Graduate Course Descriptions
**501, 502. GENERAL TOPOLOGY**.
Metric spaces, continuity, separation axioms, connectedness, compactness,
and other related topics. Prerequisite: MATH 556. (3, 3).
**513, 514. THEORY OF NUMBERS
I, II.** Congruences; divisibility; properties of prime numbers;
arithmetical functions; quadratic forms; quadratic residues. (3, 3).
**519. MATRICES. **Basic
matrix theory, eigenvalues, eigenvectors, normal and Hermitian matrices,
similarity, Sylvester's Law of Inertia, normal forms, functions of matrices.
(3).
**520. LINEAR ALGEBRA**.
An introduction to vector spaces and linear transformations; eigenvalues
and the spectral theorem. (3).
**525, 526. MODERN ALGEBRA
I, II**. General properties of groups, rings, and fields; introduction
to ideal theory. (3, 3).
**533. TOPICS IN EUCLIDEAN
GEOMETRY**. A study of incidence geometry; distance and congruence;
separation; angular measure; congruences between triangles; inequalities;
parallel postulate; similarities between triangles. (3).
**537. NON-EUCLIDEAN GEOMETRY**.
Brief review of the foundation of Euclidean plane geometry with special
emphasis given the Fifth Postulate; hyperbolic plane geometry; elliptic
plane geometry. (3).
**540. HISTORY OF MATHEMATICS.**
Development of mathematics, especially algebra, geometry, and analysis;
lives and works of Euclid, Pythagoras, Cardan, Descartes, Newton, Euler,
and Gauss. Prerequisite: Math 305 or consent of instructor. (3).
**545. SELECTED TOPICS IN
MATHEMATICS FOR SECONDARY SCHOOL** **TEACHERS.** High
school subjects from an advanced point of view; their relation to the
more advanced subjects. (3).
**555, 556. ADVANCED CALCULUS
I, II**. Limits, continuity, power series, partial differentiation,
multiple definite integrals, improper integrals, line integrals; applications.
(3, 3).
**567, 568. INTRODUCTION TO
FUNCTIONAL ANALYSIS.** Metric spaces, Normed linear spaces and
linear operators. Prerequisite: 556 or consent of instructor. (3, 3).
**569. THEORY OF INTEGRALS.**
Continuity, quasi-continuity, measure, variation, Stieltjes integrals,
Lebesgue integrals. (3).
**571. FINITE DIFFERENCES.**
Principles of differencing, summation, and the standard interpolation
formulas and procedures. (3).
**572. INTRODUCTION TO PROBABILITY
AND STATISTICS**. Emphasis on standard statistical methods and
the application of probability to statistical problems. Prerequisite:
MATH 264. (3).
**573. APPLIED PROBABILITY**.
Emphasis on understanding the theory of probability and knowing how to
apply it. Proofs are given only when they are simple and illuminating.
Among topics covered are joint, marginal, and conditional distributions,
conditional and unconditional moments, independence, the weak law of large
numbers, Tchebycheff's inequality, Central Limit Theorem. Prerequisite:
MATH 264. (3).
**574. PROBABILITY. **Topics
introduced in MATH 573 will be covered at a more sophisticated mathematical
level. Additional topics will include the Borel-Cantelli Lemma, the Strong
Law of Large Numbers, characteristic functions (Fourier transforms). Prerequisite:
MATH 573. (3).
**575, 576. MATHEMATICAL STATISTICS
I, II.** Mathematical treatment of statistical and moment characteristics;
frequence distribution; least squares; correlation; sampling theory. Prerequisite:
MATH 262. (3, 3).
**577. APPLIED STOCHASTIC
PROCESSES**. Emphasis on the application of the theory of stochastic
processes to problems in engineering, physics, and economics. Discrete
and continuous time Markov processes, Brownian Motion, Ergodic theory
for Stationary processes. Prerequisite: MATH 573 or consent of instructor.
(3).
**578. STOCHASTIC PROCESSES.**
Topics will include General Diffusions, Martingales, and Stochastic Differential
Equations. (3).
**590. TECHNIQUES IN TEACHING
COLLEGE MATHEMATICS**. Directed studies of methods in the presentation
of college mathematics topics, teaching and testing techniques. Z grade.
This course is required of all teaching assistants, each semester, and
may not be used for credit toward a degree. Prerequisite: departmental
consent. (1-3).
**597. SPECIAL PROBLEMS.**
(1-3).
**631. FOUNDATIONS OF GEOMETRY**.
Development of Euclidean geometry in two and three dimensions using the
axiomatic method; introduction to high dimensional Euclidean geometry
and to non-Euclidean geometrics. (3).
**639. PROJECTIVE GEOMETRY**.
Fundamental propositions of projective geometry from synthetic and analytic
point of view; principle of duality; poles and polars; cross ratios; theorems
of Desargues, Pascal, Brianchon; involutions. (3).
**647. TOPICS IN MODERN MATHEMATICS.
**Survey of the more recent developments in pure and applied mathematics.
Prerequisite: consent of instructor. (3).
**649. CONTINUED FRACTIONS**.
Arithmetic theory; analytic theory; applications to Lyapunov theory. Prerequisite:
consent of instructor. (3).
**653, 654. THEORY OF FUNCTIONS
OF REAL VARIABLES.** The number system; sets, convergence; measure
and integration; differentiation; variation; absolute continuity. (3,
3).
**655, 656. THEORY OF FUNCTIONS
OF COMPLEX VARIABLES I, II.** Complex functions; mappings, integration
theory, entire functions; topics of current interest. (3, 3).
**661, 662. NUMERICAL ANALYSIS
I, II.** Numerical linear algebra, error analysis, computation
of eigenvalues and eigenvectors, finite differences, techniques for ordinary
and partial differential equations, stability and convergence analysis.
(3, 3).
**663. SPECIAL FUNCTIONS**.
Advanced study of gamma functions; hypergeometric functions; generating
function; theory and application of cylinder functions and spherical harmonics.
(3).
**667, 668. FUNCTIONAL ANALYSIS
I, II. **Linear spaces; operators and functionals. (3, 3).
**669. PARTIAL DIFFERENTIAL
EQUATIONS I. **Classical theories of wave and heat equations. Prerequisite:
MATH 353 or MATH 555. (3).
**670. PARTIAL DIFFERENTIAL
EQUATIONS II. **Hilbert space methods for boundary value problems.
Prerequisite: MATH 669. (3).
**673, 674. ADVANCED PROBABILITY.
**Current topics in probability are treated at an advanced mathematical
level. Measure theoretic foundations, infinitely divisible laws, stable
laws, and multidimensional central limit theorem, strong laws, law of
the integrated logarithm. Prerequisite: MATH 654 (or may be taken concurrently).
(3, 3).
**675. ADVANCED MATHEMATICAL
STATISTICS I. **Univariate distribution functions and their characteristics;
moment generating functions and semi-invariants; Pearson's system; Gram-Charlier
series; inversion theorems. (3).
**676. ADVANCED MATHEMATICAL
STATISTICS II. **Multivariate distributions and regression systems;
multiple and partial correlation; sampling theory; statistical hypotheses;
power and efficiency of tests. (3).
**677, 678. ADVANCED STOCHASTIC
PROCESSES.** Special topics in the mathematical theory of stochastic
processes. Separability, Martingales, stochastic integrals, the Wiener
process, Gaussian processes, random walk, Ornstein-Uhlenbeck process,
semi-group theory for diffusions. Prerequisite: MATH 674. (3, 3).
**681, 682. GRAPH THEORY I,
II.** Topics in graph theory including trees, connectivity, coverings,
planarity, colorability, directed graphs. (3, 3).
**697. THESIS**. (1-12).
**700. SEMINAR IN TOPOLOGY**.
Prerequisite: consent of instructor. (May be repeated for credit). (3).
**710. SEMINAR IN ALGEBRA**.
Prerequisite: consent of instructor. (May be repeated for credit). (3).
**750. SEMINAR IN ANALYSIS**.
Prerequisite: consent of instructor. (May be repeated for credit). (3).
**780. SEMINAR IN GRAPH THEORY.**
Prerequisite: consent of instructor. (May be repeated for credit up to
a maximum of 9 hours). (3).
**797. DISSERTATION.**
(1-18).
** **
Please
send comments and questions about the page content to the Department of
Mathematics at mdept@olemiss.edu.
Please send comments regarding site design to the Department
of mathematics at mdept@olemiss.edu.
This page last modified
on
Friday, July 30, 2004 10:04 AM
The
University complies with all applicable laws regarding affirmative action
and equal opportunity in its activities and programs and does not discriminate
against anyone protected by law because of age, color, creed, disability,
marital status, national origin, pregnancy, race, religion, sex, or status
as disabled or Vietnam-era veteran. |