|
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,
matrices, and their applications. Students are
required to have a scientific calculator. Prerequisite: placement test score of 35 or more or DS 084. 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. Graphing
calculator recommended. Credit for both MA 112 and
MA 115 not allowed. Prerequisite: DS 084 or 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 real-world
situations emphasized. Graphing calculator recommended.
Credit for both MA 113 and MA 115 not allowed.
Prerequisite: MA 112 or 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
fast-paced course is designed as a review of the
algebra and trigonometry needed in calculus. Students
are encouraged to have a graphing calculator. Prerequisite: 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:
MA 112 or placement test score of 75 or more. Core
Course. |
| |
|
|
| Introduction
to calculus with emphasis on presenting the key
concepts graphically, numerically, and algebraically.
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.
Students are encouraged to have a graphing calculator.
Credit for both MA 120 and MA 125 not allowed.
Prerequisite: 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 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. Vectors and geometry. Students are encouraged to have a graphing calculator. Prerequisite: 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,
but may be repeated in different semesters. |
| 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. |
| 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:
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. Students
are encouraged to have a graphing calculator. Prerequisite:
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:
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
are encouraged to have a graphing calculator. 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 computer-related 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: MA 113, MA 115 or a placement exam score of 80 or better. |
| |
| MA 290
|
Special
Topics |
3 cr |
|
| Selected
topics in elementary undergraduate mathematics. |
| |
| 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:
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: 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: MA 237. |
| |
| MA 320 |
Foundations
of Mathematics (W) |
3 cr |
|
| The
students will develop facility with proof through
the study of logic and proof techniques as applied
to various areas of mathematics. Topics include
symbolic logic, proof techniques, relations, functions,
and structure of the number system. Prerequisite:
MA 126. |
| |
| 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:
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. Sturm-Liouville problems. Prerequisites:
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, Heine-Borel
Theorem, connectedness, continuity, Extremum Theorem,
Intermediate Value Theorem, differentiation of
functions of one variable. Prerequisites: 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: 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: 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: 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: 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 symmetrics, subgroups,
quotient groups, homomophisms, as well as examples
of rings, integral domains, and fields. Prerequisites:
MA 237 and 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:
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: 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:
MA 227, credit for or concurrent registration
in MA 238. Students are also required to have
proficiency in a programming language. |
| |
| 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
or residues; conformal representation; applications.
Credit for both MA 437 and MA 537 not allowed.
Prerequisite: 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 either MA 237 or MA 318. |
| |
| 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 and nonlinear
problems. As time permits, topics covered will
include sensitivity analysis, duality, integer
programming, transportation, assignment, transshipment,
networks, game theory, Markov processes, queuing
theory, simulation, and forecasting. Credit for
both MA 458 and MA 567 is not allowed. Prerequisites:
MA 227 and either MA 318 or MA 316. |
| |
| MA 490
|
Special
Topics |
1-3 cr |
|
| Selected
topics in advanced undergraduate mathematics.
This course may be repeated for a maximum of six
credits. |
| |
| MA 494 |
Directed
Studies |
1-3 cr |
|
| Directed
individual study. May be repeated for a maximum
of six credits. Prerequisites: Permission of the
department chair. |
| |
| MA 499 |
Honors
Senior Project |
3-6 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 utilized number systems. Prerequisite:
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: 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. |
| |
| 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. |
| |
| MA 505 |
Mathematical
Problem Solving |
3 cr |
|
| An
in-depth activity-based 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. |
| |
| MA 506 |
Statistics for Teachers |
3 cr |
|
| Prepares in-service and pre-service teachers to teach statistics in high schools using data-based approach. Uses hands-on-activities approach and simulation of situations to teach concepts and technology to teach analysis. Prerequisite: MA 126. |
| |
| MA 507
|
Applicable
Mathematics I |
3 cr |
|
| A
graduate-level introduction to topics of ordinary
differential equations, partial 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: 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:
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,
self-adjoint transformations, positive transformations,
isometries, Spectral Theorem, polar decomposition,
applications to analysis. Prerequisite: MA 518. |
| |
| MA 521 |
Discrete
Mathematics |
3 cr |
|
| Pigeonhole
principle, basic counting techniques, binomial
coefficients, inclusion-exclusion principle, recurrence
relations, generating functions, systems of distinct
representatives, finite fields. |
| |
|
|
| Fundamental
concepts, connectedness, graph coloring, planarity
and Kuratowski's theorem, four-color theorem,
chromatic polynomial, Eulerian and Hamiltonian
graphs, matching theory, network flows, NP-complete
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, Riemann-Stieltjes 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 differential forms and to the Lebesgue integral.
Prerequisite: 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: 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:
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 Radon-Nikodym theorem and applications
to probability theory are discussed, and possibly
additional topics such as Haar measure or the
Ergodic Theorem. Prerequisite: MA 536. |
| |
| MA 540 |
Differential
Geometry |
3 cr |
|
| Local
and global theory of curves and surfaces in three-dimensional
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, simplicial homology, the Euler-Poincare
formula, the Borsuk-Ulam theorem, the Lefschetz
fixed-point theorem, knot theory, and covering
spaces. Prerequisites: MA 542 and 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 MA 237 or MA 318. |
| |
| 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: MA 451 or MA 550. |
| |
| MA 555 |
Statistical
Analysis I |
3 cr |
|
| A
first course in an integrated two-course 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
two-course 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:
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: 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 and nonlinear
problems. As time permits, topics covered will
include sensitivity analysis, duality, integer
programming, transportation, assignment, transshipment,
network, game theory, Markov processes, queuing
theory, simulation, and forecasting. Credit for
both MA 567 and MA 458 is not allowed. Prerequisites:
MA 227 and either MA 318 or MA 316. |
| |
| MA 568 |
Topics
in Operations Research |
3 cr |
|
| A
second course in operations research, covering
topics of interest to the students and instructor.
Prerequisite: 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, Poincare-Bendixon
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: 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: MA 536.
|
| |
| MA 590 |
Special
Topics |
1-3 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 |
1-3 cr |
|
| Directed
individual study. Prerequisites: Approval of the
department chair. |
| |
|
|
| Prerequisite:
Approval of research prospectus by Department
Graduate Committee. |
| |
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