William A. Feldman, Chair of the Department, 301 Science Engineering Building, 575-3351
DISTINGUISHED PROFESSOR SCHEIN; UNIVERSITY PROFESSOR DUNN; PROFESSORS BREWER, COCHRAN, DUNCAN, FELDMAN, KHAVINSON, LUECKING, MADISON, SUMMERS, TUBBS; PROFESSORS EMERITI KEOWN, KIMURA, LONG, SCROGGS; ASSOCIATE PROFESSORS AKEROYD, MEAUX, MEEK, MONROE, TABACHNIKOV; ASSOCIATE PROFESSORS EMERITI GRAHAM, SEKIGUCHI; ASSISTANT PROFESSORS ARNOLD, GOODMAN-STRAUSS, JOHNSON, MILLER, RYAN
Requirements for a Major in Mathematics, B.A. Degree: MATH 2103, 2574, 4932 and 18 semester hours of courses in mathematics numbered above 3000, including 3083 and 3113. (See writing requirement below.)
Requirements for a Major in Mathematics, B.S. Degree: As a part of the requirements for a B.S. degree with a major in mathematics, the student must complete MATH 2103, 2574, 3083, 3113, 3404, 4513, 4932, and CSCI 1023/1021L. In addition, for the B.S. degree in mathematics, the student is required to complete one of the following three options: (1) a program for the student who wishes to prepare for either industrial work in mathematics or graduate work in some field other than mathematics or statistics, (2) a program for the student who is seeking a broad background in mathematics or who wishes to study mathematics at the graduate level, (3) a program for the student who wishes to emphasize statistics or who intends to study statistics at the graduate level.
The courses required for option (1) are; MATH 3423, either MATH 4353 and 4363 or STAT 3013 and 4003, plus three semester hours of electives from mathematics courses numbered above 3000. Strongly recommended electives in this program are MATH 4523 and 3443.
The courses required for option (2) are: MATH 4523, two of MATH 3443, 4113, 4703, and three hours of electives from mathematics courses numbered above 3000.
The courses required for option (3) are: MATH 3353, STAT 3013, 4003, 4001L, 4033, 4043. Strongly recommended electives in this program are STAT 5103 and 5113.
All of the electives used in fulfilling the requirements for either of the baccalaureate programs in mathematics must be approved by the student's adviser.
The science requirement for the Bachelor of Science degree in mathematics consists of two of the course sequences as listed:
BIOL 1543/1541L, (may substitute BOTY 1013/1011L and ZOOL 1004)
CHEM 1103/1101L, 1123/1121L
CSCI 1033, 2013, (prerequisite, CSCI 1023/1021L)
GEOL 1113/1111L, 1133/1131L
PHYS 2053/2051L, 2073/2071L (College Physics will not substitute)
In addition, one advanced course must be chosen from one of the chosen areas. Courses taken to satisfy this requirement must be approved by the Department of Mathematical Sciences.
A 2.00 cumulative grade-point average on all work completed in the Department of Mathematical Sciences will be required for graduation with a B.A. or B.S. degree.
Writing Requirement for both B.A. and B.S. Degrees: The writing requirement for mathematics majors will be satisfied by writing a paper based on the student's research of a mathematical topic under the direction of a faculty member. Typically, one hour of credit in MATH 400V will be awarded for successfully completing the paper. An honors paper or senior thesis will satisfy this requirement. The student should consult his or her adviser for details.
Requirements for Departmental Honors in Mathematics: The Departmental Honors Program in Mathematics is designed for the superior student and is intended to help the student develop a more comprehensive view of the nature of mathematics. The program provides a vehicle for the recognition of the achievements of work beyond the usual course of study and earns the student the distinction "Mathematics Scholar Cum Laude'' at graduation. Higher degree distinctions are recommended only in truly exceptional cases and are based upon the whole of the candidate's program of honors studies.
For graduation with honors, the candidate must satisfy the requirements set forth by the Honors Council. The candidate must also obtain at least a 3.50 grade-point average in mathematics courses numbered 2554, 2564, 2574, 3083, 3113, 3404, and 4513, as well as in the additional mathematics courses necessary to complete the requirements for the chosen option. In addition, a grade of "D'' or "F'' in any other course offered by the Department disqualifies a student for honors.
Candidates must take one year of honors mathematics in their senior year. This course will require an acceptable paper and will carry two hours of credit per semester. The quality of this paper, along with the execution of the rest of the student's honors program including the overall academic performance, will be used in determining the distinction between Honors and High Honors.
Requirements for a Minor in Mathematics: MATH 2103, 2564, and 9 hours selected from MATH 2574, 3083, 3103, 3113, 3404, and 4513.
Requirements for a Minor in Statistics: MATH 2554 and 12 hours of non-cross-listed courses in the statistics section of this catalog, including 9 hours in courses numbered 3000 and above. A student must notify the Department of his or her intent to minor.
Students in Fulbright College of Arts and Sciences who, in the opinion of the Department of Mathematical Sciences, need additional work in the fundamentals are required to take MATH 0003. Using the student's record and their ACT or Mathematics Placement Test scores, a student's adviser will suggest enrollment in appropriate courses.
Mathematics (B.A.) Teacher Certification Requirements:
1. Complete a minimum of 21 hours in primary field.
2. Complete Pre-Education (ASED) minor. (See page 205.)
3. The following courses are specifically required for certification:
HLSC 1002, Wellness Concepts, and PEAC 1621, Fitness Concepts, OR HLSC 1103, Personal Health
& Safety
3 hours of geometry (MATH 3773, Foundations of Geometry, recommended)
4. Earn a "C" or better in ENGL 1013, ENGL 1023, ENGL 3003 (or ENGL 2013, or exemption by grades
or test), COMM 1313, and MATH 1203 (or any higher mathematics course).
5. Students wanting to teach mathematics in middle school must major in mathematics and complete
PSYC 3093, Childhood and Adolescent Psychology.
Mathematics (B.S.) Teacher Certification Requirements:
1. Complete a minimum of 21 hours in primary field.
2. Complete Pre-Education (ASED) minor. (See page 205.)
3. The following courses are specifically required for certification:20
HLSC 1002, Wellness Concepts, and PEAC 1621, Fitness Concepts, OR HLSC 1103, Personal Health & Safety
COMM 1313, Fundamentals of Communication
3 hours of geometry (MATH 3773, Foundations of Geometry, recommended)
20With approval of advisor, these courses may be used as electives in student's program of study.
4. Earn a "C" or better in ENGL 1013, ENGL 1023, ENGL 3003 (or ENGL 2013, or exemption by grades
or test), COMM 1313, and MATH 1203 (or any higher mathematics course).
For requirements for advanced degrees in mathematics or statistics, see the Graduate School Catalog.
Courses: Mathematics (MATH)
0003 Beginning and Intermediate Algebra (Fa, Sp, Su) For students who have inadequate preparation for taking MATH 1203. Credit earned in this course may not be applied to the total required for a degree.
Registration in MATH 1203, 1213, or 1285 requires satisfaction of either (1) or (2) below:
1. (a) Mathematics ACT score of at least 19 (or equivalent SAT); and ACT.EA subscore of at least 9.
(b) Sufficient score(s) on the Mathematics Placement Test as indicated in the advising materials.
2. Grade of at least "C" in MATH 0003.
1203 College Algebra (Fa, Sp, Su) Credit will be allowed for only one of MATH 1203 and MATH 1285. Prerequisite: See above. UNIVERSITY CORE COURSE.
1213 Plane Trigonometry (Fa, Sp, Su) Credit will be allowed for only one of either MATH 1213 or MATH 1285. Prerequisite: See above.
1285 Precalculus Mathematics (Fa, Sp) Topics in algebra and trigonometry. To be taken by students who expect to take MATH 2554. Prerequisite: one and one-half units of high school algebra and one unit of high school trigonometry or consent. No credit can be given for those who have completed MATH 1203, and/or MATH 1213. See above.
Registration in MATH 2043, 2053, or 2554 is permitted if the following is satisfied instead of the listed prerequisite: The student scores sufficiently high according to the placement scores. This placement is indicated in the advising materials for each student.
2043 Survey of Calculus (Fa, Sp, Su) Selected topics in elementary calculus and analytic geometry for students in business, agriculture, and social sciences. Credit will be allowed for only one of MATH 2043 and MATH 2554. Prerequisite: MATH 1203.
2053 Finite Mathematics (Fa, Sp, Su) Selected topics in probability, vectors and matrices, linear programming. Terminal course for students in business, agriculture, and social sciences. This course will not prepare students to take other mathematics courses. Prerequisite: MATH 1203.
2053H Honors Finite Mathematics
2103 Discrete Mathematics (Fa, Sp) Introductory study of sets, relations, logic, proofs, algorithms, counting methods, graph theory, trees, and Boolean algebras. Prerequisite: MATH 1203 or ACT math score of 21 or above.
2213 Survey of Mathematical Structures I (Fa, Sp, Su) Sets and logic, systems of numeration, number systems and operations, elementary number theory. Prerequisite: MATH 1203.
2223 Survey of Mathematical Structures II (Fa, Sp, Su) Geometry and measurement, statistics and probability. Prerequisite: MATH 1203.
2554 Calculus I (Fa, Sp, Su) Credit will be allowed for only one of MATH 2043 and MATH 2554. Prerequisite: MATH 1203 and 1213, or 1285.
2554H Honors Calculus I (Fa) Topics in analytic geometry and calculus. Prerequisite: consent of the Honors Director and the instructor. Students may not receive credit for both MATH 2043 and MATH 2554.
2564 Calculus II (Fa, Sp, Su) Integral calculus of one variable and infinite series. Prerequisite: MATH 2554.
2564H Honors Calculus II (Sp) Integral calculus of one variable and infinite series. Prerequisite: MATH 2554 and consent of the Honors Director and the instructor.
2574 Calculus III (Fa, Sp, Su) Differential and integral calculus of several variables, vector calculus. Prerequisite: MATH 2564.
2574H Honors Calculus III (Irregular) Differential and integral calculus of several variables, vector calculus. Prerequisite: MATH 2564 and consent of the Honors Director and the instructor.
3083 Linear Algebra (Fa, Sp, Su) Systems of linear equations, vector spaces, linear transformations, matrices, determinants. Prerequisite: MATH 2554 or 2043.
3103 Combinatorial and Discrete Mathematics (Fa, Sp, Su) Basic combinatorial techniques including the study of networks, generating functions, principles of inclusion/ex-clusion, Zn, Hamming coding theory, graph theory, and block designs. Prerequisite: MATH 2103.
3113 Introduction to Abstract Algebra I (Fa, Sp) Introduction to algebraic structures with emphasis on rigorous justification of results. Prerequisite: MATH 3083.
3133 History of Mathematics (Irregular) Prerequisite: MATH 2554 and junior standing.
3203 Theory of Numbers (Irregular) Prerequisite: MATH 2554 and junior standing.
3353 Numerical Methods (Fa, Sp) Approximate solution of algebraic equations and differential equations. Applications of numerical methods and finite differences to differentiation and integration. Prerequisite: MATH 2574 and proficiency in a high-level computer language.
3404 Differential Equations (Fa, Sp, Su) First and second order ordinary differential equations, the Laplace transform, matrix systems of ordinary differential equations. Prerequisite: MATH 2574.
3423 Advanced Applied Mathematics (Fa, Sp, Su) Matrices, Fourier analysis, partial differential equations. Prerequisite: MATH 3404.
3443 Complex Variable for Application (Sp) Complex analysis, series, conformal mapping. Prerequisite: MATH 3404.
3773 Foundations of Geometry I (Fa) Axiomatic method; Euclidean geometry; non-Euclidean geometry. Prerequisite: consent of instructor.
3923H Honors Colloquium (Irregular) Covers a special topic or issue, offered as part of the honors program. May be repeated when the content is changed. Prerequisite: honors candidacy (not restricted to candidacy in mathematics) or consent of instructor.
399VH Mathematics Honors Course (1-6) May be taken for one to six hours of credit and repeated for a maximum of 12 hours. Prerequisite: junior standing and consent of instructor.
400V Directed Readings (1-6)
4053 Foundations of Mathematics (Irregular) Prerequisite: consent of instructor.
4093 Content and Methods in Teaching Algebra (Irregular) Offered in in-service classes and special summer institutes. Subject matter methods and techniques of teaching junior high school algebra. Prerequisite: graduate standing.
4103 Finite Dimensional Vector Spaces (Irregular) Linear functionals, matrix representation of linear transformations, scalar product, spectral representation of linear transformations. Prerequisite: MATH 3083 or consent of instructor.
4113 Introduction to Abstract Algebra II (Fa) Topics in abstract algebra including finite abelian groups, linear groups, factorization in cummutative rings, quadratic field extensions, Gaussian integers, Wedderburn's theorem, and multilinear algebra. Prerequisite: MATH 3113.
4153 Mathematical Modeling (Fa) Mathematical techniques for formulating, analyzing, and criticizing deterministic models taken from the biological, social, and physical sciences. Techniques include graphical methods, stability, optimization, and phase plane analysis. Prerequisite: MATH 3404.
4203 Linear Programming and Game Theory (Irregular) Solution sets, duality, and pivoting in linear programming. Feasible solutions and the simplex method. The transportation problem. Matrix games. Prerequisites: MATH 3083 and proficiency in a high-level computer language.
4253 Symbolic Logic I (Fa) Rigorous analyses of the concepts of proof, consistency, equivalence, validity, implication, and truth. Full coverage of truth-functional logic and quantification theory (predicate calculus). Discussion of the nature and limits of mechanical procedures (algorithms) for proving theorems in logic and mathematics. Informal accounts of the basic facts about infinite sets. (Same as PHIL 4253.)
4263 Symbolic Logic II (Sp) Topics include: soundness and completeness of propositional logic, soundness and completeness of quantification theory, the elements of model theory and recursion theory, Gödel's incompleteness theorems, and the limitative theorems of Tarski and Church. (Same as PHIL 4263.) Prerequisite: MATH 4253 or PHIL 4253.
4353 Numerical Linear Algebra (Sp) Numerical methods for problems of linear algebra, including the solution of very large systems, eigenvalues, and eigenvectors. Prerequisite: programming experience and MATH 3083.
4363 Numerical Analysis (Fa) General iterative techniques, error analysis, root finding, interpolation, approximation, numerical integration, numerical solution of differential equations. Prerequisite: programming experience and MATH 4513 or consent.
4433 Integral Transform Theory (Irregular) Linear differential equations, Laplace transforms, transfer functions, solution stability. Fourier transforms, the two-sided Laplace transform, limitations of these methods, the Z transform. Prerequisite: consent of instructor.
4453 Integral Equations (Irregular) Eigenvalues and eigenfunctions of linear integral operators, including the Fredholm Alternative. Volterra equations. Discussion of existence and uniqueness of solutions of nonlinear integral equations. Numerical methods. Prerequisite: MATH 4523.
4503 Differential Geometry and Vector Calculus (Irregular) Topics include: Vector differential and integral calculus, Stokes' Theorem in 3-space, classical differential geometry in 3-space (curves, surfaces), differential forms, general Stokes' Theorem, applications to hydrodynamics, and electromagnetism. Prerequisites: MATH 3083, MATH 4513, or consent.
4513 Advanced Calculus I (Fa) The real and complex number systems, basic set theory and topology, sequences and series, continuity, differentiation, Taylor's theorem. Emphasis is placed on careful mathematical reasoning. Prerequisite: MATH 2574 and 3083, or consent of instructor.
4523 Advanced Calculus II (Sp) The Riemann-Stieltjes integral, uniform convergence of functions, Fourier series, implicit function theorem, Jacobians, and derivatives of higher order. Prerequisite: MATH 4513.
4653 Introduction to Higher Geometry I Prerequisite: MATH 3113 and consent of instructor.
4663 Introduction to Higher Geometry II Pre-requisite: MATH 4653.
4703 Introduction to Point-Set Topology Prerequisite: MATH 4513.
4783 Foundations of Geometry II (Sp, Su) Trans-formational geometries and dualities; problem solving with linear, isometric, affine, inversive, and projective transformations. Selected topics from projective geometry and convex geometry. Prerequisite: MATH 3773 or consent of instructor.
4932 Mathematics Major Seminar The two-credit course would have several components designed to address students' mathematical knowledge, problem-solving and communication skills. A series of weekly seminars on topics of historical or cross-disciplinary interest would be accompanied by a weekly problem-solving seminar in which student presentations would play a part. The course would also be a forum for sharing information about career opportunities and preparation for employment.
498V Senior Thesis (1-6) Prerequisite: consent.
5013 Topics in Algebra for Teachers (Irregular) Topics from abstract and linear algebra of current interest to teachers. May be repeated for credit. Prerequisite: graduate standing and consent of instructor.
5023 Topics in Geometry for Teachers (Irregular) Topics in geometry of current interest to teachers. May be repeated for credit. Prerequisite: graduate standing and consent of instructor.
5033 Topics in Analysis for Teachers (Irregular) Topics related to calculus of current interest to secondary school teachers. May be repeated for credit. Prerequisite: graduate standing and consent of instructor.
504V Special Topics for Teachers (1-6) (Irregular) Current topics in mathematics of interest to secondary school teachers. May be repeated for credit. Prerequisite: graduate standing and consent of instructor.
5073 Mathematical Methods of Physics I Applications of complex variables, differential equations, special functions, Green's functions, and matrix analysis to problems in physics. Introduction to numerical and statistical techniques used in physics research. (Same as PHYS 5073.) Prerequisite: MATH 3423 and consent.
5083 Mathematical Methods of Physics II Applications of matrices, tensors, and linear vector spaces to problems in physics. Introduction to groups and their representations, and symmetry principles in modern physics. (Same as PHYS 5083.) Prerequisite: MATH 5073.
510V Mathematics Seminar (1-3) (Fa) Members of the faculty and advanced students meet for presentation and discussion of topics. Prerequisite: graduate standing.
5123 Algebra I (Sp) What the beginning graduate student should know about algebra: groups, rings, fields, modules, algebras, categories, homological algebra, Galois Theory. Prerequisite: MATH 3113.
5133 Algebra II (Fa) Continuation of 5123. Prerequisite: MATH 5123.
5303 Ordinary Differential Equations (Fa) Existence, uniqueness, stability, qualitative behavior, and numerical solutions. Prerequisite: programming experience, MATH 3404 and MATH 4513 or consent.
5313 Partial Differential Equations (Sp) Classification, boundary value problems, applications, numerical solutions. Prerequisites: MATH 3423 and MATH 4513, or consent.
5443 Nonlinear Systems Analysis and Control (Sp) Second-order nonlinear systems. Nonlinear differential equations. Approximate analysis methods. Lyapunov and input-output stability. Design of controllers, observers, and estimators for nonlinear systems. (Same as ELEG 5443.) Prerequisites: ELEG 4403 or MATH 5303 and consent.
5453 Functional Analysis I (Irregular) Linear vector spaces, linear operators. Prerequisite: MATH 5513.
5463 Functional Analysis II (Irregular) Spectral analysis, linear functionals, Banach algebras. Prerequisite: MATH 5453.
5503 Theory of Functions of a Real Variable I (Fa) Real number system, Lebesgue measure, Lebesgue integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus Lp spaces, Holder and Minkowski inequalities, bounded linear functionals on the Lp spaces. Prerequisite: MATH 4523.
5513 Theory of Functions of a Real Variable II (Sp) Measure and integration on abstract measure spaces, signed measures, Hahn decomposition, Radon-Nikodym theorem, Lebesgue decomposition, measures on algebras and their extensions, product measures, Fubini's theorem. Prerequisite: MATH 5503.
5523 Theory of Functions of a Complex Variable I (Fa) Complex numbers, analytic functions, power series, complex integration, Cauchy's Theorem and integral formula, maximum principle, singularities, Laurent series, Mîbius maps. Prerequisite: MATH 4513 or consent of instructor.
5533 Theory of Functions of a Complex Variable II (Sp) Riemann Mapping Theorem, analytic continuation, harmonic functions, entire functions. Prerequisite: MATH 5523.
5703 Foundations of Topology (Fa) Metric and general topological spaces, separation axioms, Urysohn's lemma, Tietze extension theorem, connectedness, compactness, and the Tychonoff theorem. Prerequisite: MATH 4513.
5713 Algebraic Topology (Fa) Homotopy, singular and relative homology, excision theorem, the Mayer-Vietoris sequence, Beti numbers, and the Euler characteristic. Prerequisite: MATH 5703.
600V Master's Thesis (1-6) (Fa, Sp, Su) Prerequisite: graduate standing and consent of instructor.
610V Directed Readings (1-6) (Irregular)
619V Topics in Algebra (1-6) Current research interests in algebra. May be repeated for credit.
659V Topics in Analysis (1-6) Current research interests in analysis. May be repeated for credit.
679V Topics in Topology (1-6) Current research interest in topology. May be repeated for credit.
700V Doctoral Dissertation (1-6)
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