124 / FIELDS OF INSTRUCTION


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 Engineering
I (3) Prereq: MAA 5404, MAP 5304, 5345, MAS 5157 or
equivalent. Orthogonal functions; theory of distributions; inte-
gral equations; eigenfunctions and Green's functions; special
functions; boundary and initial value problems, with emphasis
on potential theory (Laplace and Poisson equations); the wave
equation; and the diffusion equation.
MAP 6506-Mathematical Methods of Physics and Engineering
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; max:
18) Prereq: admission to doctoral study. Critical review of current
developments in system theory, with strong emphasis on (but not
limited to) questions of mathematical interest. Presentations by
invited speakers as well as by students and faculty affiliated with
the Center for Mathematical System Theory. Intensive discus-
sions by participants rather than ex cathedra lectures.
MAP 7477-Introduction to Mathematical System Theory 1 (3;
max: 6) Prereq: consent of instructor. Required for doctoral work
in system theory. Fundamental mathematical structures in the
description of dynamical systems, especially linear system and
finite automata. Problems of controllability, observability, struc-
ture, and identification. Topics to reflect current developments.
MAP 7478-Introduction to Mathematical System Theory II (3;
max: 6)
MAS 5157-Vector Analysis (3)
MAS 5311-Introductory Algebra I (3) Prereq: MAS 4105 or
4302. The basic algebraic systems: groups, rings, vector spaces,
and modules. Linear transformations, matrices, and determi-
nants.
MAS 5312-Introductory Algebra II (3) Prereq: MAS 5311.
MAS 6331-Algebra I (3) Prereq: MAS 5312. Solvable and
nilpotent groups, Jordan-Holdertheorem, abelian groups, Galois
theory, Noetherian rings, Dedekind domains, Jacobson radical,
Jacobson density theorem, Wedderburn-Artin theorem.
MAS 6332-Algebra II (3) Prereq: MAS 6331.
MAS 7215-Theory of Numbers 1 (3) Prereq: 2 of MAA 6407,
6617, MAS 6332. Introduction to the theory of numbers; theo-
rems on divisibility; congruences, number-theoretic functions;
primitive roots and indices; the quadratic reciprocity law; Dio-
phantine 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 6332 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; max: 9) Prereq:
consent 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 admission to candidacy. Designed for students
*with a master's degree in the field of study or for students who
have been accepted fora 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 independence. Examples
 and applications in algebra, analysis, geometry, and topology.
 MHF 6306-Mathematical Logic I (3) Languages, models, and
 theories; Godel's completeness and incompleteness theorems;
 formal number theory and axiomatic se.t theory; applications to
 other areas of mathematics.
 MHF 6307-Mathematical Logic II (3) Prereq: MHF 6306.
 MTG 5316-Introduction to Topology' 1(3) Basic axioms and
 concepts of point-set topology; compactness, connectedness,


separation axioms, metric spaces, metrization. Tietze extension
theorem. Urysohn lemma, Tychonoff theorem, fundamental
group.
MTG 5317-Introduction to Topology II (3) Prereq: MTG 5316.
MTG 6256-Differential Geometry I (3) Prereq: MAS 5157 or
equivalent. First part of a two-term sequence. Classical differen-
tial 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 Alge-
braic Geometry I (3)
MTG 6267-Introduction to Commutative Algebra and Alge-
braic Geometry II (3) Prereq: MTG 6266.
MTG 6346-topology I (3) Prereq: MTG 5317. A basic introduc-
tion 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) Prereq:
MTG 6347. Topics change yearly.
MTG 7397-Advanced Topics in Topology II (3; max: 6)




MECHANICAL ENGINEERING
College of Engineering

 GRADUATE FACULTY 1989-90
 Chairman: R. B Gaither. Graduate Coordinator: V. P.
 Roan. Graduate Research Professors: J. Duffy; A.E.S.
 Green; J. Tlusty. Ebaugh Professor: A. A. Seireg. Distin-
 guished Service Professor: E. A. Farber. Professors: D. W.
 Dareing; R. B. Gaither: C. K. Hsieh; C. C. Oliver; V. P.
 Roan. Associate Professors: R. A. Gater; H. A. Ingley, III;
 G. K. Matthew; G. Piotrowski;C. L. Proctor;J. K. Schueller.
 Assistant Professors: C. D. Crane; E. C. Hansen; W. E.
 Lear; G. J. Miller; K. S. Smith.

 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 systems, energy conversion
 systems, mechanical systems, thermal systems, manufac-
 turing, and robotics.
 Within the specializations noted above are unique
 opportunities to complete theoretical and experimental
 research investigations in a wide variety of subspecialities
 including acoustics, automatic controls, biomechanics,
 combustion, cryogenics, energy conversion, environ-
 mental control, fluid dynamics, gas dynamics, heat trans-
 fer, kinematic synthesis, machine dynamics, propulsion,
 solar energy, thermodynamics, and vibrations.

 EML 5104-Classical Thermodynamics (3) Review of the first,
 second, andthird laws. Applications to open and closed systems.
 Property evaluation using equations of state.
 EML 5105-Statistical Thermodynamics (3) Equilibrium distribu-
 tions in Bose, Fermi, and Boltzmann systems. Propertyevaluation
 from microscopic molecular models. Transport properties.
 EML 5131-Combustion I (3) Prereq: EML 5105 and consent of
 instructor. Fundamentals of combustion, reaction kinetics,
 combustion and detonation phenomena.
 EML 5152-Intermediate Heat Transfer (3) Analytical solution of
 conduction, convention and radiation problems, exact and
 approximate solution techniques. Mass transfer in multicompo-
 nent fluids.
 EML 5223-Design Synthesis in Vibrations (3) Vibration analysis
 of continuous and multidegree of freedom lumped parameter
 systems. Computer design projects allow studentto acquire some
 design experience.
 EML 5224-Engineering Acoustics and Noise Control (2) Funda-
 mentals of acoustics; instrumentation for acoustic and vibration
 measurements; field and laboratory practice; applications to
 noise control.