USC: Academic Bulletins

Professors
Colin Bennett, Ph.D., University of Newcastle upon Tyne, 1971
Susanne C. Brenner, Ph.D., University of Michigan, 1988
Stephen J. Dilworth, Ph.D., Cambridge University, 1985
Michael A. Filaseta, Ph.D., University of Illinois, 1984
Maria Girardi, Ph.D., University of Illinois, 1990
Jerrold R. Griggs, Ph.D., Massachusetts Institute of Technology, 1977
Ralph E. Howard, Ph.D., California Institute of Technology, 1982
Andrew Kustin, Ph.D., University of Illinois, 1979
George F. McNulty, Ph.D., University of California, Berkeley, 1972
Matthew Miller, Ph.D., University of Illinois, 1979, Graduate Director
Peter J. Nyikos, Ph.D., Carnegie-Mellon University, 1971
Konstantin Oskolkov, Ph.D., Steklov Institute, 1978
Pencho Petrushev, Ph.D., University of Sofia, 1977
Anton R. Schep, Ph.D., University of Leiden, 1977, Assistant Chair
Robert C. Sharpley, Ph.D., University of Texas, 1972
Manfred Stoll, Ph.D., Pennsylvania State University, 1971
David P. Sumner, Ph.D., University of Massachusetts, 1971
Li-yeng Sung, Ph.D., State University of New York at Stony Brook, 1983
László A. Székely, Ph.D., Eötvös University, 1983
Vladimir Temlyakov, Ph.D., Steklov Institute, 1981
Hong Wang, Ph.D., University of Wyoming, 1992

Associate Professors
George Androulakis, Ph.D., University of Texas, 1996
Peter G. Binev, Ph.D., University of Sofia, 1985
Daniel B. Dix, Ph.D., University of Chicago, 1988
Douglas B. Meade, Ph.D., Carnegie-Mellon University, 1989, Undergraduate Director
Ognian T. Trifonov, Ph.D., University of Sofia, 1990
Xian Wu, Ph.D., Harvard University, 1986

Assistant Professors
George Androulakis, Ph.D., University of Texas, 1996
Matthew Boylan, Ph.D., University of Wisconsin at Madison, 2002
Joshua N. Cooper, Ph.D., University of California, San Diego, 2003
Eva Czabarka, Ph.D., University of South Carolina, 1998
Lili Ju, Ph.D., Iowa State University, 2002
Linyuan (Lincoln) Lu, Ph.D., University of California, San Diego, 2002
Adela Vraciu, Ph.D., University of Michigan, 2000
Brett D. Wick, Ph.D., Brown University, 2005
Gang Yu, Ph.D., University of Georgia, 2000

Visiting Professors
Wolfgang Dahmen, Ph.D., Rheinisch-Westfalische Technische Hochschule Aachen, 1976
Gyula O.H. Katona, Ph.D., Eötvös Loránd University, 1968

Visiting Associate Professors
George C. Kyriazis, Ph.D., University of South Carolina, 1992
Daniel A. Narayan, Ph.D., Lehigh University, 2000
Attila Sali, Ph.D., Ohio State University, 1986

Visiting Assistant Professor
Geoffrey Diestel, Ph.D., University of Missouri, 2006
Antoine Flattot, Ph.D., Université Lyon 1, 2007
Diana White, Ph.D., University of Nebraska, 2007

Clinical Assistant Professor
Debra Geddings, Ph.D., University of South Carolina, 2003

Senior Instructor
Mary Ellen O’Leary, M.A., University of Michigan, 1967

Instructors
Robert F. Murphy, M.S., University of South Carolina, 2003
Ronda Sanders, M.S., University of South Carolina, 2004

Adjunct Professors
Edwin M. Dickey, Ph.D., University of South Carolina, 1982
R. Bruce Kellogg, Ph.D., University of Chicago, 1958

Distinguished Professors Emeriti
Ronald A. DeVore, Ph.D., Ohio State University, 1967, Robert L. Sumwalt Distinguished Professor Emeritus
Thomas L. Markham, Ph.D., Auburn University, 1967
James W. Roberts, Ph.D., Rutgers University, 1970
H. Edward Scheiblich, Ph.D., University of Texas, 1966
Robert M. Stephenson Jr., Ph.D., Tulane University, 1967
James H. Wahab, Ph.D., University of North Carolina, 1951

Faculty Emeriti
Richard R. Croxton, M.Ed., University of South Carolina, 1947
Peter W. Harley III, Ph.D., University of Georgia, 1966
Richard H. Hudson, Ph.D., Duke University, 1971
George W. Johnson III, Ph.D., University of Tennessee, 1971
Karl H. Matthies, Dr. Rerum Naturalium, University of Freiburg, 1956
Charles A. Nicol Jr., Ph.D., University of Texas, 1954
Paul L. Sperry, Ph.D., New Mexico State University, 1963

Overview

The department offers a program leading to the degree of Bachelor of Science in mathematics and a special five-year program leading to a Bachelor of Science degree and a Master of Science degree in mathematics. In addition, the department serves many of the disciplines within the University through course offerings which provide basic mathematical skills necessary to the pursuit of studies in these disciplines.

General Mathematics Courses

MATH 111 is a course in basic mathematics intended for students who plan to take MATH 122 or MATH 170 and who need more thorough development in algebraic methods.

MATH 111I is an intensive version of MATH 111. This course is intended for students who plan to take MATH 122 or MATH 170 and desire additional support--in the form of smaller classes and more contact hours--to develop the necessary algebraic skills.

MATH 112 is the basic trigonometry course for students who plan to take MATH 141 and have adequate preparation in algebra but need more thorough development in trigonometry. This course may not be used for mathematics credit in the College of Engineering and Information Technology.

MATH 115 is the basic precalculus course for students who plan to take MATH 141 and need more thorough development in algebra and trigonometry before entering MATH 141. This course may not be used for mathematics credit in the College of Engineering and Information Technology.

MATH 122 is intended for students in business, the social sciences, pharmacy, and other disciplines which require an introduction to computational mathematics and calculus and is open to all interested students who satisfy the general requirements listed below.

MATH 141, 142, 241 constitute the normal calculus sequence for students in the College of Arts and Sciences and the College of Engineering and Information Technology. These courses are open to all students who satisfy the general requirements listed below.

MATH 170 is a basic course in finite mathematics. It may be used to satisfy the University’s core requirements and is open to all interested students who satisfy the general requirements listed below.

Freshman Placement in Mathematics

MATH 111: Qualification through placement.

MATH 111I: Qualification through placement.

MATH 112: Qualification through placement or credit for MATH 111, either by successful completion of the course with a grade of C or better, transfer credit from another university, or successful completion of the test in MATH 111, available from the testing service.

MATH 115: Qualification through placement.

MATH 122: Qualification through placement or credit for MATH 111, either by successful completion of the course with a grade of C or better, transfer credit from another university, or successful completion of the test in MATH 111, available from the testing service.

MATH 141: Qualification through placement or credit for MATH 112 or 115, either by successful completion of the course with a grade of C or better, transfer credit from another university, or successful completion of the test in MATH 115, available from the testing service.

Students who do not qualify for MATH 141 under paragraph 1 are strongly encouraged to try to obtain credit for MATH 115 either by taking the course or the examination during the summer preceding their first fall semester.

MATH 170: Qualification through placement or credit for MATH 111 or 115, either by successful completion of the course with a grade of C or better, transfer credit from another university, or successful completion of the test in MATH 111 or 115 which is available from the testing service.

Incoming students who wish to obtain bypass credit for certain mathematics courses may do so as follows:

MATH 111: CLEP Subject Examination entitled "College Algebra" available from the testing service.
MATH 112: CLEP Subject Examination entitled "Trigonometry" available from the testing service.
MATH 115: CLEP Subject Examination entitled "College Algebra-Trigonometry" available from the testing service.
MATH 141: CLEP Subject Examination entitled "Calculus with Analytic Geometry" available from the testing service.

Advanced Placement Test in Mathematics: The Advanced Placement Mathematics tests may be used to gain credit and advanced placement in calculus. Information is available from the testing service.

Degree Requirements

(128 hours)

1. General Education Requirements (43-54)

The following courses fulfill some of the general education requirements, as well as some of the requirements of certain cognates and minors. These courses must be completed for the B.S. degree in mathematics: MATH 141, 142, and either 241 or 250 (preferred), each with a grade of C or better; CSCE 145. In addition, one of the following sequences must also be completed: (i) STAT 511 {= MATH 511} and STAT 512; (ii) either STAT 509 or STAT 515, and either STAT 516 or CSCE 146. Mathematics majors may use MATH 141, 142, and CSCE 145 to fulfill Group II of the general education requirements, MATH 511 {= STAT 511} (with a grade of C or better) for major credit, and STAT 509, 512, 515, and 516 for cognate or minor credit. Only one of STAT 509 and STAT 515 may be used for cognate or minor credit.

For an outline of other general education requirements, see "College of Arts and Sciences."

2. Major Requirements

A grade of C or better is required in each major course and in each of MATH 141, 142, and either 241 or 250. Students may enroll in each major course and in each of MATH 141, 142, and 241 a maximum of two times. Either MATH 526 or MATH 544 may be used for credit but not both. The student may repeat a maximum of three mathematics courses.

General Mathematics Option

The general mathematics track is the traditional course work leading to the B.S. in Mathematics. The mathematics education track is intended for students planning to pursue the five-year M.T. program and a career in secondary mathematics teaching.

General Mathematics Track: MATH 520, 544 (or 526), 546, 554, 574, plus three approved MATH electives numbered above 500, to include at least one of MATH 534, 550, 552 (24-26 hours)

Mathematics Education Track: MATH 531 or 532, 544 (or 526), 546, 554, 574, 580, plus 6 additional hours chosen from 511 {=STAT 511}, 520, 531, 532, 550, and 552 (24-25 hours). Students must complete a cognate in the College of Education (EDFN 300, EDTE 400, EDPY 401 and 401P, and EDTE 402 and 402P).

Applied Mathematics Option

This option is most appropriate for students interested in the sciences, engineering, business, or other fields that make significant use of mathematics.

MATH 520, 526 (recommended), 544, 546, 554, 574, plus three additional courses chosen from the following five categories:

Differential Equations and Modeling: MATH 521, 522, 523
Discrete Mathematics: MATH 570, 575, 587 {=CSCE 557}, 541, 576
Financial Mathematics and Probability: MATH 511 {=STAT 511}, 514, 515
Optimization and Computation: MATH 524, 527, 570
Analysis: MATH 550, 552

Two courses must be chosen from one category, and the third must be chosen from another category (24-25 hours).

Actuarial Mathematics Option

This option is intended for students interested in combining mathematics, statistics, and business, in particular students intending to become actuaries.

MATH 511, 520, 526 (or 544), 546, 554, 574, 570 (or 524), plus 3 hours in mathematics at 500 level (24-25 hours).

A minimum of 24 hours in business administration and statistics as follows:

Statistics (6-12 hours): STAT 512, 513, and 0-6 hours from STAT 510, 520 {=MGSC 520}.
Business Administration (12-18 hours): ACCT 222, ECON 224, FINA 363 {=ECON 363}, FINA 341 or 444, and 0-6 hours from FINA 342, 346, 443, 444, 445, MGSC 392, 393, 520 {=STAT 520}, 594, ECON 420, 594, BADM 499. For the minor in risk management and Insurance (18 hours), of the additional 6 hours, an additional 3 hours must be chosen from FINA 342, 443, 444, or 445
Computing (7-8 hours): CSCE 145, plus one elective from CSCE 146, MGSC 390, STAT 517

Intensive Option

This option is recommended for students interested in pursuing graduate studies in mathematics.

Any major above, plus an additional four approved MATH electives numbered above 500 (36-37 hours).

3. Cognate or Minor (12-18 hours)

See "College of Arts and Sciences"

4. Electives, see "College of Arts and Sciences"

The applied mathematics major is highly recommended for students who intend to pursue a professional career in mathematics or a mathematics-related discipline in government or industry. Such students are strongly encouraged to select a cognate or minor in computer science.

The actuarial mathematics major is highly recommended for students who intend to pursue a career in the actuarial profession in the insurance and financial securities industries. In addition to the required courses in business administration and statistics, students are also encouraged to choose appropriate electives from the social sciences and humanities.

Students intending ultimately to pursue graduate studies in mathematics or mathematics-related disciplines are encouraged to supplement either the general mathematics major or the applied mathematics major with courses having substantial theoretical content.

Five-Year Program

The five-year program of study is designed to permit outstanding mathematics students to obtain both a Bachelor of Science and a Master of Science degree in mathematics in five years. To be eligible for the program, students must have completed one of the preparatory sequences MATH 546-547 or MATH 554-555 by the end of the junior year and have earned 102 credit hours toward the bachelor's degree by the beginning of the senior year. Students will normally be considered for admission to the program at the end of their junior year on the recommendation of their undergraduate advisor. It is expected that such students will have attained a 3.50 overall GPA and a 3.50 GPA on all mathematics courses taken.

Upon admission to the program, students will be eligible for financial assistance from the department. During the fall semester of the senior year, students will receive consideration for employment as undergraduate assistants, and during the spring semester of the senior year, they will receive consideration for quarter-time graduate assistantships. In the fifth year and the first and second summer of graduate study, students will be eligible for half-time graduate assistantships.

Cognate or Minor for Nonmajors

Students with majors in other departments may effectively supplement their major program of study by selecting a cognate or minor in mathematics.

Cognate in Mathematics. Most courses in mathematics numbered 241 and above may be used for cognate credit.

Minor in Mathematics. The minor consists of one of MATH 241 and 250 together with at least 15 hours of mathematics courses selected from MATH 242, MATH 374, or 500-level MATH courses. At least 6 of the 15 hours must be chosen from MATH 520, 526, 544, 546, 554, 574. At most, one of MATH 241 and 250 and one of MATH 526 and 544 may be used for minor credit.

Minor in Actuarial Mathematics and Statistics. The minor consists of the prerequisite courses MATH 141, 142, 241 plus 18 hours of mathematics and statistics courses chosen as follows: MATH 511 {=STAT 511}, STAT 512, 513, and three additional courses selected from three of the following four categories:

i) MATH 514 {=STAT 522};

ii) STAT 510 or 520;

iii) MATH 526 or 544;

iv) MATH 570 or 574.

At most, one of MATH 241 and 250 and one of MATH 526 and 544 may be used for minor credit.

Course Descriptions (MATH)

111 -- Basic College Mathematics. (3) (Prereq: qualification through placement) Basic college algebra; linear and quadratic equations, inequalities, functions and graphs of functions, exponential and logarithm functions, systems of equations. Credit may not be received for both MATH 111 and 115.
111I -- Intensive Basic College Mathematics. (4) (Prereq: qualification through placement) An intensive treatment of the topics covered in MATH 111.
112 -- Trigonometry. (2) (Prereq: qualification through placement or a grade of C or better in MATH 111) Topics in trigonometry specifically needed for MATH 141, 142, 241. Circular functions, analytic trigonometry, applications of trigonometry. Credit may not be received for both MATH 112 and 115.
115 -- Precalculus Mathematics. (4) (Prereq: qualification through placement) Topics in algebra and trigonometry specifically needed for MATH 141, 142, 241. Subsets of the real line, absolute value; polynomial, rational, inverse, logarithmic, exponential functions; circular functions; analytic trigonometry. Credit may not be received for both MATH 111 and 115 or both MATH 112 and 115.
122 -- Calculus for Business Administration and Social Sciences. (3) (Prereq: qualification through placement or a grade of C or better in MATH 111 or 115) Derivatives and integrals of elementary algebraic, exponential, and logarithmic functions. Maxima, minima, rate of change, motion, work, area under a curve, and volume.
141 -- Calculus I. (4) (Prereq: qualification through placement or a grade of C or better in MATH 112 or 115) Four classroom hours and one laboratory hour per week. Functions, limits, derivatives, introduction to integrals, the Fundamental Theorem of Calculus, applications of derivatives and integrals.
142 -- Calculus II. (4) (Prereq: qualification through placement or a grade of C or better in MATH 141) Four classroom hours and one laboratory hour per week. Methods of integration, sequences and series, approximations.
151 -- Calculus Workshop I. (2) (Coreq: MATH 141) Small study group practice in applications of calculus. For elective credit only. Two 2-hour sessions per week.
152 -- Calculus Workshop II. (2) (Coreq: MATH 142) Small study group practice in applications of calculus. For elective credit only. Two 2-hour sessions per week.
170 -- Finite Mathematics. (3) (Prereq: qualification through placement or a grade of C or better in MATH 111 or 115) Elementary matrix theory; systems of linear equations; permutations and combinations; probability and Markov chains; linear programming and game theory.
172 -- Mathematical Modeling for the Life Sciences. (3) (Prereq: C or better in MATH 122 or MATH 141) Modeling with difference and differential equations, equilibria, and stability; periodic functions; vectors, matrices, eigenvalues and eigenvectors; geometric series.
174 -- Discrete Mathematics for Computer Science. (3) (Prereq: qualification through placement or a grade of C or better in MATH 112 or 115) Induction, complexity, elementary counting, combinations and permutations, recursion and recurrence relations, graphs and trees; discussion of the design and analysis of algorithms--with emphasis on sorting and searching.
198 -- Introduction to Careers and Research in the Mathematical Sciences. (1) (Prereq: Qualification through placement in MATH 142 or higher, or a grade of C or better in MATH 141) An overview of different areas of mathematical research andcareer opportunities for mathematics majors. Pass/fail only.
221 -- Basic Concepts of Elementary Mathematics I. (3) (Prereq: qualification through placement or a grade of C or better in MATH 111 or 115) The meaning of number, fundamental operations of arithmetic, the structure of the real number system and its subsystems, elementary number theory. Open only to students in elementary or early childhood teacher certification.
222 -- Basic Concepts of Elementary Mathematics II. (3) (Prereq: MATH 221) Informal geometry and basic concepts of algebra. Open only to students in elementary or early childhood teacher certification.
241 -- Vector Calculus. (3) (Prereq: qualification through placement or a grade of C or better in MATH 142) Vector algebra, geometry of three-dimensional space; lines, planes, and curves in space; polar, cylindrical, and spherical coordinate systems; partial differentiation, max-min theory; multiple and iterated integration, line integrals, and Green's theorem in the plane. Credit may not be received for both MATH 241 and MATH 250.
242 -- Elementary Differential Equations. (3) (Prereq: qualification through placement or a grade of C or better in MATH 142) Ordinary differential equations of first order, higher order linear equations, Laplace transform methods, series methods; numerical solution of differential equations. Applications to physical sciences and engineering.
250 -- Vector Analysis I. (3) (Prereq: qualification through placement or a grade of C or better in MATH 142) Vector algebra, geometry of three-dimensional space; polar, cylindrical, and spherical coordinate systems; partial differentiation, the derivative as a matrix transformation, and flow lines of a vector field; max-min theory; multiple and iterated integration. (This course is intended for mathematics majors and other students intending to take MATH 550; the treatment will be more sophisticated than is offered in MATH 241.)
300 -- Transition to Advanced Mathematics. (3) (Prereq: MATH 142) Rigor of mathematical thinking and proof writing via logic, sets, and functions. Intended to bridge the gap between lower-level (computational-based) and upper-level (proof-based) mathematics courses.
374 -- Discrete Structures. (3) (Prereq: MATH 142 and CSCE 146) Propositional and predicate logic; proof techniques; recursion and recurrence relations; sets, combinatorics, and probability; functions, relations, and matrices; algebraic structures.
399 -- Independent Study. (3-9) Contract approved by instructor, advisor, and department chair is required for undergraduate students.
401 -- Conceptual History of Mathematics. (3) (Prereq: MATH 122, or 141, or consent of the department) Topics from the history of mathematics emphasizing the 17th century to the present. Various mathematical concepts are discussed and their development traced. For elective or Group II credit only.
511 -- Probability. {=STAT 511} (3) (Prereq: a grade of C or higher in either MATH 250 or 241) Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities, moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate, and bivariate normal distributions.
514 -- Financial Mathematics I. {=STAT 522} (3) (Prereq: a grade of C or better in either MATH 250 or 241) Probability spaces. Random variables. Mean and variance. Geometric Brownian Motion and stock price dynamics. Interest rates and present value analysis. Pricing via arbitrage arguments. Options pricing and the Black-Scholes formula.
515 -- Financial Mathematics II. {=STAT 523} (3) (Prereq: MATH 514 or STAT 522 with a grade of C or better) Convex sets. Separating Hyperplane Theorem. Fundamental Theorem of Asset Pricing. Risk and expected return. Minimum variance portfolios. Capital Asset Pricing Model. Martingales and options pricing. Optimization models and dynamic programming.
520 -- Ordinary Differential Equations. (3) (Prereq: MATH 544 or 526; or consent of department) Differential equations of the first order, linear systems of ordinary differential equations, elementary qualitative properties of nonlinear systems.
521 -- Boundary Value Problems and Partial Differential Equations. (3) (Prereq: MATH 520 or MATH 250 and 242 or MATH 241 and 242) Laplace transforms, two-point boundary value problems and Green's functions, boundary value problems in partial differential equations, eigenfunction expansions and separation of variables, transform methods for solving PDE's, Green's functions for PDE's, and the method of characteristics.
522 -- Wavelets. (3) (Prereq: MATH 544 or 526 or consent of department) Basic principles and methods of Fourier transforms, wavelets, and multiresolution analysis; applications to differential equations, data compression, and signal and image processing; development of numerical algorithms. Computer implementation.
523 -- Mathematical Modeling of Population Biology. (3) (Prereq: MATH 142, BIOL 301, or MSCI 311 recommended) Applications of differential and difference equations and linear algebra modeling the dynamics of populations, with emphasis on stability and oscillation. Critical analysis of current publications with computer simluation of models.
524 -- Nonlinear Optimization. (3) (Prereq: MATH 526 or 544 or consent of department) Descent methods, conjugate direction methods, and Quasi-Newton algorithms for unconstrained optimization; globally convergent hybrid algorithm; primal, penalty, and barrier methods for constrained optimization. Computer implementation of algorithms.
525 -- Mathematical Game Theory. (3) (Prereq: MATH 526 or 544) Two-person zero-sum games, minimax theorem, utility theory, n-person games, market games, stability.
526 -- Numerical Linear Algebra. (4) (Prereq or coreq: MATH 250 [preferred] or 241) Matrix algebra, Gauss elimination, iterative methods; overdetermined systems and least squares; eigenvalues, eigenvectors; numerical software. Computer implementation. Three lectures and one laboratory hour per week. Credit may not be received for both MATH 526 and MATH 544.
527 -- Numerical Analysis. {=CSCE 561} (3) (Prereq: MATH 242 or 520) Interpolation and approximation of functions; solution of algebraic equations; numerical differentiation and integration; numerical solutions of ordinary differential equations and boundary value problems; computer implementation of algorithms.
531 -- Foundations of Geometry. (3) (Prereq: MATH 250 or 241) The study of geometry as a logical system based upon postulates and undefined terms. The fundamental concepts and relations of Euclidean geometry developed rigorously on the basis of a set of postulates. Some topics from non-Euclidean geometry.
532 -- Modern Geometry. (3) (Prereq: MATH 250 or 241) Projective geometry, theorem of Desargues, conics, transformation theory, affine geometry, Euclidean geometry, non-Euclidean geometries, and topology.
533 -- Elementary Geometric Topology. (3) (Prereq: MATH 250 or 241) Topology of the line, plane, and space, Jordan curve theorem, Brouwer fixed point theorem, Euler characteristic of polyhedra, orientable and non-orientable surfaces, classification of surfaces, network topology.
534 -- Elements of General Topology. (3) (Prereq: MATH 250 or 241) Elementary properties of sets, functions, spaces, maps, separation axioms, compactness, completeness, convergence, connectedness, path connectedness, embedding and extension theorems, metric spaces, and compactification.
540 -- Modern Applied Algebra. (3) (Prereq: MATH 250 or 241) Finite structures useful in applied areas. Binary relations, Boolean algebras, applications to optimization, and realization of finite state machines.
541 -- Algebraic Coding Theory. (3) (Prereq: MATH 526 or MATH 544 or consent of department) Error-correcting codes, polynomial rings, cyclic codes, finite fields, BCH codes.
544 -- Linear Algebra. (3) (Prereq or coreq: MATH 250 [preferred] or 241) Matrix algebra, solution of linear systems; notions of vector space, independence, basis, dimension; linear transformations, change of basis; eigenvalues, eigenvectors, Hermitian matrices, diagonalization; Cayley-Hamilton theorem. Credit may not be received for both MATH 526 and MATH 544.
546 -- Algebraic Structures I. (3) (Prereq: MATH 250 [preferred] or 241) Permutation groups; abstract groups; introduction to algebraic structures through study of subgroups, quotient groups, homomorphisms, isomorphisms, direct product; decompositions; introduction to rings and fields.
547 -- Algebraic Structures II. (3) (Prereq: MATH 546) Rings, ideals, polynomial rings, unique factorization domains; structure of finite groups; topics from: fields, field extensions, Euclidean constructions, modules over principal ideal domains (canonical forms).
550 -- Vector Analysis II. (3) (Prereq: a grade of C or higher in either MATH 250 [preferred] or 241) Vector fields, line and path integrals, orientation and parametrization of lines and surfaces, change of variables and Jacobians, oriented surface integrals, theorems of Green, Gauss, and Stokes; introduction to tensor analysis.
551 -- Introduction to Differential Geometry. (3) (Prereq: MATH 250 or 241) Parametrized curves, regular curves and surfaces, change of parameters, tangent planes, the differential of a map, the Gauss map, first and second fundamental forms, vector fields, geodesics, and the exponential map.
552 -- Applied Complex Variables. (3) (Prereq: MATH 250 or 241) Complex integration, calculus of residues, conformal mapping, Taylor and Laurent Series expansions, applications.
554 -- Analysis I. (3) (Prereq: MATH 250 [preferred] or 241) Least upper bound axiom, the real numbers, compactness, sequences, continuity, uniform continuity, differentiation, Riemann integral and fundamental theorem of calculus.
555 -- Analysis II. (3) (Prereq: MATH 554 or consent of department) Riemann-Stieltjes integral, infinite series, sequences and series of functions, uniform convergence, Weierstrass approximation theorem, selected topics from Fourier series or Lebesgue integration.
561 -- Introduction to Mathematical Logic. (3) (Prereq: MATH 250 or 241) Syntax and semantics of formal languages; sentential logic, proofs in first order logic; Godel's completeness theorem; compactness theorem and applications; cardinals and ordinals; the Lowenheim-Skolem-Tarski theorem; Beth's definability theorem; effectively computable functions; Godel's incompleteness theorem; undecidable theories.
562 -- Theory of Computation. {=CSCE 551} (3) (Prereq: CSCE 350 or MATH 526 or 544 or 574) Basic theoretical principles of computer science as modeled by formal languages and automata; computability and computational complexity. Major credit may not be received for both CSCE 355 and CSCE 551.
570 -- Discrete Optimization. (3) (Prereq: MATH 526 or 544) Discrete mathematical models. Applications to such problems as resource allocation and transportation. Topics include linear programming, integer programming, network analysis, and dynamic programming.
574 -- Discrete Mathematics I. (3) (Prereq: MATH 142) Mathematical models; mathematical reasoning; enumeration; induction and recursion; tree structures; networks and graphs; analysis of algorithms.
575 -- Discrete Mathematics II. (3) (Prereq: MATH 574) A continuation of MATH 574. Inversion formulas; Polya counting; combinatorial designs; minimax theorems; probabilistic methods; Ramsey theory; other topics.
576 -- Combinatorial Game Theory. (3) (Prereq: MATH 526, 544, or 574) Winning in certain combinatorial games such as Nim, Hackenbush, and Domineering. Equalities and inequalities among games, Sprague-Grundy theory of impartial games, games which are numbers.
580 -- Elementary Number Theory. (3) (Prereq: MATH 250 or 241) Divisibility, primes, congruences, quadratic residues, numerical functions. Diophantine equations.
587 -- Introduction to Cryptography. {=CSCE 557} (3) (Prereq: CSCE 145, MATH 250 or 241, and either CSCE 355 or MATH 574) Design of secret codes for secure communication, including encryption and integrity verification: ciphers, cryptographic hashing, and public key cryptosystems such as RSA. Mathematical principles underlying encryption. Code-breaking techniques. Cryptographic protocols.
590 -- Undergraduate Seminar. (1-3) (Prereq: consent of instructor) A review of literature in specific subject areas involving student presentations. Content varies and will be announced in the Master Schedule of Classes by suffix and title. Pass-fail grading. For undergraduate credit only.
599 -- Topics in Mathematics. (1-3) Recent developments in pure and applied mathematics selected to meet current faculty and student interest.
650 -- AP Calculus for Teachers. (3) (Prereq: current secondary high school teacher certification in mathematics and at least 6 hours of calculus) A thorough study of the topics to be presented in AP calculus, including limits of functions, differentiation, integration, infinite series, and applications. (Not intended for degree programs in mathematics.)

College of Arts and Sciences