NOTICE - This edition of the Catalog of Studies is provided as a courtesy to students who may be attending classes under these degree requirements. If you are a prospective student, or are attending class under a different set of degree requirements, please visit

http://catalogofstudies.uark.edu/

to find your class year catalog.

MATHEMATICAL SCIENCES (MASC)

William A. Feldman, Chair of the Department, 538 Hotz Hall, 575-3351

Distinguished Professor Schein • University Professor Emeritus Dunn • Professors Brewer, Cochran, Duncan, Feldman, Khavinson, Luecking, Madison, Tubbs • Professors Emeriti Keown, Kimura, Long, Scroggs, Summers • Associate Professors Akeroyd, Arnold, Goodman-Strauss, Meaux, Meek, Monroe, Ryan • Associate Professors Emeriti Graham, Sekiguchi • Assistant Professors Capogna, Hogan, Johnson, Lanzani, Petrus, Rieck, Woodland • Visiting Assistant Professors Saleeby, Vassilev (D), Vassilev (J)

Requirements for a Major in Mathematics, B.A. Degree: MATH 2103, MATH 2574, MATH 4932 and 18 semester hours of courses in mathematics numbered above 3000, including MATH 3083 and MATH 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, MATH 2574, MATH 3083, MATH 3113, MATH 3404, MATH 4513, MATH 4932, and CSCE 1023/1021L or CENG 1113/1111L. 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 MATH 4363 or STAT 3013 and STAT 4003, plus three semester hours of electives from mathematics courses numbered above 3000. Strongly recommended electives in this program are MATH 4523 and MATH 3443.

The courses required for option (2) are MATH 4523, two of MATH 3443, MATH 4113 and three hours of electives from mathematics courses numbered above 3000.

The courses required for option (3) are MATH 3353, STAT 3013, STAT 4003, STAT 4001L, STAT 4033, STAT 4043. Strongly recommended electives in this program are STAT 5103 and STAT 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 five course sequences as listed:

1. BIOL 1543/1541L and one of BIOL 2533, BOTY 1613/1611L, ZOOL 1613/1611L or MBIO 2013/2011L

2. CENG 1123/1121L and CSCE 2143

3. CHEM 1103/1101L, CHEM 1123/1121L

4. GEOL 1113/1111L, GEOL 1133/1131L

5. PHYS 2054, PHYS 2074 (College Physics will not substitute)

In addition, one advanced course must be chosen from one of the two 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 MATH 2554, MATH 2564, MATH 2574, MATH 3083, MATH 3113, MATH 3404, and MATH 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 (3 courses) selected from MATH 2574, MATH 3083, MATH 3103, MATH 3113, MATH 3404, and MATH 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. or B.S.) Teacher Certification Requirements:

1. Complete a minimum of 21 hours in primary field.

2. Complete Pre-Education (ASED) minor.

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 I, recommended)

4. Earn a 'C' or better in ENGL 1013, ENGL 1023, ENGL 2003, (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 Adolescence.

For requirements for advanced degrees in mathematics or statistics, see the Graduate School Catalog.

MATHEMATICS (MATH)

MATH0003 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.

MATH1203 College Algebra (FA, SP, SU) Credit will be allowed for only one of MATH 1203 and MATH 1285.

MATH1213 Plane Trigonometry (FA, SP, SU) Credit will be allowed for only one of MATH 1213 or MATH 1285.

MATH1285 Precalculus Mathematics (FA, SP) Topics in algebra and trigonometry. To be taken by students who expect to take MATH 2554.

MATH2043 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.

MATH2053 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 mathematical courses. Prerequisite: MATH 1203.

MATH2053H Honors Finite Mathematics (FA, SP, SU)

MATH2103 Discrete Mathematics (FA, SP, SU) 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.

MATH2103H Honors Discrete Mathematics (FA) 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.

MATH2213 Survey of Mathematical Structures I (FA, SP, SU) Sets and logic, systems of numerations, number systems and operations, elementary number theory. Prerequisite: MATH 1203.

MATH2223 Survey of Mathematical Structures II (FA, SP, SU) Geometry and measurement, statistics and probability. Prerequisite: MATH 1203.

MATH2554 Calculus I (FA, SP, SU) Derivative of functions of one variable, applications of the derivative, introduction of the integral, applications. Credit will be allowed for only one of MATH 2554 and MATH 2043. Prerequisite: MATH 1203 and MATH 1213 (or MATH 1285).

MATH2554H Honors Calculus I (FA, SP, SU) Topics in analytic geometry and calculus. Students may not receive credit for both MATH 2043 and MATH 2554.

MATH2564 Calculus II (FA, SP, SU) Integral calculus of one variable and infinite series. Prerequisite: MATH 2554.

MATH2564H Honors Calculus II (SP) Integral calculus of one variable and infinite series. Prerequisite: MATH 2554.

MATH2574 Calculus III (FA, SP, SU) Differential and integral calculus of several variables, vector calculus. Prerequisite: MATH 2564.

MATH2574H Honors Calculus III (FA, SP, SU) Differential and integral calculus of several variables, vector calculus. Prerequisite: MATH 2564.

MATH3083 Linear Algebra (FA, SP, SU) Systems of linear equations, vector spaces, linear transformations, matrices, determinants. Prerequisite: MATH 2554 or MATH 2043.

MATH3103 Combinatorial and Discrete Mathematics (FA, SP, SU) Basic combinatorial techniques including the study of networks, generating functions, principles of inclusion/ exclusion, Zn, Hamming coding theory, graph theory, and block designs. Prerequisite: MATH 2103.

MATH3113 Introduction to Abstract Algebra I (FA, SP) Introduction to algebraic structures with emphasis on rigorous justification of results. Prerequisite: MATH 3083.

MATH3133 History of Mathematics (IR) Prerequisite: MATH 2554 and junior standing.

MATH3203 Theory of Numbers (IR) Prerequisite: MATH 2554 and junior standing.

MATH3353 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.

MATH3404 Differential Equations and Laplace Transform (FA, SP, SU) First and second order ordinary differential equations, the Laplace transform, matrix systems of ordinary differential equations. Prerequisite: MATH 2574.

MATH3423 Advanced Applied Mathematics (FA, SP, SU) Matrices, Fourier analysis, partial differential equations. Prerequisite: MATH 3404.

MATH3443 Complex Variable for Application (SP) Complex analysis, series, conformal mapping. Prerequisite: MATH 3404.

MATH3773 Foundations of Geometry I (FA) Axiomatic method; Euclidean geometry; non-Euclidean geometry.

MATH3923H Honors Colloquium (IR) Covers a special topic or issue, offered as part of the honors program. May be repeated. Prerequisite: honors candidacy (not restricted to candidacy in mathematics).

MATH399VH Honors Mathematics Course (1-6) (FA, SP, SU) May be repeated for 12 hours. Prerequisite: junior standing.

MATH400V Directed Readings (1-6) (FA, SP, SU)

MATH4103 Finite Dimensional Vector Spaces (IR) Linear functionals, matrix representation of linear transformations, scalar product, spectral representation of linear transformations. Prerequisite: MATH 3083.

MATH4113 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.

MATH4203 Linear Programming and Game Theory (IR) Solution sets, duality, and pivoting in linear programming. Feasible solutions and the simplex method. The transportation problem. Matrix games. Prerequisite: MATH 3083 and proficiency in a high-level computer language.

MATH4253 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)

MATH4263 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, G]odel's incompleteness theorems, and the limitative theorems of Tarski and Church. (Same as PHIL 4263) Prerequisite: MATH 4253 or PHIL 4253.

MATH4353 Numerical Linear Algebra (SP) Numerical methods for problems of linear algebra, including the solution of very large systems, eigenvalues, and eigenvectors. Prerequisite: MATH 3083 and programming experience.

MATH4363 Numerical Analysis (FA) General iterative techniques, error analysis, root finding, interpolation, approximation, numerical integration, numerical solution of differential equations. Prerequisite: MATH 4513 and programming experience.

MATH4503 Differential Geometry and Vector Calculus (IR) 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. Prerequisite: MATH 3083 and MATH 4513.

MATH4513 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 MATH 3083.

MATH4523 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.

MATH4932 Mathematics Major Seminar (FA, SP, SU) The two-credit course has 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 is accompanied by a weekly problem-solving seminar in which student presentations could play a part. The course also is a forum for sharing information about career opportunities and preparation for employment.

MATH498V Senior Thesis (1-6) (FA, SP, SU)

MATH5013 Topics in Algebra for Teachers (IR) Topics from abstract and linear algebra of current interest to teachers. May be repeated. Prerequisite: graduate standing.

MATH5033 Topics in Analysis for Teachers (IR) Topics related to calculus of current interest to secondary school teachers. May be repeated. Prerequisite: graduate standing.

MATH504V Special Topics for Teachers (1-6) (IR) Current topics in mathematics of interest to secondary school teachers. May be repeated. Prerequisite: graduate standing.

MATH510V Mathematical Seminar (1-3) (FA) Members of the faculty and advanced students meet for presentation and discussion of topics. Prerequisite: graduate standing.

MATH5123 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.

MATH5133 Algebra II (FA) Continuation of 5123. Prerequisite: MATH 5123.

MATH5303 Ordinary Differential Equations (FA) Existence, uniqueness, stability, qualitative behavior, and numerical solutions. Prerequisite: MATH 3404 and MATH 4513 and programming experience.

MATH5313 Partial Differential Equations (SP) Classification, boundary value problems, applications, numerical solutions. Prerequisite: MATH 3423 and MATH 4513.

MATH5503 Theory of Functions of a Real Variable I (FA) Real number system, Lebesque measure, Lebesque integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus L^P spaces, Holder and Minkowski inequalities, bounded linear functionals on the L^P spaces. Prerequisite: MATH 4523.

MATH5513 Theory of Functions of a Real Variable II (SP) Measure and integration on abstract measure spaces, signed measures, Hahn decomposition, Radon-Nikdoym theorem, Lebesque decomposition, measures on algebras and their extensions, product measures, Fubini's theorem. Prerequisite: MATH 5503.

MATH5523 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, Mibius maps. Prerequisite: MATH 4513.

MATH5533 Theory of Functions of a Complex Variable II (SP) Riemann Mapping Theorem, analytic continuation, harmonic functions, entire functions. Prerequisite: MATH 5523.

MATH5703 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.

MATH5713 Algebraic Topology (FA) Homotopy, singular and relative homology, excision theorem, the Mayer-Vietoris sequence, Beti numbers, and the Euler characteristic. Prerequisite: MATH 5703.

MATH600V Master's Thesis (1-6) (FA, SP, SU) Prerequisite: graduate standing.

MATH610V Directed Readings (1-6) (IR)

MATH619V Topics in Algebra (1-6) (FA, SP, SU) Current research interests in algebra. May be repeated.

MATH659V Topics in Analysis (1-6) (FA, SP, SU) Current research interests in analysis. May be repeated.

MATH679V Topics in Topology (1-6) (FA, SP, SU) Current research interest in topology. May be repeated.

MATH700V Doctoral Dissertation (1-6) (FA, SP, SU)