MATHEMATICS / 105


EMA 6905-Individual Work in Materials Science and
Engineering (1-4; max: 8),
EMA 6910-Supervised Research (1-5) S/U.
EMA 6936-Seminar in Materials Science and Engineering (1)
Required of all students in Materials Science and Engineering.
Course continued for two seminars. H.
EMA 6937-Seminar in Metallurgy and Ceramic Science (1-2)
EMA 6938-Special Topics in Materials Science and Engineer-
ing (1-4; max: 6)
EMA 6940-Supervised Teaching (1-5) S/U.
EMA 6971-Research for Master's Thesis (1-15) S/U.
EMA 7008-Product Liability: Effective Use of Engineering
Experts (2) Available for credit toward graduation in the Col-
lege of Law. Basic engineering concept underlying product
failure and safety, causal relationships, proof of negligence and
standards of care. No engineering background required.
EMA 7980-Research for Doctoral Dissertation (1-15) S/U.

MATHEMATICS
College of Liberal Arts and Sciences
 GRADUATE FACULTY 1982-83
 Chairman: A. R. Bednarek. Associate Chairman: Z. R.
 Pop-Stojanovic. Graduate Coordinator: L. Block.
 Graduate Research Professors: R. E. Kalman; S. M. Ufam.
 Professors: A. R. Bednarek; J. K. Brooks; L. Cesari; S.
 Chen; N. Dinculeanu; D. Drake; J. E. Keesling; J. Mar-
 tinez; C. W. Nelson; V. M. Popov; Z. R. Pop-Stojanovic;
 M. Rao; M. L. Teply; R. Triggiani, A. K. Varma. Associate
 Professors: P. Bacon; L. S. Block; T. T. Bowman; B. L.
 Brechner; D. A. Cenzer; B. H. Edwards; M. P. Hale, Jr.;
 J. A. Larson; 1. Lasiecka; P. J. McKenna; T. O. Moore;
 G. X. Ritter; S. A. Saxon; K. N. Sigmon; T. Walsh; N. L.
 White; D. C. Wilson. Assistant Professor: R. L. Long.
 The Department of Mathematics offers the degrees of
 Doctor of Philosophy, Master of Science, and Master of
 Arts, and the Master of Arts in Teaching and Master of
 Science in Teaching, each with a major in mathematics.
 There are opportunities for concentrated study in a
 number of specific areas of pure and applied
 mathematics at both the master's and doctoral levels. The
 faculty directs studies and research in algebra, number
 theory, analysis, geometry, topology, logic, differential
 equations, dynamical systems, control theory, probability
theory, mathematical systems theory, numerical analysis,
approximation theory, combinatorial analysis, graph
theory, computer applications, and biomathematics.
 In addition to the requirements of the Graduate School,
the minimum prerequisite for admission to the program
of graduate studies in mathematics is the completion,
with an average grade of B or better, of at least 24 credits
of undergraduate mathematics, including a full year of
calculus and three semesters of appropriate work beyond
the calculus. Students lacking part of the requirements
will be required to make up the deficiency early in their
graduate work.
 Prerequisites to individual courses should be deter-
mined before registration by consultation with the in-
structor concerned.
 Some of the courses listed are offered only as needed.
Since times of offering courses are estimated a year in
advance, certain changes may be made if needs are
known by the department.
 The courses MAA 5226, 5227, MAS 5331 and 5332 are
required for all advanced degree programs in
mathematics.
 The requirements for the master's degree include 32
semester hours of. course work and a comprehensive
written examination. A thesis is not required. There are
two master's programs available, one in pure


mathematics and one in applied mathematics. A student
normally takes two years to complete either program.
 The requirements for a doctoral degree include 36
 hours of 6000-level course work in mathematics. No
 hours of teaching, colloquium, dissertation, or individual
 work will count toward this requirement.
 The doctoral student must pass a written and oral com-
 prehensive preliminary examination administered by the
 department to become a candidate for the degree. The
 doctoral student must pass reading knowledge examina-
 tions in one of the following foreign languages: French,
 German, or Russian.
 The dissertation is an important requirement for the
 doctoral degree in mathematics. The topics for the disser-
 tation may be chosen from a number of areas of current
 research in pure and applied mathematics.
 Every graduate student is expected to attend the regular
 colloquium.
 Details concerning all requirements for graduate
 degrees in mathematics can be obtained by writing
 the Mathematics Department Graduate Selection
 Committee.
 MAA 5102-Advanced Calculus for Engineers and Physical
 Scientists I (3)
 MAA 5103-Advanced Calculus for Engineers and Physical
 Scientists 11 (3) Prereq: MAA 5102.
 MAA 5226-Modern Analysis I (3) Prereq: MAC3313. Topology
 of metric spaces, numerical sequences and series, continuity,
 differentiation, the Riemann-Stieltjes integral, sequences and
 series of functions, the Stone-Weierstrass theorem, functions
 of several variables. Stokes' theorem, the Lebesque theory.
 MAA 5227-Modern Analysis II (3) Prereq: MAA 5226.
 MAA 5402-Introduction to Complex Variables for Engineers
 and Physical Scientists (3)
 MAA 5506-Introduction to Functional Analysis I (3)
 MAA 5507-Introduction to Functional Analysis II (3) Prereq:
 MAA 5506.
 MAA 6236-Mathematical Analysis for Statisticians (3) Coreq:
 STA 6326. Set theory, cardinality, metric spaces, limits, conti-
 nuity, differentiation, approximation of functions, series of func-
 tions. Applications to probability and statistics stressed.
 MAA 6406-Complex Analysis 1 (3) Prereq: MAA 5227. Rapid
 survey of properties of complex numbers, linear transformations,
 geometric forms and necessary concepts from topology. Com-
 plex integration, Cauchy's theorem and its corollaries. Taylor's
 series and the implicit function theorem in complex form. Con-
 formality and the Riemann-Caratheodory mapping theorem.
 Theorems of Bloch, Schottky, and the big and little theorems
 of Picard. Harmonicity and Dirichlet's problems.
 MAA 6407-Complex Analysis 11 (3) Prereq: MAA 6406.
 MAA 6616-General Theory of Measure and Integration 1 (3)
 Prereq: MAA 5227. The Daniell approach to integration, abstract
 measure theory, abstract Lebesque integral, convergence
 theorems for integrals, Riesz representation theorem. LP
 spaces, various modes of convergence. Banach spaces, Hahn-
 Banach theorem, open-mapping theorem, uniform-bounded-
 ness principle. Hilbert spaces, differentiation of functions of one
 real variable. Vitali's covering theorem, differentiability of
 monotone functions. Absolutely continuous functions and in-
 definite integral, the Lebesque-Radon-Nikodym theorem.
 MAA 6617-General Theory of Measure and Integration 11 (3)
 Prereq: MAA 6616.
 MAA 6626-Advanced Topics in Integration I (3; max: 6)
 Prereq: MAA 6617 and MTG 6347. Current topics in integra-
 tion, reference to function spaces and to spaces provided with
 algebraic or topological structures.
 MAA 6627-Advanced Topics in Integraton II (3; max: 6)
 Prereq: MAA 6626.
 MAA 7526-Advanced Topics in Functional Analysis I (3; max:
 6) Prereq: MAA 6617, MAS 6347. Algebraic and topological ap-
 proach to current material and methods in analysis.
 MAA 7527-Advanced Topics in Functional Analysis II (3; max:
6) Prereq: MAA 7526.
MAD 5405-Numerical Methods of Differential Equations (3)