Core
Course. 


An
introduction to calculus with an emphasis on
the following concepts: Limit of a function; the derivatives of
algebraic, trigonometric, exponential, and logarithmic functions;
applications of the logarithmic functions; applications of the
derivative to curve sketching; optimization problems including examples
in the physical/natural sciences and economics; introduction of the
definite integral; Fundamental Theorem of Integral Calculus. Credit for
both MA 120 and MA 125 not allowed. Prerequisite: C
or better in MA 113 or MA 115 or placement
test score of 85 or more. Core Course. 

NOTE: MA 110, MA 112, MA 113, MA
115, MA 120, and MA 125 have strict prerequisites. The mathematics placement exam is available at
http://mps.southalabama.edu/mps/ 


A continuation of MA 125.
Techniques of symbolic and numerical integration; applications of the
definite integral to geometry, physics, economics, and probability;
indeterminate forms; improper integrals; introduction to differential
equations; sequences and series; Taylor polynomials and Taylor series.
Prerequisite: C or better in MA 125. Core Course. 

MA
150 
Contemporary
Mathematics and Statistics 
1
cr 

Seminar



This course gives an overview of
modern mathematics and statistics from the point of view of the
practitioners. The course is designed for majors in mathematics and
statistics at all levels as well as those students who are considering
mathematics or statistics as a major or minor area of study. Topics
usually included are elements of geometry, algebra, analysis, methods
of statistical inference, the role of the computer in analytical
sciences; these topics vary from semester to semester. This course
cannot be taken for credit simultaneously with ST 150. [Note Deletion here]

NOTE: May be offered for Honors
Credit. 

MA
201 
Mathematics
for Elementary Teachers I 
3
cr 

An examination of some of the
major ideas encountered in the teaching of elementary mathematics.
Topics include introduction to problem solving, sets, relations, logic,
numeration systems, elementary number theory, properties and operations
for whole numbers, integers, rational numbers, and real numbers. Prerequisite: Fulfillment of the General
Studies mathematics requirement. Prerequisite:
C or better in MA 110 or Ma 112 or higher level course. 
NOTE: MA 201 does not fulfill
graduation requirements for any curriculum other than College of
Education. 

MA
202 
Mathematics
for Elementary Teachers II 
3
cr 

Topics covered are those that a
prospective elementary or middle school teacher should expect to
encounter in the teaching of geometry in elementary or middle school.
Topics include geometric shapes, measurement, triangle congruence and
similarity, coordinate geometry, geometric transformation.
Prerequisite: C or better in MA 201. 
NOTE: MA 202 does not fulfill
graduation requirements for any curriculum other than College of
Education. 


Vectors; functions of several
variables; partial derivatives; local linearity; directional
derivatives; the gradient; differential of a function; the chain rule;
higher order partial derivatives; quadratic approximations;
optimization of functions of several variables; multiple integrals and
their applications; parametric curves and surfaces; vector fields; line
and surface integrals; vector calculus. Prerequisite: C or better in MA 126. Core Course. 

MA
237 
Linear
Algebra I 
3
cr 

An introduction to linear
algebra. Topics include vector spaces, linear transformations,
determinants, the eigenvalue problem and applications.
Prerequisite: C or better in MA
126. Core Course. 

MA
238 
Applied
Differential Equations I 
3
cr 

First order differential
equations. Higher order linear differential equations. Systems of first
order linear differential equations. Laplace Transforms. Methods for
approximating solutions to first order differential equations.
Applications. Students should have taken or be taking MA 227. Core Course. 

MA
267 
Discrete
Mathematical Structures 
3
cr 

This course is an introduction to
discrete mathematics for students majoring in computerrelated areas.
Students will be introduced to concepts and methods that are essential
to theoretical computer science. A strong emphasis is placed on
developing skills in mathematical reasoning and understanding and
writing proofs. Topics include sets, functions, induction, recursion,
combinatorics and graphs. Prerequisites: C or
better in MA 113 or C or better in
MA 115 or a mathematics placement exam score of
80 or
better. 

MA
290 
Special
Topics 
3
cr 

Selected topics in elementary
undergraduate mathematics. This course may be
repeated for a maximum of six credits.


MA
303 
Mathematics
for Elementary Teachers III 
3
cr 

An exploration of problem solving
strategies. Problems exemplifying the various problem solving
strategies studied. Emphasis on the development of problem solving
skills by exploring interesting problems which demand for their
solution that the student select from a wide variety of possible
strategies and use a wide variety of conceptual tools. Prerequisite: C or better in MA
202. 
NOTE: MA 303 does not fulfill
graduation requirements for any curriculum other than elementary
education. 

MA
311 
Introduction
to Number Theory 
3
cr 

An introduction to classical
number theory with a balance between theory and computation. Topics
include mathematical induction, divisibility properties, properties of
prime numbers, the theory of congruences, number theoretic functions,
continued fractions. Prerequisite: C or better
in MA 126. 

MA
316 
Linear
Algebra II 
3
cr 

A continuation of MA 237. Topics
include inner product spaces, spectral theorem for symmetric operators,
complex vector spaces, Jordan canonical form. Additional topics such as
duality and tensor products to be included at the discretion of the
instructor. Prerequisite: C or better in MA
237. 

MA
320 
Foundations
of Mathematics (W) 
3
cr 

The students will develop
facility with proofs through the study
of logic and proof techniques as applied to various areas of
mathematics. Topics include symbolic logic, proof techniques,
relations, functions, and the
structure of the number system. Prerequisite: C
or better in EH102 and MA 125. 

MA
321 
Elementary
Geometry 
3
cr 

The students will review the
major topics (from secondary school curriculum) of plane and solid
geometry from the modern viewpoint; axioms, undefined terms,
definitions, theorems and proofs. Prerequisite: C
or better in MA 320. 

MA
332 
Differential
Equations II 
3
cr 

Series solutions of second order
linear equations. Numerical methods. Nonlinear differential equations
and stability. Partial differential equations and Fourier series.
SturmLiouville problems. Prerequisites: C or
better in MA 227 and MA 238. 

MA
334 
Advanced
Calculus I 
3
cr 

This is the first of a two course
sequence designed to provide students with the theoretical context of
concepts encountered in MA 125 through MA 227. Topics covered include
Completeness Axiom, sequences of real numbers, suprema and infima,
Cauchy sequences, open sets and accumulation points in Euclidean space,
completeness of Euclidean space, series of real numbers and vectors,
compactness, HeineBorel Theorem, connectedness, continuity, Extremum
Theorem, Intermediate Value Theorem, differentiation of functions of
one variable. Prerequisites: C or better in MA 227
and MA 237. 

MA
335 
Advanced
Calculus II 
3
cr 

This is the second of a two
course sequence designed to provide students with the theoretical
context of concepts encountered in MA 125 through MA 227. Topics
covered include integration of functions of one variable, pointwise and
uniform convergence, integration and differentiation of series,
differentiable mappings of several variables, chain rule, product rule
and gradients, Mean Value Theorem, Taylor's Theorem, Inverse Function
Theorem, Implicit Function Theorem. Prerequisite:
C or better in MA
334. 

MA
354 
Computer
Assisted Mathematical Modeling (W) (C) 
3
cr 

Formulation, development, testing
and reporting of mathematical models of various real world problems.
Deterministic and stochastic models, optimization, simulation. Emphasis
on the careful mathematical formulations and the appropriate use of
computer software, both as an aid in the solution of mathematical
problems and as a tool in the process of model evaluation, simulation,
reporting. A term project will be an important component of this
course. The course is taught in a laboratory setting with computers as
lab equipment. Prerequisites: C or better in EH
102, MA
227, and MA 238. 

MA
367 
Combinatorial
Enumeration 
3
cr 

An introduction to the
mathematical theory of counting. Basic counting principles,
permutations and combinations, partitions, recurrence relations, and a
selection of more advanced topics such as generating functions,
combinatorial designs, Ramsey theory, or group actions and Poyla
theory. Prerequisite: C or better in MA
126 or consent of instructor. 

MA
410 
History
of Mathematics (W) 
3
cr 

Historical survey of general
development of mathematics with a balance of historical perspective and
mathematical structure. Prerequisite:
C or better in EH
102 and either senior standing or permission of instructor
or department chair. 

MA
413 
Algebra
I (W) 
3
cr 

An introduction to group theory
and ring theory. Topics include permutations and symmetries, subgroups, quotient groups,
homomophisms, as well as examples of rings, integral domains, and
fields. Prerequisites: MA 237 and C or better in
EH
102 and C or
better in one of the following: MA
311, MA 320, MA
334. 

MA
414 
Algebra
II (W) 
3
cr 

A continuation of MA 413 focusing
on rings and fields. Topics include rings, ideals, integral domains,
fields and extension fields. Geometric constructions and Galois theory
are introduced. Prerequisite: C or better in MA
413. 


An introduction to topology with
emphasis on the geometric aspects of the subject. Topics covered
include surfaces, topological spaces, open and closed sets, continuity,
compactness, connectedness, product spaces, and identification and
quotient spaces. Credit for both MA 434 and MA 542 is not allowed.
Prerequisite: C or better in MA 335. 

MA
436 
Numerical
Analysis 
3
cr 

Selected numerical algorithms are
analyzed. Topics include error analysis, machine arithmetic, roundoff,
root finding using fixed point methods, interpolation, numerical
integration, differential equations, eigenvalue /eigenvector problems,
least squares analysis, boundary value problems. Prerequisite: C or better in MA 227,
credit for or concurrent registration in MA 238. 

MA
437 
Complex
Variables 
3
cr 

Arithmetic of complex numbers;
regions in the complex plane; limits, continuity, and derivatives of
complex functions; elementary complex functions; mappings by elementary
functions; contour integration; power series; Taylor series; Laurent
series; calculus of residues;
conformal representation; applications. Credit for both MA 437 and MA
537 not allowed. Prerequisite: C or better in MA
238. 


A comprehensive introduction to
probability, the mathematical theory used to model uncertainty,
covering the axioms of probability, random variables, expectation,
classical discrete and continuous families of probability models, the
law of large numbers and the central limit theorem. Credit for both MA
451 and MA 550 is not allowed.
Prerequisites: MA 227 and MA 237. 

MA
458 
Operations
Research (W) 
3
cr 

An introduction to linear
programming. The course will include a study of the simplex method as
well as using computers to solve linear systems
of equations. As time permits, topics covered will include
sensitivity analysis, duality, integer programming, transportation,
assignment, transshipment, and
networks. Credit for both MA 458 and MA 567 is not allowed.
Prerequisites: C or better in
EH
102 and
MA
227 and MA 237. 

MA 467 
Mathematical Logic 
3 cr 
An
introduction to formal firstorder logic, firstorder metatheory, and
its extensions. Topics include axiom systems and their models,
completeness, compactness, and recursive sets and functions. Identical
with PHL 467. Credit cannot be received for both PHL 467 and MA 467.
Prerequisites: PHL 321 or C or better in any
300level or higher MA course. 

MA 481 
Cryptography 
3 cr 
This
course gives an introduction to classical and modern methods of message
encryption and decryptions (cryptography) as well as possible attacks
to cryptosystems (cryptanalysis). Topics include information theory,
classical (symmetric) cryptosystems (DES, AES), publickey (asymmetric)
cryptosystems (DifficHellman, RSA, El Garnal), oneway and trapdoor
functions, Hash functions, cryptanalysis, cryptographic protocols
(identification, authentication, secret sharing, oblivious transfer,
zeroknowledge), emoney and ecommerce. Credit for both MA 481 and MA 581 is not allowed.
Prerequisite: C or better in MA 311. 

MA
490 
Special
Topics 
13
cr 

Selected topics in advanced
undergraduate mathematics. This course may be repeated for a maximum of
six credits. 

MA
494 
Directed
Studies 
13
cr 

Directed individual study. May be
repeated for a maximum of six credits. Prerequisites: Permission of the
department chair. 

MA
499 
Honors
Senior Project 
36
cr 

With the guidance and advice of a
faculty mentor, honors students will identify, and carry out a
research project in mathematics. The outcome of the research project
will include a formal presentation at the annual Honors Student
Colloquium. The senior project will be judged and graded by three
members of the faculty, chaired by the faculty mentor. 

MA
501 
Number
Systems 
3
cr 

A case study of axiom systems and
the deductive method for graduate students in Mathematics Education. It
is expected that students in this course will practice and improve
their logical skills, better understand proof as a mathematical
activity, and study the similarities and differences between several
commonly used number systems.
Prerequisite: C or better in MA 321 or
MA 413 or permission of the instructor. 

MA
502 
Introduction
to Abstract Algebra 
3
cr 

An introduction to the
fundamental concepts of modern algebra such as groups, rings, and
fields through concrete examples. The course is designed for graduate
students in the College of Education. Prerequisite: C or better in MA 501. 

MA
503 
Introduction
to Analysis 
3
cr 

A careful look at the elements,
procedures, and applications of differential and integral calculus.
Prerequisites: MA 501 and one year of calculus. This course is designed for students in the
College of Education. 

MA
504 
Introduction
to Geometry 
3
cr 

An introduction to the
foundations of geometry using both synthetic and metric approaches.
Euclidean, finite, projective, and hyperbolic geometries are discussed.
The axioms for various geometries are discussed. This course is designed for students in the
College of Education. 

MA
505 
Mathematical
Problem Solving 
3
cr 

An indepth activitybased
approach to the methods and strategies for mathematical problem solving
for students in Mathematical Education. Problems selected from logic,
algebra, analysis, geometry, combinatorics, number theory and
probability. This course is designed for
students in the College of Education. 

MA
506 
Statistics
for Teachers 
3
cr 

Prepares
inservice and preservice teachers to teach statistics in high schools
using databased approach. Uses handsonactivities approach and
simulation of situations to teach concepts and technology to teach data analysis. Prerequisite:
MA 126. This course is designed for students
in the College of Education. 

MA
507 
Applicable
Mathematics I 
3
cr 

A graduatelevel introduction to
topics of ordinary differential equations, and their applications in
physics and engineering. 

MA
508 
Applicable
Mathematics II 
3
cr 

A continuation of MA 507 with
more emphasis on theory of partial differential equations, as well as
their applications in physics and engineering problems. 

MA
511 
Abstract
Algebra I 
3
cr 

A graduate level introduction to
group theory. Topics include quotient groups, homomorphism, group
actions, Sylow theorems, composition series, simple groups, free
groups, fundamental theorem of abelian groups. 

MA
512 
Abstract
Algebra II 
3
cr 

A graduate level introduction to
ring theory and fields. Topics include ring homomorphism, quotient
rings, ideals, rings of fractions, Euclidean domains, principal ideal
domains, unique factorization domains, modules, finite fields, field
extensions. Prerequisite: C or better in MA 511. 

MA
515 
Number
Theory 
3
cr 

Modular arithmetic, arithmetic
functions; prime numbers, algebraic number theory. 

MA
516 
Topics
in Number Theory 
3
cr 

A second course in number theory,
covering topics of interest to the students and instructor.
Prerequisite: C or better in MA 515. 

MA
518 
Linear
Algebra I 
3
cr 

Fields, vector spaces, dual
spaces, quotient spaces, multilinear forms, linear transformations,
algebras, adjoints, eigenvalues. 

MA
519 
Linear
Algebra II 
3
cr 

Triangular form, nilpotence,
Jordan form, inner products, selfadjoint transformations, positive
transformations, isometries, Spectral Theorem, polar decomposition,
applications to analysis. Prerequisite: C or
better in MA 518. 

MA
521 
Discrete
Mathematics 
3
cr 

Pigeonhole principle, basic
counting techniques, binomial coefficients, inclusionexclusion
principle, recurrence relations, generating functions, systems of
distinct representatives, finite fields. 


Fundamental concepts,
connectedness, graph coloring, planarity and Kuratowski's theorem,
fourcolor theorem, chromatic polynomial, Eulerian and Hamiltonian
graphs, matching theory, network flows, NPcomplete graph problems,
Markov chains, matroids. 

MA
535 
Real
Analysis I 
3
cr 

An introduction to real analysis.
Topics include the metric topology of the reals, limits and continuity,
differentiation, RiemannStieltjes integral. Prerequisite: An
undergraduate course in advanced calculus. 

MA
536 
Real
Analysis II 
3
cr 

A continuation of MA 535. Topics
covered include sequences and series of functions, differentiation and
integration in several variables, an introduction to the Lebesgue
integral and differential forms as time
allows. Prerequisite: C or better in MA
535. 

MA
537 
Complex
Analysis 
3
cr 

Arithmetic of complex numbers;
regions in the complex plane; limits, continuity, and derivatives of
complex functions; elementary complex functions; mappings by elementary
functions; contour integration; power series; Taylor series; Laurent
series; calculus of residues; conformal representation; applications.
Credit for both MA 537 and MA 437 is not allowed. Prerequisite: C or better in MA 238. 

MA
538 
Topics
in Complex Analysis 
3
cr 

A second course in complex
analysis, covering topics of interest to the students and instructor.
Prerequisite: C or better in MA 537. 

MA
539 
Measure
Theory 
3
cr 

Foundations of the general theory
of measure and integration, with particular attention to the Lebesgue
integral. Function spaces, product measure and Fubini's theorem, the
RadonNikodym theorem and applications to probability theory are
discussed, and possibly additional topics such as Haar measure or the
Ergodic Theorem. Prerequisite: C or better in MA
536. 

MA
540 
Differential
Geometry 
3
cr 

Local and global theory of curves
and surfaces in threedimensional space. 


An introduction to topology with
emphasis on the geometric aspects of the subject. Topics covered
include surfaces, topological spaces, open and closed sets, continuity,
compactness, connectedness, product spaces, and identification and
quotient spaces. Credit for both MA 542 and MA
434 is not allowed. 


A continuation of MA 542. Topics
covered include the fundamental group, triangulations, classification
of surfaces, homology, the EulerPoincare formula, the BorsukUlam
theorem, the Lefschetz fixedpoint theorem, knot theory, covering
spaces, and applications.
Prerequisites: C or better in MA 542 or MA 434
and permission of the instructor. 


A comprehensive introduction to
probability, the mathematical theory used to model uncertainty,
covering the axioms of probability, random variables, expectation,
classical discrete and continuous families of probability models, the
law of large numbers and the central limit theorem. Credit for both MA
550 and MA 451 is not allowed.
Prerequisites: MA 227 and C or
better
in MA 237. 

MA
551 
Theory
of Statistics 
3
cr 

A comprehensive introduction to
the mathematical foundations of statistics. Sufficient statistics and
information, parameter estimation, maximum likelihood and moment
estimation, optimality properties of estimators and confidence
intervals. Hypothesis testing, likelihood ratio tests and power
functions. Credit for both MA 551 and ST 470 is not allowed.
Prerequisite: C or better in MA 451 or
MA 550. 

MA
555 
Statistical
Analysis I 
3
cr 

A first course in an integrated
twocourse sequence in applied statistical theory and methods for
research workers in technical fields. Coverage includes probability and
basic probability models, mathematical expectations, random sampling
processes and central limit theorem, estimation, hypothesis testing and
power analysis, some applications of the theory of least squares.
Computer assisted data analysis is used. 

MA
560 
Statistical
Analysis II 
3
cr 

A second course (continuation of
MA 555) in an integrated twocourse sequence in applied statistical
theory and methods for research workers in technical fields. Coverage
includes regression analysis, design and analysis of experiments,
factorial experiments, analysis of covariance, nonparametric analytical
techniques, analysis of count data. Computer assisted data analysis is
used. Prerequisite: C or better in MA
555. 

MA
565 
Numerical
Analysis 
3
cr 

An introduction to Numerical
Analysis. Topics include error analysis, systems of linear equations,
nonlinear equations, integration, ordinary differential equations among
others. Prerequisite: C or better in MA
535. 

MA
567 
Operations
Research 
3
cr 

An introduction to linear
programming. The course will include a study of the simplex method as
well as using computers to solve linear systems
of equations. As time permits, topics covered will include
sensitivity analysis, duality, integer programming, transportation,
assignment, transshipment, and networks. Credit for both MA 567 and MA 458 is not allowed. Prerequisites:
MA
227 and C or better in MA 237. 

MA
568 
Topics
in Operations Research 
3
cr 

A second course in operations
research, covering topics of interest to the students and instructor.
Prerequisite: C or better in MA 567. 

MA
571 
Ordinary
Differential Equations 
3
cr 

An introduction to ordinary
differential equations from a dynamical systems perspective. Topics
include existence and uniqueness theorems, dependence on initial data,
linear systems and exponential of operators, stability of equilibria,
PoincareBendixon theorem. Additional topics such as applications to
population dynamics, classical mechanics, periodic attractors among
others will be included at the discretion of the instructor.
Prerequisite: C or better in MA 518. 

MA
572 
Partial
Differential Equations 
3
cr 

An introduction to partial
differential equations emphasizing spectral methods. Topics include
elementary Hilbert spaces, Fourier series and integrals and their
applications to the study of the basic partial differential equations
of mathematical physics. More advanced topics such as asymptotic
properties and regularity of solutions and nonlinear equations among
others will be included at the discretion of the instructor.
Prerequisite: C or better in MA 536. 

MA 581 
Cryptography 
3 cr 
This
course gives an introduction to classical and modern methods of message
encryption and decryptions (cryptography) as well as possible attacks
to cryptosystems (cryptanalysis). Topics include information theory,
classical (symmetric) cryptosystems (DES, AES), publickey (asymmetric)
cryptosystems (DifficHellman, RSA, El Garnal), oneway and trapdoor
functions, Hash functions, cryptanalysis, cryptographic protocols
(identification, authentication, secret sharing, oblivious transfer,
zeroknowledge), emoney and ecommerce. Credit for both MA 481 and MA
581 is not allowed. Prerequisite: C or better in
MA 311. 

MA
590 
Special
Topics 
13
cr 

Selected topics in elementary
graduate mathematics. This course may be repeated for a maximum of six
credits. 


Student seminar. Topics covered
vary. This course may be repeated indefinitely, but only two credits
count towards the degree. Grading system: satisfactory/unsatisfactory. 

MA
594 
Directed
Studies 
13
cr 

Directed individual study. May be repeated for up to six hours of credit. Prerequisites:
Approval of the department chair. 


Prerequisite: Approval of
research prospectus by Department Graduate Committee. 




