2017 - Spring Semester - University of Houston
Skip to main content

2017 - Spring Semester



GRADUATE COURSE SPRING 2017 

This schedule is subject to changes. Please contact the Course Instructor for confirmation.

SENIOR UNDERGRADUATE COURSES 
Course Sec #
Course Title Course Day & Time Rm # Instructor 
Math 4309 15672 Mathematical Biology TuTh, 2:30-4 p.m. M 115 R. Azevedo

Math 4332/6313

12060/13695

Introduction to Real Analysis II TuTh, 10-11:30 a.m. F 154 D. Labate
Math 4351 21457 Differential Geometry II MW, 1-2:30 p.m. SW 219 M. Ru
Math 4355 21456 Mathematics of Signal Representation TuTh, 1-2:30 p.m. CAM 101 D. Labate
Math 4364 19420 Intro. to Numerical Analysis in Scientific Computing MW, 4-5:30 p.m. CBB 118 T. Pan
Math 4365 17384 Numerical Methods for Differential Equations MW, 1-2:30 p.m. SW 423 J. He

Math 4377/6308

14513/13696

Advanced Linear Algebra I TuTh, 2:30-4 p.m. CBB 104 E. Kao

Math 4377/6308

18470/18471

Advanced Linear Algebra I (online) Online Online J. Morgan

Math 4378/6309

12061/13697 

Advanced Linear Algebra II TuTh, 2:30-4 p.m. F 154 D. Wagner
Math 4380 12062 A Mathematical Introduction to
Options
TuTh, 1-2:30 p.m. CAM 103 I. Timofeyev
Math 4389 12063 Survey of Undergraduate Mathematics MWF 9-10 a.m. SEC 201/Hybrid M. Almus



GRADUATE ONLINE COURSES 

Course Section Course Title Course Day & Time  Instructor 
Math 5330 13515 Abstract Algebra Arrange (online course) K. Kaiser
Math 5332 12089 Differential Equations Arrange (online course) G. Etgen
Math 5386 15302 Regression and Linear Models Arrange (online course) C. Peters
Math 5397 26816 Dynamical Systems Arrange (online course) A. Török


GRADUATE COURSES 

Course

Section Course Title Course Day & Time  Rm # Instructor 
Math 6303 12096 Modern Algebra II MWF, 10-11 a.m. AH 2 M. Tomforde
Math 6308 13696 Advanced Linear Algebra I TuTh, 2:30-4 p.m. CBB 104 E. Kao
Math 6308 18471 Advanced Linear Algebra I (online) Online Online J. Morgan
Math 6309 13697 Advanced Linear Algebra II MWF, Noon-1 p.m. F 154 D. Wagner
Math 6313 13695 Introduction to Real Analysis TuTh, 10-11:30 a.m. F 154 D. Labate
Math 6321 12113 Theory of Functions of a Real Variable MWF, 11 a.m.-Noon AH 2 M. Kalantar
Math 6353 21449 Complex Analysis & Geo II MW, 1-2:30 p.m. AH 301 G. Heier
Math 6361 13699 Applicable Analysis TuTh, 4-5:30 p.m. AH 11 G. Auchmuty
Math 6367 12114 Optimization Theory TuThu, 11:30 a.m.-1 p.m. SW 221 R. Glowinski
Math 6371 12115 Numerical Analysis MW, 1-2:30 p.m. SEC 203 Y. Kuznetsov
Math 6373 21450 Automatic Learning & Data Mining TuTh, 11:30 a.m.-1 p.m. CAM 103 R. Azencott
Math 6378 17464 Basic Scientific Computing TuTh, 1-2:30 p.m. AH 301 R. Sanders
Math 6383 12116 Probability Statistics  TuTh, 10-11:30 a.m. SW 423 W. Fu
Math 6395 21452 Analytic Functions, Hardy Spaces and Operator Function Theory MWF, Noon-1 p.m. AH 2 D. Blecher
Math 7321 21453 Functional Analysis TuTh, 1-2:30 p.m. M 104 B. Bodmann
Math 7326 21454 Dynamical Systems MWF, 11 a.m.-Noon AH 301 V. Climenhaga
Math 7350 12176 Geometry of Manifolds MW, 4-5:30 p.m. AH 10 W. Ott

-------------------------------------------Course Details-------------------------------------------------

SENIOR UNDERGRADUATE COURSES

Math 4309 (15672) - Mathematical Biology

Prerequisites:

MATH 3331 and BIOL 3306 or consent of instructor.

Text(s): A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by Sarah P. Otto and Troy Day; ISBN-13:9780691123448
Description:

Topics in mathematical biology, epidemiology, population models, models of genetics and evolution, network theory, pattern formation, and neuroscience. Students may not receive credit for both MATH 4309 and BIOL 4309.

<< back to top >>
 

 
Math 4332 (12060) - Introduction to Real Analysis II
Prerequisites: MATH 4331 or consent of instructor
Text(s): Real Analysis with Real Applications | Edition: 1; Allan P. Donsig, Allan P. Donsig; ISBN: 9780130416476
Description:

Further development and applications of concepts from MATH 4331. Topics may vary depending on the instructor's choice. Possibilities include: Fourier series, point-set topology, measure theory, function spaces, and/or dynamical systems.

<< back to top >>
 
Math 4351 (21457) - Differential Geometry II
Prerequisites:

MATH 4350.

Text(s): Instructor's notes will be provided.
Description:

Continuation of the study of Differential Geometry from MATH 4350. Holonomy and the Gauss-Bonnet theorem, introduction to hyperbolic geometry, surface theory with differential forms, calculus of variations and surfaces of constant mean curvature, abstract surfaces (2D Riemannian manifolds). 

<< back to top >>
 
Math 4355 (21456) - Mathematics of Signal Representation
Prerequisites:

MATH 2433 and six additional hours of 3000-4000 level Mathematics

Text(s):

A First Course in Wavelets with Fourier Analysis | Edition: 2 by Albert Boggess, Francis J. Narcowich, ISBN-13: 9780470431177

Description:

Fourier series of real-valued functions, the integral Fourier transform, time-invariant linear systems, band-limited and time-limited signals, filtering and its connection with Fourier inversion, Shannon’s sampling theorem, discrete and fast Fourier transforms, relationship with signal processing. 

<< back to top >>
Math 4364 (19420)- Numerical Analysis in Scientific Computing
Prerequisites:

MATH 3331 and COSC 1410 or equivalent or consent of instructor.

Instructor's Prerequisite Notes: 

1. MATH 2331, In depth knowledge of Math 3331 (Differential Equations) or Math 3321 (Engineering Mathematics)

2. Ability to do computer assignments in FORTRAN, C, Matlab, Pascal, Mathematica or Maple.

Text(s):

Numerical Analysis (9th edition), by R.L. Burden and J.D. Faires, Brooks-Cole Publishers, ISBN:9780538733519

Description: This is an one semester course which introduces core areas of numerical analysis and scientific computing along with basic themes such as solving nonlinear equations, interpolation and splines fitting, curve fitting, numerical differentiation and integration, initial value problems of ordinary differential equations, direct methods for solving linear systems of equations, and finite-difference approximation to a two-points boundary value problem. This is an introductory course and will be a mix of mathematics and computing.

<< back to top >>
 
Math 4365 (17384) - Numerical Methods for Differential Equations
Prerequisites: MATH 3331, or equivalent, and three additional hours of 3000–4000 level Mathematics.
Text(s): TITLE:TBA, AUTHOR:TBA, ISBN:TBA
Description: Numerical differentiation and integration, multi-step and Runge-Kutta methods for ODEs, finite difference and finite element methods for PDEs, iterative methods for linear algebraic systems and eigenvalue computation.

<< back to top >>
 
Math 4377 (14513) - Advanced Linear Algebra I
Prerequisites: MATH 2331 or equivalent, and three additional hours of 3000–4000 level Mathematics.
Text(s): Linear Algebra | Edition: 4; Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; ISBN: 9780130084514
Description:

Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors.

Additional Notes: This is a proof-based course. It will cover Chapters 1-4 and the first two sections of Chapter 5. Topics include systems of linear equations, vector spaces and linear transformations (developed axiomatically), matrices, determinants, eigenvectors and diagonalization.

<< back to top >>
Math 4377 (18470) - Advanced Linear Algebra I (Online)
Prerequisites: MATH 2331 or equivalent, and six additional hours of 3000–4000 level Mathematics.
Text(s): Linear Algebra | Edition: 4; Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; ISBN: 9780130084514
Description: Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors.

<< back to top >>
Math 4378 (12061) - Advanced Linear Algebra II
Prerequisites: MATH 4377
Text(s): Linear Algebra, Fourth Edition, by S.H. Friedberg, A.J Insel, L.E. Spence,Prentice Hall, ISBN 0-13-008451-4; 9780130084514
Description:

Similarity of matrices, diagonalization, Hermitian and positive definite matrices, normal matrices, and canonical forms, with applications.

Instructor's Additional notes: This is the second semester of Advanced Linear Algebra. I plan to cover Chapters 5, 6, and 7 of textbook. These chapters cover Eigenvalues, Eigenvectors, Diagonalization, Cayley-Hamilton Theorem, Inner Product spaces, Gram-Schmidt, Normal Operators (in finite dimensions), Unitary and Orthogonal operators, the Singular Value Decomposition, Bilinear and Quadratic forms, Special Relativity (optional), Jordan Canonical form.

<< back to top >>

<< back to top >>
Math 4380 (12062) - A Mathematical Introduction to Options
Prerequisites:  MATH 2433 and MATH 3338
Text(s):  An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation | Edition: 1; Desmond  Higham; 9780521547574
Description:  Arbitrage-free pricing, stock price dynamics, call-put parity, Black-Scholes formula, hedging, pricing of European and American options.
<< back to top >>

<< back to top >>
Math 4389 (12063) - Survey of Undergraduate Mathematics
Prerequisites:  MATH 3330MATH 3331MATH 3333, and three hours of 4000-level Mathematics.
Text(s):  Instructor will use her own notes
Description:  A review of some of the most important topics in the undergraduate mathematics curriculum.
 
<< back to top >>

ONLINE GRADUATE COURSES

<< back to top >>
MATH 5330 (13515) - Abstract Algebra
Prerequisites: Graduate standing. 
Text(s):

Abstract Algebra , A First Course by Dan Saracino. Waveland Press, Inc. ISBN 0-88133-665-3
(You can use the first edition. The second edition contains additional chapters that cannot be covered in this course.)

Description:

Groups, rings and fields; algebra of polynomials, Euclidean rings and principal ideal domains. Does not apply toward the Master of Science in Mathematics or Applied Mathematics. 

Other Notes: This course is meant for  students who wish to pursue a Master of Arts in Mathematics (MAM). Please contact me  in order to find out whether this course is suitable for you and/or your degree plan. Notice that this course cannot be used for  MATH 3330, Abstract Algebra. 

<< back to top >>
MATH 5332 (12089) - Differential Equations
Prerequisites: Graduate standing. MATH 5331.
Text(s): TBA
Description:

Linear and nonlinear systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; higher dimensional systems; Laplace transforms. Theory and applications illustrated by computer assignments and projects. Applies toward the Master of Arts in Mathematics degree; does not apply toward the Master of Science in Mathematics or the Master of Science in Applied Mathematics degrees.

<< back to top >>

<< back to top >>
MATH 5386 (15302) - Regression and Linear Models
Prerequisites: Graduate standing. Two semesters of calculus, one semester of linear algebra, and MATH 5385, or consent of instructor. 
Text(s): Introduction to Linear Regression Analysis | Edition:5; Montgomery, Peck, Vining; ISBN: 9780470542811; Wiley
Description:

Simple and multiple linear regression, linear models, inferences from the normal error model, regression diagnostics and robust regression, computing assignments with appropriate software. Applies toward Master of Arts in Mathematics degree; does not apply toward the Master of Science in Mathematics or the Master of Science in Applied Mathematics degrees. 

Note: This course is VEE approved for the regression component only. Approval Code: 4458-11008. For more information on VEE approved courses, click here.

MATH 5397 (26816) - Dynamical Systems
Prerequisites: Graduate standing. Three semesters of Calculus or consent of instructor.  Basic knowledge of ODE's is helpful, but not required
Text(s):

Steven H. Strogatz: Nonlinear Dynamics and Chaos (with Applications to Physics, Biology, Chemistry, and Engineering) Second Edition, 2014.

Print ISBN: 9780813349107

Ebook ISBN: 9780813349114

Description:

We will discuss applications of nonlinear dynamics, following the book by Strogatz. Topics that will be considered include (for more details, check the book's table of contents): an introduction to Ordinary Differential Equations (ODE's), one-dimensional ODE's and their bifurcations; two-dimensional ODE's (linear case, limit cycles and the Poincare-Bendixson Theorem, the Hopf bifurcation), chaotic systems (logistic family, Lorenz equations, Henon map). For visualization we will use tools that do not require programming, with the option to additionally run/write Matlab code.

 

<< back to top >>

GRADUATE COURSES

<< back to top >>
MATH 6303 (12096) - Modern Algebra II
Prerequisites:  Graduate standing. MATH 4333 or MATH 4378 or consent of instructor
Text(s):

Abstract Algebra, 3rd Edition by David S. Dummit and Richard M. Foote.

ISBN-13: 978-0471433347

ISBN-10: 0471433349

Description: Topics from the theory of groups, rings, fields, and modules. 

 

<< back to top >>
MATH 6308 (14458) - Advanced Linear Algebra I
Prerequisites: Graduate standing. MATH 2331 and a minimum of 3 semester hours transformations, eigenvalues and eigenvectors.
Text(s): Linear Algebra | Edition: 4; Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; ISBN: 9780130084514
Description:

Transformations, eigenvalues and eigenvectors.

Additional Notes: This is a proof-based course. It will cover Chapters 1-4 and the first two sections of Chapter 5. Topics include systems of linear equations, vector spaces and linear transformations (developed axiomatically), matrices, determinants, eigenvectors and diagonalization.

<< back to top >>
MATH 6308 (20438) - Advanced Linear Algebra I (online)
Prerequisites: Graduate standing. MATH 2331 and a minimum of 3 semester hours transformations, eigenvalues and eigenvectors.
Text(s): Linear Algebra | Edition: 4; Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; ISBN: 9780130084514
Description: Transformations, eigenvalues and eigenvectors. An expository paper or talk on a subject related to the course content is required

<< back to top >>
MATH 6309 (13697) - Advanced Linear Algebra II 
Prerequisites:  Graduate standing and MATH 6308
Text(s): Linear Algebra, Fourth Edition, by S.H. Friedberg, A.J Insel, L.E. Spence,Prentice Hall, ISBN 0-13-008451-4; 9780130084514
Description:  Similarity of matrices, diagonalization, hermitian and positive definite matrices, canonical forms, normal matrices, applications. An expository paper or talk on a subject related to the course content is required. 

<< back to top >>
MATH 6313 (13695)- Introduction to Real Analysis II
Prerequisites:  Graduate standing and MATH 6312.
Text(s):  TBA
Description:  Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals. An expository paper or talk on a subject related to the course content is required. 

<< back to top >>
MATH 6321 (12113) - Theory of Functions of a Real Variable
Prerequisites:

Graduate standingMATH 4332 or consent of instructor.

Instructor's Prerequisite Notes: MATH 6320

Text(s):

Primary (Required): Real Analysis: Modern Techniques and Their Applications, Gerald Folland (2nd edition); ISBN: 9780471317166.

Supplementary (Recommended): Real Analysis for Graduate Students, Richard F. Bass, (2nd edition); ISBN: 9781481869140

Description:

Lebesque measure and integration, differentiation of real functions, functions of bounded variation, absolute continuity, the classical Lp spaces, general measure theory, and elementary topics in functional analysis. 

Instructor's Additional Notes: Math 6321 is the second course in a two-semester sequence intended to introduce the theory and techniques of modern analysis. The core of the course covers elements of functional analysis, Radon measures, elements of harmonic analysis, the Fourier transform, distribution theory, and Sobolev spaces. Additonal topics will be drawn from potential theory, ergodic theory, and the calculus of variations.

<< back to top >>

<< back to top >>
MATH 6353 (21449) - Complex Analysis & Geo II
Prerequisites: Graduate standing. Math 6352 or consent of instructor.
Text(s):

Principles of Algebraic Geometry | Edition: 1, Author: Phillip Griffiths, Joseph Harris; ISBN: 9780471050599 (recommended)

Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series, Author: R.K. Lazarsfeld; ISBN: 9783540225331 (recommended)

Description: Idea sheaves with its applications and advanced techniques in transdental algebraic geometry. 

<< back to top >>
MATH 6361 (13699) - Applicable Analysis
Prerequisites: Graduate standing. MATH 4332 or consent of instructor.
Text(s):
The instructor will provide lecture notes on the material. A reference text is L.D. Berkowitz, Convexity and Optimization in Rn, Wiley-Interscience 2002. 
Description:

This course provides an introduction to the mathematical analysis of finite dimensional optimization problems. Topics to be studied include the existence of, and the extremality conditions that hold at, solutions of constrained and unconstrained optimaization problems.  Elementary theory of convex sets, functions and constructions from convex analysis will be introduced and used. Concepts include subgradients, conjugate functions and some duality theory.  Specific problems to be studied include energy and least squares methods for solving linear equations, important inequalities, eigenproblems and some nonlinear programming problems from applications. 

<< back to top >>
MATH 6367 (12114)- Optimization Theory
Prerequisites: Graduate standing. MATH 4331 and MATH 4377.
Text(s):

-Instructor will provide notes.

-R. Glowinski, J.L. Lions, JW He, Exact and Approximate Controllability for Distributed Systems: A Numerical Approach, Cambridge University Press, New York, NY, 2008. ISBN: 9780521885720 (recommended)

Description: Constrained and unconstrained finite dimensional nonlinear programming, optimization and Euler-Lagrange equations, duality, and numerical methods. Optimization in Hilbert spaces and variational problems. Euler-Lagrange equations and theory of the second variation. Application to integral and differential equations.

<< back to top >>
MATH 6371 (12115) - Numerical Analysis
Prerequisites: Graduate standing.
Text(s): Numerical Mathematics (Texts in Applied Mathematics), 2nd Ed., V.37, Springer, 2010. By A. Quarteroni, R. Sacco, F. Saleri. ISBN: 9783642071010
Description: Ability to do computer assignments. Topics selected from numerical linear algebra, nonlinear equations and optimization, interpolation and approximation, numerical differentiation and integration, numerical solution of ordinary and partial differential equations. 

<< back to top >>
MATH 6373 (21450) - Automatic Learning & Data Mining
Prerequisites: Graduate standing. Probability & Statistics
Text(s): Instructor will provide his own notes.
Description:

Automatic Learning of unknown functional relationships Y = F(X) between an output  Y and high-dimensional inputs X , involves algorithms dedicated  to the intensive analysis of large "training sets"  of N "examples" of inputs/outputs pairs (Xn,Yn ), with n= 1…N to discover efficient "blackboxes" approximating the unknown function X->F(X). Automatic learning was first applied  to emulate intelligent tasks involving complex patterns identification,   in artificial vision, face recognition, sounds identification, speech understanding, handwriting recognition, texts classification and retrieval, etc. Automatic learning has now been widely extended to the analysis of high dimensional biological data sets  in  proteomics and  genes interactions networks, as well as to smart mining of massive data sets gathered on the Internet.  

The course will study  major  machine learning algorithms derived from Positive Definite Kernels  and their associated Self-Reproducing Hilbert spaces. We will study the implementation, performances, and drawbacks of  Support Vector Machines classifiers, Kernel based Non Linear Clustering, Kernel based Non Linear Regression, Kernel PCA. We will explore connections between kernel based learning  and Dictionary Learning as well as Artificial Neural Nets with emphasis on  key conceptual features  such as generalisation capacity. We will present classes of Positive Definite Kernels designed to handle the  long "string descriptions" of  proteins involved in genomics and proteomics.

The course  will focus  on understanding key concepts through  their mathematical formalization,  as well as  on computerized algorithmic implementation and intensive testing on  actual data sets

<< back to top >>


<< back to top >>
MATH 6378 (17464) - Basic Scientific Computing
Prerequisites: Graduate standingMATH 4364 and MATH 4365 or equivalent, and either COSC 1304 or COSC 2101 or equivalents. 
Text(s): Instructor will provide his own notes.
Description: A project-oriented course in fundamental techniques for high performance scientific computation. Hardware architecture and floating point performance, code design, data structures and storage techniques related to scientific computing, parallel programming techniques, applications to the numerical solution of problems such as algebraic systems, differential equations and optimization. Data visualization. 

<< back to top >>
MATH 6383 (12116) - Probability Statistics
Prerequisites:

Graduate standing MATH 3334, MATH 3338 and MATH 4378.

Instructor's Prerequisites:TBA 

Text(s):

Recommended Text: John A. Rice : Mathematical Statistics and Data Analysis, 3rd editionBrooks / Cole, 2007. ISBN-13: 978-0-534-39942-9. 

Reference Texts: 

-P. MuCullagh and J.A. Nelder: Generealized Linear Models, 2nd ed. 1999 Chapman Hall/CRC. ISBN: 978-0412317606

-Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining, Timothy J. Robinson, Generalized Linear Models: with Applications in Engineering and the Sciences, 2nd ed. Wiley, 2010. ISBN: 978-0-470-45463-3. 

Description:

A survey of probability theory, probability models, and statistical inference. Includes basic probability theory, stochastic processes, parametric and nonparametric methods of statistics. 

Instructor's Description: This course is designed for graduate students who have been exposed to basic probability and statistics and would like to learn more advanced statistical theory and techniques in modelling data of various types, including continuous, binary, counts and others. The selected topics will include basic probability distributions, likelihood function and parameter estimation, hypothesis testing, regression models for continuous and categorical response variables, variable selection methods, model selection, large sample theory, shrinkage models, ANOVA and some recent advances.



<< back to top >>
MATH 6395 (21452) - Analytic Functions, Hardy Spaces and Operator Function Theory
Prerequisites: Graduate Standing. Some parts of the Real Variables sequence would be helpful, e.g. Math 6320
Text(s): Banach Spaces of Analytic Functions (Dover Books on Mathematics), by Kenneth Hoffman; ISBN: 978-0486458748. Instructor will also provide some typed notes, drawn from several texts.
Description: Brief description:  We will start with some important theorems in complex analysis related to normal families of analytic functions.  We then will study the basic theory of the disk algebra and the important theory of Hardy spaces (which we have not taught at UH for some years).  We will  follow Hoffman's book closely here. In the second half of the course we will discuss some operator function theory e.g. related to the invariant subspace problem (Beurling's theorem and generalizations). We will also discuss abstract operator algebras on a Hilbert space and their theory, and connections to noncommutative function theory. The course will end with a choice of student projects depending on what they are each interested in, for example a treatment of noncommutative integration and noncommutative Hardy spaces.

<< back to top >>
MATH 7321 (21453) - Functional Analysis
Prerequisites:

Graduate standing. 

Text(s): Textbook: 
Description:
Linear topological spaces, Banach and Hilbert spaces, duality, and spectral analysis. 

<< back to top >>
MATH 7326 (21454) - Dynamical Systems
Prerequisites:

Graduate standing. Math 6320 or equivalent background in measure theory.  Some familiarity with smooth manifolds would be useful but will not be assumed.

Text(s): Textbook:  Katok and Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge,  ISBN-13: 978-0521575577,  ISBN-10: 0521575575 
Additional reference text (not required): Rufus Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, 2008 (2nd Revised Edition), Springer Lecture Notes in Mathematics #470, ISBN 9783540776055
Description: This course will give an introduction to the theory of dynamical systems, with particular emphasis on those systems displaying hyperbolic (chaotic) behavior.  After a general overview, we will describe the key properties of uniformly hyperbolic systems, including structural stability and finite Markov partitions.  Then we will explain how tools from thermodynamics can be used to deduce statistical properties of the system, especially for the "physically relevant" Sinai-Ruelle-Bowen measure.  Finally, we will give a brief overview of the more physically realistic class of nonuniformly hyperbolic systems, including the multiplicative ergodic theorem, Pesin theory, and countable-state Markov codings.

<< back to top >>
MATH 7350 (12176) - Geometry of Manifolds
Prerequisites: Graduate standing. MATH 6342.
Text(s): Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218) 2nd Edition, John Lee, ISBN-13: 978-1441999818; ISBN-10: 1441999817
Description: Math 7350 is an introduction to the theory of differentiable manifolds.  Topics include vector bundles, embedding theory, tensors, integration on manifolds, flows, elements of Lie theory, and Riemannian metrics.
<< back to top >>

<< back to top >>