Senior and Graduate Math Course Offerings 2006 Fall
MATH 4377: ADVANCED LINEAR ALGEBRA (section# 13279) |
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| Time: | 0100-0230PM - MW - |
| Instructor: | TOMFORDE |
| Prerequisites: | Math 2431 + a minimum of 3 semester hours of 3000 level mathematics |
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| Description: | |
MATH 4377: ADVANCED LINEAR ALGEBRA (section# 10879) |
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| Time: | 0230-0400PM - TTH - |
| Instructor: | HAUSEN |
| Prerequisites: | Math 2431 + a minimum of 3 semester hours of 3000 level mathematics |
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| Description: | |
MATH 5330: ABSTRACT ALGEBRA (section# 13411) |
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| Time: | ARRANGE (online course) |
| Instructor: | Kaiser |
| Prerequisites: | Math 3330 or equivalent. |
| Text(s): | Abstract Algebra, A First Course by Dan Saracino. Waveland Press, Inc. ISBN 0-88133-665-3 |
| Description: | The course will cover the basic elements of Groups, Rings and Fields. |
MATH 5331: LINEAR ALGEBRA W/ APPLICATIONS (section# 10888) |
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| Time: | ARRANGE (online course) |
| Instructor: | ETGEN |
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| Description: | |
MATH 5350: INTRO TO DIFFERENTIAL GEOMETRY (section#13898) |
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| Time: | ARRANGE (online course) |
| Instructor: | M.Ru |
| Prerequisites: | Math 2433(or equivalent) or consent of instructor. |
| Text(s): | A set of notes on curves and surfaces will be written by Dr. Ru. |
| Description: | The course will be an introduction to the study of Differential Geometry-one of the classical (and also one of the more appealing) subjects of modern mathematics. We will primarily concerned with curves in the plane and in 3-space, and with surfaces in 3-space. We will use multi-variable calculus, linear algebra, and ordinary differential equations to study the geometry of curves and surfaces in R3. Topics include: Curves in the plane and in 3-space, curvature, Frenet frame, surfaces in 3-space, the first and second fundamental form, curvature of surfaces, Gauss's theorem egrigium, minimal surfaces. |
MATH 5386: REGRESSION & LINEAR MODELS (section#10889 ) |
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| Time: | ARRANGE (online course) |
| Instructor: | PETERS |
| Prerequisites: | Statistics or consent of instructor. |
| Text(s): | Introduction to Linear Regression Analysis", 3th edition, by Montgomery, Peck, and Vining, Wiley. |
| Description: | Simple and multiple linear regression, linear models with qualitative variables, inferences about model parameters, regression diagnostics, variable selection, other topics as time permits. The course will include computing projects. |
MATH 6320: REAL VARIABLES (Section# 10934 ) |
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| Time: | 1100-1200 - MWF - |
| Instructor: | Ji |
| Prerequisites: | 4331-4332 or equivalent. |
| Text(s): | Gerald B. Folland, Real Analysis: Modern Techniques and their Applications, John Wiley and Sons, ISBN 0471317160. |
| Description: | |
MATH 6342: TOPOLOGY (Section# 10937) |
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| Time: | 0530-0700PM - MW - |
| Instructor: | A. Torok |
| Prerequisites: | MATH 4331 (mainly Chapter 2 of "Principles of Mathematical Analysis" by W. Rudin) or consent of the instructor. Note: the prerequisites are different from those listed in the Graduate Catalog. |
| Text(s): | J. R. Munkres, Topology, Publisher: Prentice Hall; 2nd edition, 1999, ISBN: 0131816292 Students can use instead the first edition of this book: J. R. Munkres, Topology; A First Course, Publisher: Prentice Hall, 1974, ISBN: 0139254951 |
| Description: | An axiomatic development of point set topology: compactness, connectedness, quotient spaces, separation properties, Tychonoff's theorem, the Urysohn lemma, Tietze's theorem, characterization of separable metric spaces, completeness and function spaces. |
MATH 6360: APPLICABLE ANALYSIS (Section# 10938 ) |
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| Time: | 11:30-01:00pm - TTH - |
| Instructor: | GLOWINSKI |
| Prerequisites: | Graduate standing or consent of instructor. |
| Text(s): | The course will be essentially self-contained but some of the material to be discussed can be found in:
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| Description: | Following Part I of the course where various functional spaces of practical importance have been introduced, we will focus on the solution of variational problems from Image Processing (L^1 fitting, in particular). The following topics will be systematically discussed:
The methodology to be discussed can be applied to a variety of variational problems |
MATH 6366: OPTIMIZATION AND VARIATIONAL METHODS (Section# 10939) |
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| Time: | 0400-0530PM - MW - |
| Instructor: | Hoppe |
| Prerequisites: | Calculus, Linear Algebra |
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| Description: | This course focuses on convex optimization in the framework of convex analysis, including duality, minmax, and Lagrangians. The course consists of two parts. In part I, we consider convex optimization in a finite dimensional setting which allows an intuitive, geometrical approach. The mathematical theory will be introduced in detail and on this basis efficient algorithmic toolswill be developed and analyzed. In part II, we will be concerned with convex optimization in function space. We will provide the prerequisites from the Calculus of Variations and generalize the concepts from part I to the infinite dimensional setting.听 |
MATH 6370: NUMERICAL ANALYSIS (section # 10940 ) |
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| Time: | 0400-0530PM - TTH - |
| Instructor: | E. Dean |
| Prerequisites: | Graduate standing or consent of the instructor. Students should have had a course in advanced Linear Algebra (Math 4377-4378),an introductory course in Analysis (Math 4331-4332 ) and an ability to computer assignments. |
| Text(s): | Introduction to Numerical Analysis, by J. Stoer and R. Bulirsch (Springer-Verlag) 3rd Edition. |
| 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 quadrature, systems of linear and nonlinear algebraic equations. Note: This is the first semester of a two semester course. |
Math 6377: BASIC TOOLS FOR APPLIED MATH (Section# 10942) |
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| Time: | 0400-0530PM - TTH - |
| Instructor: | Sanders |
| Prerequisites: | Second year Calculus. Elementary Matrix Theory. Graduate standing or consent of instructor. |
| Text(s): | Lecture notes will be supplied by the instructor. |
| Description: | Finite dimensional vector spaces, linear operators, inner products, eigenvalues, metric spaces and norms, continuity, differentiation, integration of continuous functions, sequences and limits, compactness, fixed-point theorems, applications to initial value problems. |
Math 6382: PROBABILITY STATISTICS (Section# 10943) |
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| Time: | 1130-0100 - TTH - |
| Instructor: | Robert Azencott |
| Prerequisites: | MATH 3334, MATH 3338 and MATH 4378, or consent of instructor. |
| Text(s): | Recommended Texts
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| Description: | Emphasis will be placed on a thorough understanding of the basic concepts as well as developing problem solving skills. Topics covered include: combinatorial analysis, independence and the Markov property, Markov chains, the major discrete and continuous distributions, joint distributions and conditional probability, modes of convergence. These notions will be examined through examples and applications. |
Math 6384: DISCRETE TIME MODEL IN FINANCE (Section# 10944) |
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| Time: | 0530-0700PM - TTH - |
| Instructor: | Kao |
| Prerequisites: | Math 6382, or equivalent background in probability. |
| Text(s): | Introduction to Mathematical Finance: Discrete-Time Models, by Stanley R. Pliska, Blackwell, 1997. |
| Description: | This course is for students who seek a rigorous introduction to the modern financial theory of security markets. The course starts with single-periods and then moves to multiperiod models within the framework of a discrete-time paradigm. We study the valuation of financial, interest-rate, and energy derivatives and optimal consumption and investment problems. The notions of risk neutral valuation and martingale will play a central role in our study of valuation of derivative securities. The discrete time stochastic processes relating to the subject will also be examined. The course serves as a prelude to a subsequent course entitled Continuous-Time Models in Finance. |
Math 6386: COMPUTATIONAL STATISTICS (Section# 13401) |
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| Time: | 04:00-05:30PM , MW, |
| Instructor: | PETERS |
| Prerequisites: | Math 4377 and Math 4331 or consent of instructor. |
| Text(s): | "Introductory Statistics with R", by Peter Dalgaard, Springer. |
| Description: | An introduction to methods and software for basic computing tasks in statistics, descriptive, graphical and exploratory techniques, sampling and simulation, modeling and fitting, and inference procedures. Most of the computing will be done with the packages R and Splus, although some use will be made of spreadsheet programs and MATLAB. |
Math 6395: Wavelet Analysis (Section# 12900) |
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| Time: | 0400-0530PM -MW - |
| Instructor: | Manos Papadakis |
| Prerequisites: | MATH 6320 and MATH 4355 or consent of the instructor. |
| Text(s): | A First Course on Wavelets", by E. Hernandez and G. Weiss, CRC, 1996. |
| Description: | The Fourier transform on Euclidean spaces and Plancherel's theorem. Fundamentals of frames in Hilbert spaces (familiarity with Hilbert spaces, projections, subspaces and bounded operators on Hilbert spaces is assumed), Multiresolution analysis, Scaling functions and Multiresolution (MRA) wavelets; Examples of MRAs, Shannon's sampling theorem; Fast Wavelet transforms and filter banks, The construction of compactly supported wavelets; Spline wavelets on the real line, The unitary extension principle Separable, non-separable multiresolution analysis and Fast Wavelet transforms; Isotropic multiresolution analysis and transforms, Directional representations: Kingsbury's complex wavelets, Wedglets, beamlets, curvelets and sheerlets. |
Math 6397: NUM SOL STOCHASTIC DIFF EQTNS (Section# 12901) |
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| Time: | 0100-0230PM - MW - |
| Instructor: | TIMOFEYEV |
| Prerequisites: | |
| Text(s): | Numerical Solution of SDE Through Computer Experiments by Peter Eris Kloeden, Eckhard Platen, Henri Schurz Publisher: Springer ISBN: 3540570748 |
| Description: | The main emphasis will be on numerical methods for the stochastic differential equations and Markov chains. In the beginning an overview of the necessary background in probability and stochastic DE's will be given. Very few formal proofs will be covered, but a brief overview of Probability, Markov processes, Wiener process, Ito calculus, Fokker-Planck equation, Ornstein-Uhlenbeck process will be provided. |
Math 6397: DUALITY MTHD & OPERATOR SPACES(Section# 12902) |
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| Time: | 0900-1000AM - MWF - |
| Instructor: | BLECHER |
| Prerequisites: | Real variables Math 6320/21. A functional analysis course would be great, although strong students without this could read up on it concurrently. |
| Text(s): | Complete typed notes will be provided. |
| Description: | Brief description: The purpose of this course is two-fold, 1) to offer analysis graduate students a course in topics which are not currently covered in the functional analysis course, but which many of them really need to know, and others may be interested in for general knowledge, and 2) to provide an introduction to the theory of operator spaces. The first part of > the course will be on topological vector spaces, and in particular, weak topologies, and some basic results in convexity theory. The second part of the course is devoted to the basic theory of operator spaces. This will of course use their duality, which will use material from the first part. We will also briefly review the theory of C*-algebras which we shall need. The later parts of the course will be optional (students will not be tested on more advanced material) and will be more specialized. There will probably be one midterm test, and a final project. |
Math 6397: TIME SERIES ANALYSIS (Section# 12904) |
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| Time: | 1000-1130AM - TTH - |
| Instructor: | Kao |
| Prerequisites: | MATH 6383 Probability and Statistics Matrix Algebra |
| Text(s): | Time Series Analysis Princeton University Press, by James D. Hamilton 1994, ISBN 0691-04289-6 |
| Description: | This course covers the basic ideas in time series analysis. Topics include stationary processes, ARIMA models, nolinear time series analysis, cointegration, kalman filters and state-space model, and regime-switching models, This course is to be followed by an advanced course to be offered in the sping 2007 entitled "Analysis of Financial and Energy Time Series." |
Math 6397: MATHEMATICAL HEMODYNAMICS (Section# 13906) |
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| Time: | 11:30am -01:00 - TTH - |
| Instructor: | CANIC |
| Prerequisites: | Multivariable Calculus, Real and Complex Analysis |
| Text(s): | None required. Texbooks that will be used are:
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| Description: | Review of basic linear PDEs. Analysis of quasilinear PDEs with concentration to hyperbolic conservation laws. For more infomation, click here |
| Math 6397: Gibbs fields and their applications to automated Image Analysis (section# 13863) (Cancel) | |
| Time: | 0100-0230PM - TTH - |
| Instructor: | Robert Azencott |
| Prerequisites: | Math 3338 or equivalent. Other background topics required in probability theory will be covered in the course. |
| Text(s): | Reference books :
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| Description: | Gibbs fields are probabilistic models designed to analyze the behaviour of large systems of "particles" or "processors" in interaction ; they have been introduced by physicists for "statistical mechanics" describing the magnetisation of large nets of small magnets, and have generated exciting applications to modelize very large sets of digital images, in order to solve "low-level" artificial vision tasks , such as textures modelizations and segmentation, etc. The main probabilistic topics impacting this course involve the dynamics of homogeneous and non-homogeneous Markov chains on (huge) finite spaces, Bayesian inference, efficient estimation of parameters in stochastic models , multidimensional Gaussian processes, Monte-Carlo simulations. We will present image analysis applications and sketch simulated annealing techniques for minimization of functions of very large numbers of discrete variables |
Math 7320: FUNCTIONAL ANALYSIS (Section# 12907) |
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| Time: | 1000-1100AM - MWF - |
| Instructor: | PAULSEN |
| Prerequisites: | Math 6320-6321 |
| Text(s): | A Course in Functional Analysis, John B. Conway |
| Description: | We will begin with the geometry of Hilbert spaces and operators on Hilbert space. We will then study Banach spaces, locally convex and weak topologies and finish with a deeper look at operators on Banach spaces. |