Senior and Graduate Course Offerings Spring 2002
For further information, contact the Department of Mathematics at 651 PGH, University of Houston, Houston, TX 77204-3008; Telephone (713) 743-3517 or e-mail to pamela@math.uh.edu.
| MATH 4315: GRAPH THEORY WITH APPLICATIONS (Section 12893) | |
| Time: | 4-5:30 MW Rm. 16 AH |
| Instructor: | S. Fajtlowicz |
| Prerequisites: | Discrete Mathematics |
| Text(s): | The course will be based on instructor's notes |
| Description: | Eulerian tours and Euler characteristic formula. Map coloring problems and 4-color theorem. Trivial planar graphs with application to fullerness - new forms of carbon. Hamiltonian tours. Ramsey Theory, Matching and Erdos's probabilistic method. |
| MATH 4332: INTRODUCTION TO REAL ANALYSIS (Section 09518) | |
| Time: | 2:30-4 MW Rm. 315 PGH |
| Instructor: | M. Friedberg |
| Prerequisites: | Math 4331 or consent of instructor |
| Text(s): | Principles of Mathematical Analysis Walter Rudin, McGraw-Hill, 3rd Edition. |
| Description: | Sequences and series of functions, functions of several variables, Lebesgue Theory. |
| MATH 4333: ADVANCED ABSTRACT ALGEBRA (Section 09519) | |
| Time: | 10-11 MWF Rm. 202AH PGH |
| Instructor: | TBA |
| Prerequisites: | Math 3330 or equivalent. |
| Text(s): | TBA |
| Description: | Topics from Ring Theory, Field Theory and Group Theory including polynomial rings, quotient rings, field extensions and finite fields. Structure theorems from group theory as time permits. |
| MATH 4351: DIFFERENTIAL GEOMETRY (Section 11925) | |
| Time: | 4-5:30 MW 345 PGH |
| Instructor: | A. Torok |
| Prerequisites: | MATH 4350 or consent of instructor. |
| Text(s): | Differential Geometry of Curves and Surfaces, Manfredo Do Carmo, Prentice Hall. |
| Description: | This is the continuation of Math 4350 taught in Fall 2001. The course will continue the study of surfaces, including some applications to curves: Gaussian curvature, vector fields, geodesics, Gauss-Bonnet formula, Poincare index theorem, Fary-Milnor theorem. Other topics might also be included. For more details, please check www.uh.edu/~torok. |
| MATH 4360: INTEGRAL EQUATIONS (Section 11942) | |
| Time: | 1-2:30 TTH Rm. 315 PGH |
| Instructor: | P. Walker |
| Prerequisites: | A first course in differential equations. |
| Text(s): | None. |
| Description: | An introduction to linear transformations in Hilbert space with examples drawn primarily from integral equations. Spectral theory. |
| MATH 4365: NUMERICAL ANALYSIS (Section 09521) | |
| Time: | 5:30-7 TTH Rm. 209 PGH |
| Instructor: | E. Dean |
| Prerequisites: | Course in Linear Algebra nd Ordinary Differential Equations such as Math 2431-3431 or Math 3321. Ability to do computer assignments in either Fortran or C. This is the second semester of a two semester course. The first semester is not a prerequisite. |
| Text(s): | Numerical Analysis, R. L. Burden and J.D. Faires, 7th Edition, Prentice-Hall. |
| Description: | We will develop and analyze numerical methods for approximating the solutions of common mathematical problems. The emphasis this semester will be on the solution of initial value problems for ordinary differential equations, iterative methods for solving linear systems of algebraic equations and approximating eigenvalues, and elementary methods for partial differential equations. This is an introductory course and will be a mix of mathematics and computing. |
| MATH 4377: ADVANCED LINEAR ALGEBRA (Section 12040) (Section 12040) | |
| Time: | 1-2:30 TTH 218 AH |
| Instructor: | C. Peters |
| Prerequisites: | Math 2431 and a minimum of 3 hours of 3000 or 4000 level mathematics |
| Text(s): | Linear Algebra, Kenneth Hoffman and Ray Kunze, Prentice Hall, 2nd<\sup> Edition, 1971. |
| Description: | Linear systems of equations, elementary row operations, matrices, determinants, vector spaces, subspaces, linear transformations, eigenvalues and eigenvectors. |
| MATH 4378: ADVANCED LINEAR ALGEBRA (Section 09523) | |
| Time: | 11:30-1 TTH 204 AH |
| Instructor: | J. Johnson |
| Prerequisites: | Math 4377 or consent of instructor. |
| Text(s): | Linear Algebra, K. Hoffman and R. Kunze, 2nd<\sup> Edition, Prentice-Hall. |
| Description: | Topic to be covered in this course include linear equations, vector spaces, polynomials, linear transformations, and matrices. |
| MATH 4386: MATHEMATICAL STATISTICS (Section 11941) | |
| Time: | 1-2:30 MW Rm. 315 PGH |
| Instructor: | C. Peters |
| Prerequisites: | Math 4385. |
| Text(s): | Introduction to Linear Regression Analysis, Montgomery, Peck & Vining, Wiley 2001, 3rd Edition. |
| Description: | Diagnostics for multiple regression, variable selection and model order section methods, generalized linear models, time series. Other topics as time permits. |
| MATH 4397: MATH OF SIGNAL PROCESSING (Section 11963) | |
| Time: | 5:30-7 MW 350 PGH |
| Instructor: | M. Papadakis |
| Prerequisites: | Math 2431 or Math 3321. Also Math 1432. |
| Text(s): | Fourier Series and Integral Transforms, A. Pinkus, S. Zafrany, Cambridge UP, 1997. |
| Description: | The linear algebra of inner product spaces. Finite orthogonal and orthonormal systems, Gram-Schmidt orthogonalization, norms, convergence in the norm, infinite orthonormal bases. Fourier Series of real valued functions, Uniform and pointwise convergence of Fourier Series, Parseval's theorem and L2 convergence of Fourier Series. Integral Fourier transforms: Definition, properties, Riemann Lebesgue lemma, Inverse Fourier transform, convolutions and time-invariant linear systems, Plancherel's theorem, Analytic functions and power series, Band-limited and time-limited signals (functions), filtering and its connection with Fourier inversion. An intuitive introduction to tempered distributions and the Dirac delta function. Shannon's sampling theorem, Laplace transforms and its inversion. The following will be covered if time permits. 2-D Fourier transform, Discrete Fourier transform (Fourier transform on finite cyclic groups), Short-time Fourier transform and windowed Fourier transforms and (if time permits) and introduction to JPEG. |
| MATH 6300: CARDINAL AND ORDINAL NUMBERS (Section 11964) | |
| Time: | 2:30-4 TTH, 216 AH (Note time and room change!) |
| Instructor: | J. Johnson |
| Prerequisites: | Graduate standing or consent of instructor. |
| Text(s): | Manual of Axiomatic Set Theory, Frank D. Quigley. |
| Description: | Topics to be covered in this course include well-ordered sets, Zom's lemma, Hausdorff maximality principle, axiom of choice, well-ordering principle and transfinite induction. |
| MATH 6303: MODERN ALGEBRA (Section 09574) | ||
| Time: | 1-2:30 TTH 348 PGH | |
| Instructor: | J. Hausen | |
| Prerequisites: | Graduate Standing or consent of instructor. | |
| Text(s): | Algebra, Pierre Grillet, John Wiley & Sons, New York, 1999. (ISBN 0-471-25243-3). | |
| Description: | This is the continuation of Math 6302 where the basics of group, ring, and module theory were covered as well as the concept of a category. Topics in the spring will include free, projective and injective modules, direct sums and direct products, dual categories, products, coproducts and free objects in categories, functors, and tensor products. As time permits, additional topics from group, ring, field and module theory may be chosen taking student interest into account. Homework assignments will be an integral part of the course. | |
| MATH 6321: FUNCTIONS OF A REAL VARIABLE (Section 09594) | |
| Time: | 2:30-4 MW 350 PGH |
| Instructor: | D. Blecher |
| Prerequisites: | Math 6320 or some knowledge of basic integration theory (with consent of instructor). |
| Text(s): | None. Notes supplies. (RECOMMENDED) Lebesgue Integration on Euclidean Spaces, Frank Jones, Jones & Bartlett; Real Analysis (3rd Edition), H.L. Royden, Prentice Hall; Real and Complex Analysis, W. Rudin, McGraw Hill; Measure Theory, D.L. Cohn, Birkhauser. |
| Description: | This semester we will be continuing to develop the basic principles of measure, integration, and real analysis. This body of knowledge is essential to many parts of mathematics (in particular to analysis and probability). We will cover the following topics: Signed and complex measures. The Radon-Nikodym theorem. The duality of Lp spaces. Differentiation and integration of measure and functions on Rn. Basic connections with probability theory (distributions, density, independence). The Riesz representation theorem. Banach and Hilbert spaces. Suggested topics by students. After each chapter will schedule a problem solving workshop, based on he homework assigned for that chapter. You should attempt all homework problems, although it is not expected that you solve all of them. Most of the problems are there to help you learn and INTERNALIZE the material. You are encouraged to work with others, form study groups, and so on. However, you should not simply copy homework. |
| MATH 6323: FUNCTIONS OF A COMPLEX VARIABLE (Section 11935) | |
| Time: | 2:30-4 TTH 350 PGH |
| Instructor: | M. Ru |
| Prerequisites: | Math 6322. |
| Text(s): | Introduction to Complex Analysis, J. Noguchi. |
| Description: | This is the second semester of a two semester sequence. We will first finish Chapter 6 and Chapter 7, and then introduce some more advanced topics. |
| MATH 6327: PARTIAL DIFFERENTIAL EQUATIONS (Section 11936) | |
| Time: | 2:30-4 MW 204 AH |
| Instructor: | S. Canic |
| Prerequisites: | Calculus I, II, III, Real Analysis. |
| Text(s): | Partial Differential Equations, L.C. Evans, AMS, Graduate Studies in Mathematics, Vol. 19. |
| Description: | Basic theory for linear PDEs; nonlinear first order PDEs; Holder spaces solutions; Sobolev spaces solutions. |
| MATH 6343: POINT SET TOPOLOGY (Section 09595) | |
| Time: | 4-5:30 TTH 350 PGH |
| Instructor: | M. Friedberg |
| Prerequisites: | Math 6342 or consent of instructor. |
| Text(s): | Topology, James R. Munkres, 2nd Edition, Prentice-Hall, 2000. |
| Description: | This is the second half of a two semester course. Function space topologies, countability and separation axioms, metrization theorems, the Fundamental Group of a space. |
| MATH 6361: APPLICABLE ANALYSIS (Section 09596) | |
| Time: | 12-1:00 MWF 128 SR |
| Instructor: | B. Keyfitz |
| Prerequisites: | Math 6360 or consent of instructor. |
| Text(s): | An Introduction to Functional Analysis and Computational Mathematics, V.I Lebeder, Birkhauser, Boston, 1997., Introductory Real Analysis,, N. Kolmogorov and S.V. Fomin, Dover, New York, 1975. |
| Description: | Linear Functionals on Banach spaces; dual spaces. Operators on Banach and Hilbert spaces: the uniform Boundedness and open mapping principles. Applications to convex programming and control theory. Variational Methods; the Lax-Milgram Theorem. Quadratic functions; Ritz-Galerkin method. Introduction to the calculus of variations. |
| MATH 6367: OPTIMIZATION THEORY (Section 11940) | |
| Time: | 4-5:30 MW 309 PGH |
| Instructor: | G. Auchmuty |
| Prerequisites: | Math 6361. Math 6366 is not required for this course and it is not a continuation of Math 6366-though the material is related. |
| Text(s): | None required but there are a number of reference texts. |
| Description: | This course will cover material from the classical calculus of variations for 1-dimensional integrands. Topics will include the Euler Lagrange equations and extremality conditions for constrained minimization, existence-uniqueness results and second derivative analysis. We will emphasize specific problems including 2-point boundary value problems, Sturm-Liouville eigen problems and some problems from geometry and mechanics. Depending on student interest the course may also include some duality theory and/or an introduction to optimal control theory. |
| MATH 6371: NUMERICAL ANALYSIS (Section 09597) | |
| Time: | 5:30-7 TTH 350 PGH |
| Instructor: | T. Pan |
| Prerequisites: | Graduate standing or consent of the instructor. |
| Text(s): | Introduction to Numerical Analysis, J. Stoer and R. Bulirsch, Second Edition, Springer-Verlag, New York, 1993. (ISBN 3-540-97878-X). Introduction to Numerical Linear Algebra and Optimization, P.G. Ciarlet, Cambridge University Press, 1995. (ISBN 0-521-33948-7). |
| Description: | We will focus on numerical linear algebra, including direct methods for the solution of linear systems, eigenvalue problems, iterative methods for the solution of large linear systems, conjugate gradient method, multigrid method. We will also cover briefly numerical solutions of partial differential equations. |
| MATH 6395: COMPLEX ANALYSIS AND GEOMETRY II (Section 11955) | |
| Time: | 4-5:30 MW 314 PGH |
| Instructor: | S. Ji |
| Prerequisites: | Differential Geometry (Math 7350); complex Analysis (Math 6322, 6323). |
| Text(s): | Principles of Algebraic Geometry, Griffith & Harris. |
| Description: | Vector bundles, line bundles, Kodaira Embedding Theorem, Currents. |
| MATH 6397: LOGIC WITH APPLICATIONS (Section 11956) | |
| Time: | 4-5:30 TTH 128 SR (Note time change!) |
| Instructor: | K. Kaiser |
| Prerequisites: | Logic with Applications I, or any previous exposure to logic or graduate algebra. |
| Text(s): | Logic for Applications, Anil Nerode and and Richard A. Shore, Text and Monographs in Computer Science, Springer-Verlag. (ISBN 0-387-94893-7). Reasoning about Knowledge, R. Fagin, J.Y. Halpern, Y. Moses, M.Y. Vardi, The MIT Press, Cambridge, Mass. (ISBN 0-262-06162). |
| Description: | Horn Clause Logic (Prolog), Forcing and Non-Classical Logic systems, Epistemic Logic (logic about knowledge) and other selected topics. |
| MATH 6397: BASIC SCIENTIFIC COMPUTING (Section 12064) | |
| Time: | 4-5:30 TTH 201 AH |
| Instructor: | R. Sanders |
| Prerequisites: | Elementary Numerical Analysis. Knowledge of C and/or Fortran. Graduate standing or consent of instructor. |
| Text(s): | Check with instructor. |
| Description: | Fundamental techniques in high performance scientific computation. Hardware architecture and floating point performance. Pointers and dynamic memory allocation. Data structures and storage techniques related to numerical algorithms. Parallel programming techniques. Code design. Applications to numerical algorithms for the solution of systems of equations, differential equations and optimization. Data visualization. This course also provides an introduction to computer programming issues and techniques related to large scale numerical computation. |
| MATH 6397: AIR QUALITY MODELING II (Section 11954) | |
| Time: | 5:30-7 TTH MW 218 AH |
| Instructor: | J. He |
| Prerequisites: | Graduate standing or consent of instructor. |
| Text(s): | Fundamentals of Atmospheric Modeling, M.Z. Jacobson, Cambridge Univ. Press, 1998 (ISBN 0521637171). |
| Description: | Atmospheric aerosols are comprised of a complex mixture of a variety of organic and inorganic substances that can be primary or secondary nature and span several orders of magnitude in size. This complexity together with significant gaps in knowledge of the formation and transformation processes provides an ambitious tasks for the development of atmospheric models for particulate matter. However potential impacts of these particles and the new standards for particulate matter require the development and application of sophisticated Air Quality Models for particles. The goal of this course is to identify the lessons that can be learned from the current state of particulate matter models and the needs for further development of these models. A key question here is to define the level of model complexity that is required to obtain sufficient information on atmospheric particles while keeping the computational burdens feasible. Therefore the following questions will be addressed: 1) Which processes need to be included into a PM air quality model? 2) How important is the contribution of secondary organic particles resulting from anthropogenic and biogenic precursors to the PM load? 3) Which numerical implementations are suitable for aerosol modeling? |
| MATH 6398: KNOWLEDGE BASED ALGORITHMS II (Section 11953) | |
| Time: | 4-5:30 MW 347 PGH |
| Instructor: | S. Fajtlowicz |
| Prerequisites: | Graduate standing in the College of NSM or approval of the instructor. |
| Text(s): | None. |
| Description: | We will discuss computer programs capable of making mathematical conjectures and scientific hypotheses. These ideas are based mostly on experiences with computer program Graffiti whose conjectures inspired number of papers, some by the most prominent mathematicians and more recently a few papers in chemistry. We will discuss also some other attempts to develop such (or similar) programs including works of Nobel laureates Herbert Simon and Francis Crick and critical approach of Roger Penrose in the context of what came to be known as AI debate. Some versions of Graffiti will be used by students to learn or to expand their knowledge of one of several possible subjects of their own choice, Texas style--the method developed by UT Professor L.A. Moore. One significant difference will be that rather than to be led to discovery of known results, the students will work exclusively on conjectures of Red Burton--an educational version of Graffiti, often without getting any hints whether these conjectures are true or false. This will create more realistic scenario for graduate and undergraduate research experience. Active participants will have opportunity to discover new original results and possibly even new scientific hypotheses. |
| MATH 7394: TOPICS IN MATHEMATICAL BIOLOGY II (Section 11957) | |
| Time: | 10-11:30 TTH 350 PGH |
| Instructor: | W. Fitzgibbon |
| Prerequisites: | Fall 2001 Math 7394 course in Mathematical Biology or Consent of the instructor. |
| Text(s): | Mathematical Models in Population Biology and Epidemiology. |
| Description: | We shall be concerned with continuous models of biological process. The dynamics of interacting populations, predator prey systems, epidemiological models, neural models, bioeconomics, and spatial effects if time permits. |
| MATH 7394: COMPUTATIONAL METHODS FOR NEWTONIAN & NON-NEWTONIAN INCOMPRESSIBLE VISCOUS FLOWS (Section 11958) | |
| Time: | 11:30-1 TTH 345 PGH |
| Instructor: | R. Glowinski |
| Prerequisites: | Basic Numerical Linear Algebra; Basic Numerical Methods for Ordinary Differential Equations; some knowledge of Mechanics and/or Physics may be helpful. |
| Text(s): | None. |
| Description: | The main goal of this course is to introduce the student to basic numerical methods for the solution of the Navier-Stokes type equations modeling incompressible flow (Newtonian or not). These methods will combine finite element approximations to various types of time-discretization schemes. |
| MATH 8398: ADVANCED NUMERICAL ALGORITHMS (Section 11959) | |
| Time: | 1-2:30 MW 345 PGH |
| Instructor: | Y. Kuznetsov |
| Prerequisites: | Graduate standing or consent of instructor. |
| Text(s): | Check with instructor. |
| Description: | This new course consists in three parts. In the first part we consider macro-hybrid mixed finite element approximations for the diffusion equations in heterogeneous media, including the situation when the meshes don't match at the interfaces between subdomains. The second part is devoted to the variational formulations and finite element discretizations of the Maxwell equations in piece-wise homogeneous media. In the last part we design and investigate new iterative solvers for the finite element systems from the previous two parts of the course including the advanced multigrid methods. |
*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.