Department of Mathematics - University of Houston
Senior and Graduate Course Offerings Fall 2000
For further information, contact the Department of Mathematics at 651 PGH, University of Houston, Houston, TX 77204-3476; Telephone (713) 743-3517 or e-mail to pamela@math.uh.edu.
| MATH 4315 GRAPH THEORY WITH APPLICATIONS (Section 08609) | |
| Time: | 4-5:30 TTH Rm. 209 PGH |
| Instructor: | S. Fajtlowicz |
| Prerequisites: | Discrete Mathematics (Math 3336) |
| Text(s): | None. The course will be based on my notes. |
| Description: | The course is an introduction to graph theory and some of its applications including trees, Eulerian and Hamiltonian graphs, probabilistic methods and fullerenes - the new form of carbon. I will emphasize algorithmic methods and describe a number of open computational problems. |
| MATH 4331: INTRODUCTION TO REAL ANALYSIS (Section 08610) | |
| Time: | 4-5:30 MW Rm. 348 PGH |
| Instructor: | A. Torok |
| Prerequisites: | Math 3333 or 3334. |
| Text(s): | Principles of Mathematical Analysis, Walter Rudin, McGraw-Hill, Latest Edition. |
| Description: | Elements of topology; sequences and series; continuity, differentiability and integrations of functions of one and several variables; the inverse function theorem and other fundamental results. Rigorous proofs are an essential part of this course. |
| MATH 4335: PARTIAL DIFFERENTIAL EQUATIONS (Section 08611) | |
| Time: | 2:30-4 TTH Rm. 268 PGH |
| Instructor: | S. Canic |
| Prerequisites: | Linear Algebra and Advanced Calculus. |
| Text(s): | Lecture notes will be provided. |
| Description: | Basic existence and uniqueness of solutions to the initial value problem for systems of ODEs. The method of characteristics for first order PDEs. Some eigenvalue problems with applications to solving linear PDEs. Transform methods. |
| MATH 4337: POINT SET THEORY (Section 11169) | |
| Time: | 2:30-4 TTH Rm. 211 PGH |
| Instructor: | M. Friedberg |
| Prerequisites: | Math 3333 or 3334 or consent of instructor. Students should have completed the Calculus sequence and have had some mathematics at the 3000 level and preferably also at the 4000 level. |
| Text(s): | Check with instructor. |
| Description: | The course will be an introduction to topology and will include a discussion of metric spaces, the general definition of a topology and a study of some of the elementary properties of topological spaces. |
| MATH 4340: NONLINEAR DYNAMICS AND CHAOS (Section 11170) | |
| Time: | 2-3 MWF Rm. 268 PGH |
| Instructor: | M. Field |
| Prerequisites: | Calculus and a first course in linear algebra. Interest. |
| Text(s): | Chaos, An Introduction to Dynamical Systems, Kathleen T. Alligood, Tim D. Sauer, James A. Yorke, Springer, 1997. |
| Description: | An introduction to nonlinear dynamics and chaos. Among topics we discuss will be the logistic map, periodic points, period doubling, sensitive dependance on initial conditions, chaos and symbolic dynamics. |
| MATH 4364: NUMERICAL ANALYSIS (Section 08613) | |
| Time: | 5:30-7 TTH Rm. 211 AH |
| Instructor: | J. He |
| Prerequisites: | Math 2431, 3431; COSC 1301 or 2101 or equivalent. |
| Text(s): | Numerical Analysis, Burden & Faires. |
| Description: | Selected topics: Solutions of eequations in one variable, interpolation and polynomial approximation, numberical differentiation and integration, Initial-value problems for ordinary differential equations, direct methods for solving linear systems. |
| MATH 4377: ADVANCED LINEAR ALGEBRA (Section 08614) | |
| Time: | 4-5:30 TTH Rm. 211 AH |
| Instructor: | K. Kaiser |
| Prerequisites: | Math 2431. |
| Text(s): | Linear Algebra, Hofmann-Kunze, 2nd or 3rd Edition. |
| Description: | The general theory of Vector Spaces and Linear Transformations will be developed in an axiomatic fashion. Some topics include the algebra of polynomials, determinants and multilinear forms. Besides weekly homework assignments, I will give about six Quizzes and three major Tests plus the Final. |
| MATH 4377: ADVANCED LINEAR ALGEBRA (Section 08615) | |
| Time: | 1-2:30 MW Rm. 315 PGH |
| Instructor: | C. Peters |
| Prerequisites: | Math 2431 and at least 3 hrs. advanced Mathematics, or consent of instructor. |
| Text(s): | The Theory of Matrices, Peter Lancaster & Miron Tismenetsky, Academic Press, 2nd Edition. |
| Description: | Systems of linear equations, Gaussian elimination, matrices, elementary operations, rank, inverse of a matrix, determinants, vector spaces, subspaces, linear independence and bases, inner products, orthonormal bases, linear transformations, eigenvectors and eigenvalues, Hermitian and unitary matrices, applications. |
| MATH 4383: NUMBER THEORY (Section 11171) | |
| Time: | 10-1:30 TTH Rm. 315 PGH |
| Instructor: | J. Hardy |
| Prerequisites: | Math 3330. |
| Text(s): | Check with instructor. |
| Description: | Topics will include divisibility, primes and their distribution, congruences, Fermat/Euler Theorems, Number-theoretic functions, primitive roots, Quadratic Reciprocity, Pythagorean Triples and related topics. |
| MATH 6198: TEACHING PRACTICUM (Section 12529) | |
| Time: | TO BE ARRANGED |
| Instructor: | J. Hausen |
| Prerequisites: | First year graduate assistantship. |
| Text(s): | None. |
| Description: | Course will meet two hours a week for the first half of the semester. Required of all first-year Teaching Fellows. Introduction to teaching and assisting at the University of Houston. |
| MATH 6298: INTROUDUCTION TO COMPUTING RESOURCES (Section 12539) | |
| Time: | 1-3 M Rm. 648 PGH |
| Instructor: | A. Torok |
| Prerequisites: | Computer and presentation skills. Graduate standing or concent of instructor |
| Text(s): | Check with instructor. |
| Description: | The purpose of this course is to familiarize students
with the computer tools that are relevant for mathematical research
in today's environment. It is intended primarily for graduate students
and math majors, but it is useful for anybody interested in these
topics. The topics we plan to discuss include the Unix and Linux operating
systems, a multi-functional text editor (emacs), software for
mathematical publications (TeX and its dialects), languages for
formal and numerical computations (Maple, Mathamtica, Mathlab),
web-publishing (HTML) and Internet use (mail,
electronic archives etc.). We will also mention a few principles
of writing and presenting a mathematical paper.
The course will consists of weekly workshops accompanied by hands-on applications in the computer lab of the Math Department, followed by individual projects. These projects (e.g., typesetting a short mathematical paper, designing a web-page, writing programs in various languages) will give the students the opportunity to practice the notions they are being taught. The material used for this course will be either available on the web or handed out in class. |
| MATH 6302: MODERN ALGEBRA (Section 08624) | |
| Time: | 1-2:30 TTH Rm. 350 PGH |
| Instructor: | J. Johnson |
| Prerequisites: | Math 4333 or Math 4378, or consent of instructor. |
| Text(s): | Algebra, Thomas W. Hungerford, Springer-Verlag; Graduate Texts in Mathematics #73. |
| Description: | Topics from the theory of groups, rings, and fields with special emphasis on modules and universal constructions. |
| MATH 6320: FUNCTIONS OF A REAL VARIABLE (Section 08632) | |
| Time: | 4-5:30 MW Rm. 345 PGH |
| Instructor: | G. Auchmuty |
| Prerequisites: | Math 4331-32. |
| Text(s): | Lebesque Integration on Euclidean Space, Jones & Bartlett. |
| Description: | Topology and metrics; Lebesque measure and measurability; measurable functions and Lebesque integration; Lp spaces and convolutions; Fourier Transforms. |
| MATH 6342: POINT SET TOPOLOGY (Section 08635) | |
| Time: | 2:30-4 TTH Rm.211 AH |
| Instructor: | I. Melbourne |
| Prerequisites: | Math 4331 or consent of instructor. |
| Text(s): | Topology, A First Course, J. R. Munkres, Prentice-Hall Publishers. |
| Description: | Aim to cover Chapters 2, 3 and 4 during the Fall semester. Metric spaces, products, quotients, connectedness, compactness, etc. Countability and separation axioms. |
| MATH 6360: APPLICABLE ANALYSIS (Section 08636) | |
| Time: | 10-11:30 TTH Rm. 203 AH |
| Instructor: | W. Fitzgibbon |
| Prerequisites: | Math 4331-32 |
| Text(s): | Linear Operator Theory in Science & Engineering, A.W. Naylor and G.R. Sell, Springer Verlag. |
| Description: | Metric spaces and the contraction mapping theorem. Applications to the solvability of finite dimensional equations. Existence and uniqueness of solutions of ordinary differential equations and integral equations. Introduction to Hilbert spaces and the solvability of linear operator equations. |
| MATH 6370: NUMERICAL ANALYSIS (Section 08637) | |
| Time: | 4-5:30 TTH Rm. 268 PGH |
| Instructor: | E. Dean |
| Prerequisites: | Graduate standing or consent of instructor. |
| Text(s): | Introduction to Numerical Analysis, J. Stoer and R. Bulirsch,(Springer-Verlag), 2nd Edition, New York, 1993. |
| Description: | We will develop and analyze numerical methods for approximating the solutions of common mathematical problems. The emphasis this semester will be on floating point arithmetic, error analysis, interpolation, numerical differentiation and integration, solving nonlinear equations, numerical linear algebra, and numerical solutions of ordinary differential equations. The focus of the course will be on motivating the algorithms and rigorously analyzing their effectiveness. |
| MATH 6372: NUMERICAL ORDINARY DIFFERENTIAL EQUATIONS (Section 12338) | |
| Time: | 2:30-4 MW Rm. 345 PGH |
| Instructor: | S. Nepomnyashchikh |
| Prerequisites: | A first course in differential equations, some advanced calculus, the Taylor series, and a little elementary material on matrix algebra. |
| Text(s): | Check with instructor. |
| Description: | This is a one semester course on numerical methods for ordinary differential equations. Due to the fundamental role of differential equations in science and engineering it has been a long task of numerical analysis to generate numerical solutions to differential equations. The aim of this course is to provide both a theoretical and a practical account of the state of art in modern numerical methods for the solution of ordinary differential equations. It should be useful for students interested in using numerical methods as well as those working in the area of numerical methods. After a simple introduction we consider one-step methods (Euler, Runge-Kutta) for a single equation of the first order, for systems of equations of the first order, for systems of equations of higher order. Multistep methods for equations of the first order and special equations of the second order are a focus of the second part of the course. Numerical methods for solving nonlinear boundary value problems of the second order are considered in teh third part of the course. The fourth past of the course provides an introduction to numerical solving of stiff ordinary differential equations. |
| MATH 6374: NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS (Section 11172) | |
| Time: | 11:30-1 TTH Rm. 347 PGH |
| Instructor: | R. Glowinski |
| Prerequisites: | Numerical linear algebra; numerical methods for ordinary differential equations; some basic knowledge in partial differential equations. |
| Text(s): | None. |
| Description: | The main goals of this course are: 1) introducting the readers to the approximation of classical partial differential equations from applied science and engineering (heat and wave equations, Navier-Stokes equations). 2) discuss solution methods for the finite bifurcation systems obtained by approximating the partial differential equation (Newton's method, conjugate gradient, etc...). |
| MATH 6380: FUNCTIONAL ANALYSIS IN STOCHASTIC PROCESSES (Section 11173)<\td> | |
| Time: | 5:30-7 TTH Rm. 154 F |
| Instructor: | A. Bobrowski |
| Prerequisites: | The course will be self-contained; i.e., all necessary results from functional analysis will be proven before applying them to stochastic problems. Nevertheless, participants are advised to get acquainted with the notions of Hilbert and Banach space in advanced. Also, overall familiarity with basic probability concepts is crucial for thorough understanding of the topics covered. Finally, a basic knowledge of measure theory will be required. |
| Text(s): | See text listing posted (graduate advisors notice with course announcement). |
| Description: | A number of textbooks (see listings) on stochastic processes are filled with functional analytic arguments. In fact, several branches of functional analysis were developed almost solely for the purpose of serving stochastic processes. On the other hand, for decades, functional analysis has been providing to stochastic processes already prepared tools and even whole tool-boxes. And this is how this should be: "real life problems" (in our case problems arising in stochastic processes) need to inspire analyst, and he/she should extract the mathematical structure from them, both to exhibit its beauty and to serve future applications. Such interaction sof functional analysis with other branches of matheamtics are, of course, not limited to those with the theory of stochastic processes. Nevertheless the interplay with stochastic processes is of special beauty and interest. The course is to provide introduction to this vast field. It should attract attention of both students of functional analysis and those whose major itnerest is probability/statistics. . |
| MATH 6382: PROBABILITY AND STATISTICS (Section 11174) | |
| Time: | 12-1 MWF Rm. 345 PGH |
| Instructor: | B. Keyfitz |
| Prerequisites: | Advanced calculus, linear algebra. |
| Text(s): | INTRODUCTION TO PROBABILITY MODELS,
Sheldon Ross, Academic Press (latest edition - 4th or later -
ISBN of 4th is 0-125-98464-2).
AN INTRODUCTION TO THE MATHEMATICS OF FINANCE, Sheldon Ross, Cambridge University Press (ISBN 0-521-77043-2) (Both are required). |
| Description: | Sample spaces, event, and probability measures. Random variables, distributions, expected values, basic distributions, limit theorems, Poisson processes, renewal theory, Markov chains, Browinan motion, stochastic integrals. Applications in Statistics and in Finance. |
| MATH 6395: FOURIER TRANSFORMS AND WAVELETS IN SIGNAL ANALYSIS (Section 11175) | |
| Time: | 2:30-4 TTH Rm. 301 AH |
| Instructor: | M. Papadakis |
| Prerequisites: | The course will be offered for students at the graduate level attending one of the following graduate programs: ECE, COSC, MATH, Applied MATH, GEOL, PHY. Graduate students from other departments should consult the instructor before enrolling. Outstanding senior undergraduate students may also enroll with the instructor's consent. ECE 6364 and 6342 or GEOL 7341 and 7336 or MATH 4332 and 4377 or ELEE 6330 and 6334 or PHY 6303 and MATH 4377 or consent of the instructor (for cases of graduate or undergraduate students with outstanding performance ONLY). It is recommended that all students regardless of their graduate curriculum have taken MATH 4377, or the sequence MATH 4331-4332. Basic knowledge of MATLAB is also recommended. |
| Text(s): | Check with instructor. |
| Description: | Integral Fourier transforms in one and two dimension, Discrete Fourier transofrm, applications to signal processing; Sampling analog signals, Fourier series and some of the convergence properties, Discrete time-invariant filters; Time-freequency analysis, Windowed Fourier transforms; Continuous Wavelet transform, Wigner-Ville transform; Multiresoltuion analysis, Fast Wavelet transforms and filter banks, separable multiresoltuion analysis, 2D Fast Wavelet transform. |
| MATH 7320: FUNCTIONAL ANALYSIS (Section 11265) | |
| Time: | 4-5:30 MW Rm. 268 PGH |
| Instructor: | D. Blecher |
| Prerequisites: | Graduate standing and consent of instructor. We will mostly avoid measure theory, so don't be too concerned if you lack that background. After each chapter we will schedule a rpoblem solving workshop, based on the homework assigned for that chapter.<\td> |
| Text(s): | There will be a xeroxed set of lecture notes available. There are several good books on the market, such as Pedersen's Analyis Now or Conway's A Course in Functional Analysis. |
| Description: | The first semester will be a leisurely and general presentation, starting from scratch, of the basic facts in Linear Analysis, Banach spaces and Hilbert spaces. The second semester will be a more technical development of the theory of linear operators on Hilbert space. We will also cover topics which the students request. We will probably only make it to the middle of section III in the first semester. (See posting for Course Outline of 2-semester Syllabus). |
| MATH 7324: BIFURCATION THEORY (Section 11266)<\td> | |
| Time: | 1-2:30 TTH Rm. 268 PGH |
| Instructor: | M. Golubitsky |
| Prerequisites: | Undergraduate linear algebra and ordinary differential equations. |
| Text(s): | M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. 1, Springer-Verlag, 1984. |
| Description: | Steady-state and Hopf bifurcation, Liapunov-Schmidt reduction, singularity theory, and classification of bifrucation problems by codimension. Both theory and applications will be discussed. |
| MATH 7350: GEOMETRY OF MANIFOLDS (Section 11267) | |
| Time: | 10-11:30 TTH Rm. TBA |
| Instructor: | S. Ji |
| Prerequisites: | Math 3331 and 3334, or equivalent. |
| Text(s): | Riemannian Geometry. |
| Description: | Differential manifolds, Riemannian metrics, Riemannian connections, Geodesics, carvatures. |
| MATH 7394: VARIATION AND FINITE ELEMENT METHODS (Section 11269) | |
| Time: | 1-2:30 MW Rm. 248 PGH |
| Instructor: | Y. Kuznetsov |
| Prerequisites: | Graduate standing and consent of instructor |
| Text(s): | Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics, D. Braess, Cambridge University Press, 1997. The Mathematical Theory of Finite Element Methods, S.C. Brenner and L.R. Scott, Springer-Verlag, 1994. |
| Description: | The finite element method is one of the most
widely used technique for numerical solution of partial differential
equations in science and engineering. The purpose of this
course is to give an introduction to the finite element
methods with emphasis to practical applications in physics and mechanics as well as to
implementation aspects. In the beginning of the course we introduce the variational formulations for some basic partial differential problems and provide an introduction to basic functional analysis, thoery of differential operators and approximation theory. In the second part the mathematical theory of the finite element methods, including the error analysis, will be presented. We consider several commonly used variatns of the finite element methods for solving elliptic and parabolic problems: conforming FE methods with Lagrange and Hermite elements, mixed and nonconforming the FE methods, FE methods with nonmatching grids. The algebraic aspects of the method will be considered within the third part of the course. We introduce the basic matrix operations needed in FE methods as well as some commonly used algorithms for numerical soltuion of arising algebraic systems. Finally we apply the finite element methods to some problems of practical interest in fluid dynamics (potential and Stokes flows), solid mechanics (Lame equations), electromagnetics and acoustics. |
| MATH 7396: FINITE VOLUME METHOD FOR TRANSPORT DOMINATED PDE (Section 11270) | |
| Time: | 4-5:30 TTH Rm. 204 AH |
| Instructor: | R. Sanders |
| Prerequisites: | Graduate standing and consent of instructor |
| Text(s): | Check with instructor |
| Description: | |
*NOTE: TEACHING FELLOWS ARE REQUIRED TO REGISTER FOR THREE REGULARLY SCHEDULED MATH COURSES FOR A TOTAL OF 9 HOURS. PH.D STUDENTS WHO HAVE PASSED THEIR PRELIM EXAM ARE REQUIRED TO REGISTER FOR ONE REGULARLY SCHEDULED MATH COURSE AND 6 HOURS OF DISSERTATION.