MECHANICAL ENGINEERING / 113


are the following: population dynamics, epidemiology, ge-
netics, enzyme kinetics, cell differentiation and
morphogenesis, nerve impulse generation, and aggregation
of slime mold: The course is designed to benefit graduate
students in biological sciences, as well as mathematics.
MAP 6488-Biomathematics Seminar II (3) Prereq: MAP
6487. Continuation of MAP 6487.
MAP 6505-Mathematical Methods of Physics and Engineer-
ing I (3) Prereq: MAA 5402, MAP 5304, 5345, MAS 5156 or
equivalent. Orthogonal functions; theory of distributions;
integral equations; eigenfunctions and Green's functions;
special functions; boundary and initial value problems, with
emphasis on potential theory (Laplace and Poisson equa-
tions); the wave equation; and the diffusion equation.
MAP 6506--Mathematical Methods of Physics and Engineer-
ing II (3) Prereq: MAP 6505.
MAP 7436-Seminar in Applied Mathematics I (3; max: 6)
Various topics in applications of mathematics both classical
and in areas of current research..
MAP 7437-Seminar in Applied Mathematics II (3; max: 6)
MAP 7475-Seminar in Mathematical System Theory (3) Pre-
req: admission to doctoral study. Critical review of current
developments in system theory, with strong emphasis on
(but not limited to) questions of mathematical interest. Pres-
entations by invited speakers as well as by students and fac-
ulty affiliated with the Center for Mathematical System The-
ory. Intensive discussions by participants rather than ex
cathedra lectures. May be repeated.
MAP 7477-Introduction to Mathematical System Theory I
(3) Prereq: consent of instructor. Required for doctoral work
in system theory. Fundamental mathematical structures in
the description of dynamical systems, especially linear sys-
tem and finite automata. Problems of controllability, ob-
servability, structure, and identification. Topics to reflect
current developments. H.
MAP 7478-Introduction to Mathematical System Theory II
(3) May be repeated.
MAS 5156-Vector Analysis (3)
MAS 5331-Introductory Algebra I (3) Prereq: MAS 4103 or
4312. The basic algebraic systems: groups, rings, vector
spaces, and modules. Linear transformations, matrices, and
determinants.
MAS 5332-Introductory Algebra II (3) Prereq: MAS 5331.
MAS 5334-Rings, Modules, and Linear Algebra (3) Prereq:
undergraduate linear algebra. Structure of principal ideal
domains and their modules, with application to abelian
groups and linear transformations.
MAS 6158-Tensor Analysis (3) Prereq: MAS 5156 or equiva-
lent. Tensor algebra, tensor calculus, covariant differentia-
tion. Riemannian spaces, curvature tensor, the Ricci and
Einstein tensors, geodesics, parallel displacement; applica-
tions to differential geometry, physics, and engineering.
MAS 6346-Algebra I (3) Prereq: MAS 5332. Solvable and
nilpotent groups, Jordan-Holder theorem, abelian groups,
Galois theory, Noetherian rings, Dedekind domains,
Jacobson radical, Jacobson density theorem, Wedderburn-
Artin theorem.
MAS 6347-Algebra II (3) Prereq: MAS 6346.
MAS 7215-Theory of Numbers I (3) Prereq:-2 of MAA 6407,
6618, MAS 6347. Introduction to the theory of numbers; the-
orems on divisibility; congruences, number-theoretic func-
tions; primitive roots and indices; the quadratic reciprocity
law; Diophantine equations and continued functions.
MAS 7216-Theory of Numbers II (3) Prereq: MAS 7215.
MAS 7396-Advanced Topics in Algebra I (3; max: 6) Prereq:
MAA 6407, 6617, MAS 6347 or MTG 6347. Current topics in
algebra.
MAS 7397-Advanced Topics in Algebra II (3; max: 6) Prereq:
MAS 7396.
MAT 6905-Individual Work (3; max: 9)
MAT 6910-Supervised Research (1-5; max: 5) S/U.
MAT 6932-Special Topics in Mathematics (3) Prereq: con-
sent of graduate adviser, who should be consulted well in
advance of registration.
MAT 6971-Research for Master's Thesis (1-15) S/U.
MAT 7979-Advanced Research (1-9) Research for doctoral
students before admissiorl.to candidacy. Designed for stu-
dents with a master's degree in the field of study or for stu-
dents who have been accepted for a doctoral program. Not


open to students who have been admitted to candidacy.
S/U.
MAT 7980-Research for Doctoral Dissertation (1-15) S/U.
MHF 5107-Introduction to Set Theory (3) Basic axioms and
concepts of set theory, axiom of choice, Zorn's lemma,
Schroder-Bernstein theorem, cardinal numbers, ordinal
numbers, and the continuum hypothesis.
MHF 5207-Foundations of Mathematics (3) Models and
proofs. Foundations of the real and natural number systems,
Algorithms, Turing Machines, undecidability and independ-
ence. Examples and applications in algebra, analysis, geome-
try, and topology.
MHF 6306-Mathematical Logic I (3) Languages, models,
and theories; Godel's completeness and incompleteness
theorems; formal number theory and axiomatic set theory;
applications to other areas of mathematics.
MHF 6307-Mathematical Logic II (3) Prereq: MHF 6306.
MTG 5316-Introduction to Topology I (3) Basic axioms and
concepts of point-set topology, compactness, connected-
ness, separation axioms, metric spaces, metrization. Tietze
extension theorem. Urysohn lemma, Tychonoff theorem.
MTG 5317-Introduction to Topology II (3) Prereq: MTG
5316.
MTG 6256-Differential Geometry I (3) Prereq; MAS 5156 or
equivalent. First part of a two-term sequence: Classical dif-
ferential geometry of curves and surfaces, differentiable
manifolds, tensor analysis, affine connection, Riemannian
geometry. Lie groups, Lie algebras, applications to physics.
MTG 6257-Differential Geometry II (3) Prereq: MTG 6256.
MTG 6266-Introduction to Commutative Algebra and Al-
gebraic Geometry I (3)
MTG 6267-Introduction to Commutative Algebra and Al-
gebraic Geometry II (3) Prereq: MTG 6266.
MTG 6276-Theory of Convexity I (3) Affine sets, convex
sets and cones, convex functions, closures of convex func-
tions, continuity of convex functions, separation theorems,
directional derivatives and subgradients, ordinary convex
programs and Lagrange multipliers. Fenchel's duality the-
orem, saddle-functions.
MTG 6277-Theory of Convexity II (3) Prereq: MTG 6276.
MTG 6346-Topology I (3) Prereq: MTG 5317. A basic in-
troduction to advanced topology. Topics covered include
general topology, algebraic topology, homotopy theory and
topology of manifolds.
MTG 6347-Topology II (3) Prereq: MTG 6346.
MTG 7396-Advanced Topics in Topology I (3; max: 6) Pre-
req: MTG 6347. Topics change yearly.
MTG 7397-Advanced Topics in Topology f1 (3; max: 6)


MECHANICAL ENGINEERING
College of Engineering
 GRADUATE FACULTY 1984-85
Chairman: R. B. Gaither. Graduate Coordinator: V. P.
Roan. Graduate Research Professors: A. E. S. Green; J.
Tlusty. Distinguished Service Professor: E. A. Farber.
Professors: J. Duffy; R. B. Gaither; C. K. Hsieh; R. K.
Irey; I. Mahig; C. C. Oliver; V. P. Roan; G. N. Sandor.
Associate Professors: R. A. Gater; H. A. Ingley, III; G. K.
Matthew; G. Piotrowski. Assistant Professors: E. C.
Hansen; G. J. Miller; C. L. Proctor; T. I. P. Shih.
 Programs are available leading to the degrees of
Master of Science, Master of Engineering, Engineer,
and Doctor of Philosophy. General areas within
which students may specialize are biomechanical sys-
tems, energy conversion systems, mechanical systems,
and thermal systems.
 Within the specializations noted above are unique
opportunities to complete theoretical and experimen-
tal research investigations in a wide variety of sub-
specialties including acoustics, automatic controls,
biomechanics, combustion, cryogenics, energy con-
version, environmental control, fluid dynamics, gas
dynamics, heat transfer, kinematic synthesis, machine