2023  Spring Semester
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Please view either the UH Class Schedule page or your Class schedule in myUH for the most current/updated information.)
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GRADUATE COURSES  SPRING 2023
This schedule is subject to changes. Please contact the Course Instructor for confirmation.
(updated 01/17/23)
Course 
Section 
Course Title 
Course Day/Time 
Rm # 
Instructor 
Math 4309  12392  Mathematical Biology  MW, 2:30—4PM, (F2F)  SEC 104  R. Azevedo 
Math 4315  17794  Graph Theory with Applications  TuTh, 4—5:30PM, (F2F)  CBB 214  K. Josic 
Math 4322  16274  Introduction to Data Science and Machine Learning  TuTh, 11:30AM—1PM, (F2F)  SEC 104  C. Poliak 
Math 4323  15666  Data Science and Statistical Learning  MWF, 11AM—Noon, (F2F)  SEC 104  W. Wang 
Math 4332/6313  11165  Introduction to Real Analysis II  TuTh, 1—2:30PM, (F2F)  F 162  M. Kalantar 
Math 4335  20411  Partial Differential Equations I  MWF, 9—10AM, (F2F)  CBB 214  G. Jaramillo 
Math 4351  20834  Calculus on Manifolds  MWF, Noon—1PM, (F2F)  CBB 214  M. Nicol 
Math 4362  14935  Theory of Differential Equations and Nonlinear Dynamics  MWF, 10—11AM, (F2F)  SEC 201  A. Török 
Math 4364  13420  Intro. to Numerical Analysis in Scientific Computing  MW, 4—5:30PM, (F2F)  SEC 205  T.W. Pan 
Math 4364  20284  Intro. to Numerical Analysis in Scientific Computing  TuTh, 8:30—10AM, (F2F)  SEC 205  L. Cappanera 
Math 4365  12870  Numerical Methods for Differential Equations  TuTh, 11:30AM—1PM, (F2F)  CBB 214  J. He 
Math 4370  20540  Mathematics for Physicists  MWF, 9—10AM, (F2F)  AH 301  A. Cardoso Barato 
Math 4377/6308  13148  Advanced Linear Algebra I  MW, 1—2:30PM, (F2F)  SEC 202  A. Quaini 
Math 4378/6309  11166  Advanced Linear Algebra II  MW, 1—2:30PM, (F2F)  F 154  A. Mamonov 
Math 4380  11167  A Mathematical Introduction to Options  TuTh, 2:30—4PM, (F2F)  F 162  E. Kao 
Math 4389  11168  Survey of Undergraduate Mathematics  TuTh, 1—2:30PM, (F2F)  GAR G201  M. Almus 
Course 
Section 
Course Title 
Course Day & Time 
Instructor 
Math 5330  11727  Abstract Algebra 
(Asynch./oncampus exams)  A. Haynes 
Math 5332  11175  Differential Equations 
(Asynch./oncampus exams)  G. Etgen 
Math 5385  16296  Statistics  (Asynch./oncampus exams)  J. Kwon 
Course 
Section 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 6303  11176  Modern Algebra II  TuTh, 2:30—4PM  S 115  G. Heier 
Math 6308  13149  Advanced Linear Algebra I  MW, 1—2:30PM  SEC 202  A. Quaini 
Math 6309  11784  Advanced Linear Algebra II  MW, 1—2:30PM  F 154  A. Mamonov 
Math 6313  11783  Introduction to Real Analysis  TuTh, 1—2:30PM  F 162  M. Kalantar 
Math 6321  11181  Theory of Functions of a Real Variable  MWF, 10—11AM  S 115  A. Vershynina 
Math 6361  17797  Applicable Analysis  TuTh, 1—2:30PM  S 202  D. Onofrei 
Math 6367  11182  Optimization Theory  MW, 1—2:30PM  S 102  R. Hoppe 
Math 6371  11183  Numerical Analysis  MW, 5:30—7PM  S 102  M. Olshanskiy 
Math 6383  11184  Probability Statistics  TuTh, 11:30AM—1PM  FH 130  M. Jun 
Math 6397  20344  Math of Deep Learning  TuTh, 10—11:30AM  S 115  D. Labate 
Math 6397  20393  Bayesian Inverse Problems and Uncertainty Quantification  MW, 4—5:30PM  S 202  A. Mang 
Math 6397  20396  Algebraic Topology  TuTh, 11:30AM—1PM  S 115  D. Blecher 
Math 7321  25318  Functional Analysis  TuTh, 10—11:30AM  SW 219  B. Bodmann 
Math 7326  20389  Dynamical Systems  TuTh, 1—2:30PM  S 201  W. Ott 
Course 
Section 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 6359  16309  Applied Statistics & Multivariate Analysis  F, 1—3PM (Synch—oncampus exams)  online  C. Poliak 
Math 6373  15440  Deep Learning and Artificial Neural Networks  MW, 1—2:30PM (F2F)  CBB 214  R. Azencott 
Math 6381  18626  Information Visualization **  F, 3—5PM (Synch—oncampus exams)  online  D. Shastri 
Math 6397  20890  Case Studies in Data Analysis  W, 5:30—8:30PM (F2F)  AH 301  L. Arregoces 
Math 6397  20891  Financial & Commodity Mkts  W, 5:30—8:30PM (F2F)  SEC 203  J. Ryan 
Course Details
SENIOR UNDERGRADUATE COURSES
Math 4309  Mathematical Biology 

Prerequisites:  
Text(s):  Required texts: A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, Sarah P. Otto and Troy Day; (2007, Princeton University Press) ISBN13:9780691123448 Reference texts: (excerpts will be provided)

Description: 
Catalog 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. 
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Prerequisites:  MATH 3325 or MATH 3336 and three additional hours at the MATH 30004000 level. 
Text(s):  Intro to Statistical Learning, Gareth James, 9781461471370 
Description:  Introduction to basic concepts, results, methods, and applications of graph theory. 
Math 4322  Introduction to Data Science and Machine Learning


Prerequisites:  MATH 3339 
Text(s):  Intro to Statistical Learning, Gareth James, 9781461471370 
Description: 
Theory and applications for such statistical learning techniques as linear and logistic regression, classification and regression trees, random forests, neutral networks. Other topics might include: fit quality assessment, model validation, resampling methods. R Statistical programming will be used throughout the course. 
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Math 4323  Data Science and Statistical Learning


Prerequisites:  MATH 3339 
Text(s):  Intro to Statistical Learning, Gareth James, 9781461471370 
Description:  Theory and applications for such statistical learning techniques as maximal marginal classifiers, support vector machines, Kmeans and hierarchical clustering. Other topics might include: algorithm performance evaluation, cluster validation, data scaling, resampling methods. R Statistical programming will be used throughout the course. 
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Math 4332  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, pointset topology, measure theory, function spaces, and/or dynamical systems. 
Math 4335  Partial Differential Equations I


Prerequisites:  MATH 3331, or equivalent, and three additional hours of 30004000 level Mathematics. 
Text(s):  TBA 
Description: 
Initial and boundary value problems, waves and diffusions, reflections, boundary values, Fourier series. 
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Math 4351  Calculus on Manifolds


Prerequisites:  MATH 2415 and six additional hours of 30004000 level Mathematics. 
Text(s):  TBA 
Description: 
Differential forms in R^n (particularly R^2 and integration, the intrinsic theory of surfaces through differential forms, the GaussBonnet theorem, Stokes’ theorem, manifolds, Riemannian metric and curvature. Other topics at discretion of instructor. 
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Math 4362  Theory of Differential Equations an Nonlinear Dynamics


Prerequisites:  MATH 3331, or equivalent, and three additional hours of 30004000 level Mathematics. 
Text(s):  Nonlinear Dynamics and Chaos (2nd Ed.) by Strogatz. ISBN: 9780813349107 
Description: 
ODEs as models for systems in biology, physics, and elsewhere; existence and uniqueness of solutions; linear theory; stability of solutions; bifurcations in parameter space; applications to oscillators and classical mechanics. 
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Math 4364 (13420)  Introduction to 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, BrooksCole Publishers, ISBN:9780538733519 
Description: 
Catalog Description: Root finding, interpolation and approximation, numerical differentiation and integration, numerical linear algebra, numerical methods for differential equations. Instructor's 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 finitedifference approximation to a twopoints boundary value problem. This is an introductory course and will be a mix of mathematics and computing. 
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Math 4364 (20284) Introduction to 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, BrooksCole Publishers, ISBN:9780538733519 
Description: 
Catalog Description: Root finding, interpolation and approximation, numerical differentiation and integration, numerical linear algebra, numerical methods for differential equations. Instructor's 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 finitedifference approximation to a twopoints boundary value problem. This is an introductory course and will be a mix of mathematics and computing. 
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Math 4365  Numerical Methods for Differential Equations


Prerequisites:  MATH 3331, or equivalent, and three additional hours of 3000–4000 level Mathematics. 
Text(s):  TBA 
Description:  Numerical differentiation and integration, multistep and RungeKutta methods for ODEs, finite difference and finite element methods for PDEs, iterative methods for linear algebraic systems and eigenvalue computation. 
Math 4370  Mathematics for Physicists


Prerequisites:  MATH 2415, and MATH 3321 or MATH 3331 
Text(s):  TBD 
Description:  Vector calculus, tensor analysis, partial differential equations, boundary value problems, series solutions to differential equations, and special functions as applied to juniorsenior level physics courses. 
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Math 4377  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 proofbased course. It will cover Chapters 14 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. 
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Math 4378  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 0130084514; 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, CayleyHamilton Theorem, Inner Product spaces, GramSchmidt, Normal Operators (in finite dimensions), Unitary and Orthogonal operators, the Singular Value Decomposition, Bilinear and Quadratic forms, Special Relativity (optional), Jordan Canonical form. 
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Math 4380  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:  Arbitragefree pricing, stock price dynamics, callput parity, BlackScholes formula, hedging, pricing of European and American options. 
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Math 4389  Survey of Undergraduate Mathematics  
Prerequisites:  MATH 3330, MATH 3331, MATH 3333, and three hours of 4000level Mathematics. 
Text(s):  Instructor notes 
Description:  A review of some of the most important topics in the undergraduate mathematics curriculum. 
ONLINE GRADUATE COURSES
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MATH 5330  Abstract Algebra


Prerequisites:  Graduate standing. 
Text(s): 
Abstract Algebra , A First Course by Dan Saracino. Waveland Press, Inc. ISBN 0881336653 
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. 
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MATH 5332  Differential Equations


Prerequisites:  Graduate standing. MATH 5331. 
Text(s):  The text material is posted on Blackboard Learn, under "Content". 
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. 
MATH 5341  Mathematical Modeling


Prerequisites:  Graduate standing. Three semesters of calculus or consent of instructor. 
Text(s):  TBD 
Description: 
Proportionality and geometric similarity, empirical modeling with multiple regression, discrete dynamical systems, differential equations, simulation and optimization. Computing assignments require only common spreadsheet software and VBA programming. 
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MATH 5385  Statistics


Prerequisites:  Graduate standing 
Text(s):  Two semesters of calculus and one semester of linear algebra or consent of instructor. 
Description: 
Data collection and types of data, descriptive statistics, probability, estimation, model assessment, regression, analysis of categorical data, analysis of variance. Computing assignments using a prescribed software package (e.g., R or Matlab) will be given. Applies toward the Master of Arts in Mathematics degree; does not apply toward Master of Science in Mathematics or the Master of Science in Applied Mathematics degrees. 
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MATH 6303  Modern Algebra II


Prerequisites: 
Graduate standing. MATH 4333 or MATH 4378 Additional Prerequisites: students should be comfortable with basic measure theory, groups rings and fields, and pointset topology 
Text(s): 
No textbook is required. 
Description: 
Topics from the theory of groups, rings, fields, and modules. Additional Description: This is primarily a course about analysis on topological groups. The aim is to explain how many of the techniques from classical and harmonic analysis can be extended to the setting of locally compact groups (i.e. groups possessing a locally compact topology which is compatible with their algebraic structure). In the first part of the course we will review basic point set topology and introduce the concept of a topological group. The examples of padic numbers and the Adeles will be presented in detail, and we will also spend some time discussing SL_2(R). Next we will talk about characters on topological groups, Pontryagin duality, Haar measure, the Fourier transform, and the inversion formula. We will focus on developing details in specific groups (including those mentioned above), and applications to ergodic theory and to number theory will be discussed. 
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MATH 6308  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 proofbased course. It will cover Chapters 14 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. 
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MATH 6309  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 0130084514; 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. 
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MATH 6313  Introduction to Real Analysis II


Prerequisites:  Graduate standing and MATH 6312. 
Text(s):  Kenneth Davidson and Allan Donsig, “Real Analysis with Applications: Theory in Practice”, Springer, 2010; or (out of print) Kenneth Davidson and Allan Donsig, “Real Analysis with Real Applications”, Prentice Hall, 2001. 
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. 
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MATH 6321  Theory of Functions of a Real Variable


Prerequisites: 
Graduate standing. MATH 4332 or consent of instructor. Instructor's Prerequisite Notes: MATH 6320 
Text(s): 
Primary (Required): Real Analysis for Graduate Students, Richard F. Bass Supplementary (Recommended): Real Analysis: Modern Techniques and Their Applications, Gerald Folland (2nd edition); ISBN: 9780471317166. 
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 twosemester 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. 
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MATH 6361  Applicable Analysis


Prerequisites: 
Graduate standing. MATH 3334, MATH 3338 or MATH 3339, and MATH 4378. Students must be in the Statistics and Data Science, MS Program 
Text(s): 
Speak to the instructor for textbook information. 
Description: 
Solvability of finite dimensional, integral, differential, and operator equations, contraction mapping principle, theory of integration, Hilbert and Banach spaces, and calculus of variations. 
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MATH 6367  Optimization Theory


Prerequisites:  Graduate standing. MATH 4331 and MATH 4377. 
Text(s): 

Description: 
Constrained and unconstrained finite dimensional nonlinear programming, optimization and EulerLagrange equations, duality, and numerical methods. Optimization in Hilbert spaces and variational problems. EulerLagrange equations and theory of the second variation. Application to integral and differential equations. Additional Description: This course consists of two parts. The first part is concer ned with an introduction to Stochastic Linear Programming (SLP) and Dynamic Programming (DP). As far as DP is concerned, the course focuses on the theory and the appli cation of control problems for linear and nonlinear dynamic systems both in a deterministic and in a stochastic frame work. Applications aim at decision problems in finance. In the second part, we deal with continuoustime systems and optimal control problems in function space with em phasis on evolution equations. 
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MATH 6371  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. 
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MATH 6383  Probability Statistics


Prerequisites:  Graduate standing. MATH 3334, MATH 3338 and MATH 4378. 
Text(s): 
Recommended Text: John A. Rice : Mathematical Statistics and Data Analysis, 3rd editionBrooks / Cole, 2007. ISBN13: 9780534399429. Reference Texts: 
Description: 
Catalog Description: A survey of probability theory, probability models, and statistical inference. Includes basic probability theory, stochastic processes, parametric and nonparametric methods of statistics. 
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MATH 6397 (20344)  Math of Deep Learning


Prerequisites:  Graduate standing. Students attending this course are expected to have a solid background in linear algebra, undergraduate real analysis (MATH 43314332) and basic probability. 
Text(s): 
Reference texts:

Description: 
This is a course of mathematics exploring foundational and theorical concepts underlying the development and applications of intelligent systems and deep learning algorithms. The emphasis of the course will be theoretical aspects. The aim of the course is to provide the necessary background to start a graduate research project in this emerging area of investigation. 
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MATH 6397 (20393)  Bayesian Inverse Problems and Uncertainty Quantification


Prerequisites:  Graduate standing. Credit for or concurrent enrollment in MATH 4331 and MATH 4377/4378, or consent of instructor. Students are expected to have a good grounding in basic real analysis and linear algebra. Basic knowledge about optimization theory (MATH 6366/6367) and (deterministic) inverse problems is helpful but not required. 
Text(s): 
No particular textbook is required. The following lists several good references for various topics related to this course (which go far beyond the material covered in class). References for Bayesian (statistical) inverse problems and uncertainty quantification are: 
Description:  Course syllabus: https://www.math.uh.edu/~andreas/resources/material/2023SPmath6397syllabus.pdf 
MATH 6397 (20396)  Algebraic Topology


Prerequisites:  Graduate standing. A course in general topology, or consent of the instructor. 
Text(s): 

Description: 
The course will begin with reviewing the fundamental group, and will cover much of the second half of Munkres’ book (which contains many important and beautiful topics), with additions from other books such as Hatcher’s Algebraic topology. We emphasize the many striking applications. Special requests will be honored if possible. 
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MATH 7321  Functional Analysis


Prerequisites:  Graduate standing. MATH 7320 or instructor consent 
Text(s):  W. Rudin, Functional Analysis, 2nd edition, McGraw Hill, 1991 
Description:  Catalog Description: This course is part of a two semester sequence covering the main results in functional analysis, including Hilbert spaces, Banach spaces, and linear operators on these spaces. Instructor's Description: This is a continuation of what was discussed in 7320. The second semester will mostly be a more technical development of the theory of linear operators on Hilbert space and related subjects, including topics relevant in quantum theory, such as positivity and states. Some of the main topics covered include: Banach algebras and the Gelfand transform. C*algebras and the functional calculus for normal operators. The spectral theorem for normal operators. Trace, HilbertSchmidt, and Schatten classes. 
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Prerequisites:  Graduate standing. MATH 6320 
Text(s):  TBD 
Description:  Catalog Description: Ergodic theory, topological and symbolic dynamics, statistical properties, infinitedimensional dynamical systems, random dynamical systems, and themodynamic formalism. Instructor's Description: TBA 