2020  Spring Semester
(Disclaimer: Be advised that some information on this page may not be current due to course scheduling changes.
Please view either the UH Class Schedule page or your Class schedule in myUH for the most current/updated information.)
(NEW) University of Houston Textbook Adoption login:
Please use this link to Create your account and Submit your textbook information for your course. This login is specifically designed to allow faculty to submit their own textbook information (PDF Instructionsscreenshots).
GRADUATE COURSES  SPRING 2020
This schedule is subject to changes. Please contact the Course Instructor for confirmation.
Course  Class # 
Course Title

Course Day & Time  Rm #  Instructor 
Math 4309  15605  Mathematical Biology  MW, 1—2:30PM  SEC 104  R. Azevedo 
20638 
Graph Theory w/Applications  TuTh, 4—5:30PM 
CBB 118 
K. Josic 

Math 4323 
28786 
Data Science and Statistical Learning  MWF, 11AM—Noon  SEC 101  C. Poliak/W. Wang 
12497 
Introduction to Real Analysis II  TuTh, 8:30—10AM  F 162  B. Bodmann  
Math 4362  21796  Theory of Differential Equations and Nonlinear Dynamics  MWF, 10—11AM  AH 202  G. Jaramillo 
Math 4364  18290  Intro. to Numerical Analysis in Scientific Computing  MW, 4—5:30PM  CBB 124  T. Pan 
Math 4364  22419  Intro. to Numerical Analysis in Scientific Computing  Online  Online  J. Morgan 
Math 4365  16883  Numerical Methods for Differential Equations  TuTh, 11:30AM—1PM  SEC 202  J. He 
17674 
Advanced Linear Algebra I  TuTh, 10—11:30AM  F 154  G. Heier  
12498 
Advanced Linear Algebra II  TuTh, 10—11:30AM  SEC 105  A. Mamonov  
Math 4380  12499  A Mathematical Introduction to Options  MW, 1—2:30PM  SEC 203  I. Timofeyev 
Math 4389  12500  Survey of Undergraduate Mathematics  MWF, Noon—1PM  CBB 124  D. Blecher 
Math 4397  27738 
Mathematical Methods for Physics 
MW, 2:30—4PM 
SW 219 
L. Wood 
Course  Class #  Course Title  Course Day & Time  Instructor 
Math 5330  13701  Abstract Algebra  Arrange (online course)  K. Kaiser 
Math 5332  12513  Differential Equations  Arrange (online course)  G. Etgen 
Math 5344  22571  Introduction to Scientific Computing  Arrange (online course)  J. Morgan 
Math 5397  23376  Data Science and Mathematics  Arrange (online course)  S. Ji 
Math 5397  23377  Dynamical Systems  Arrange (online course)  A. Török 
Course 
Class #  Course Title  Course Day & Time  Rm #  Instructor 
Math 6303  12517  Modern Algebra II  TuTh, 11:30AM—1PM  AH 203  M. Kalantar 
Math 6308  17675  Advanced Linear Algebra I  TuTh 10—11:30AM  F 154  G. Heier 
Math 6309  13850  Advanced Linear Algebra II  TuTh, 10—11:30AM  SEC 105  A. Mamonov 
Math 6313  13848  Introduction to Real Analysis  TuTh, 8:30—10AM  F 162  B. Bodmann 
Math 6321  12532  Theory of Functions of a Real Variable  TuTh, 1—2:30PM  SW 423  W. Ott 
Math 6327  23390  Partial Differential Equations  TuTh, 4—5:30PM  SEC 202  G.Auchmuty 
Math 6361  13851  Applicable Analysis  TuTh, 2:30—4PM  CBB 124  A. Mamonov 
Math 6367  12533  Optimization Theory  MW, 2:30—4PM  S 202  R. Hoppe 
Math 6371  12534  Numerical Analysis  MW, 4—5:30PM  AH 7  M. Olshanskii 
Math 6374  23391  Numerical Partial Differential Equations  MW, 1—2:30PM  SW 221  Y. Kuznetsov 
Math 6378  30507  Basic Scientific Computing  MW, 4—5:30PM  AH 301  R. Sanders 
Math 6383  12535  Probability Statistics  MWF, Noon—1PM  AH 7  W. Fu 
Math 6385  20639  ContinuousTime Models in Finance  TuTh, 2:30—4PM  SEC 201  E. Kao 
Math 6395  23392  Number Theory  MWF, 11AM—Noon  SEC 104  A. Haynes 
Math 6397  23394  Selected Topics in Math  TBD  TBD  TBD 
Math 6397  23396  Quantum Computation Theory  TuTh, 11:30AM—1PM  SW 229  A. Vershynina 
Math 6397  28397  Mathematics of Machine Learning  MWF, 10—11AM  AH 2  D. Labate 
Math 7352  23397  Reimannian Geometry  MW, 1—2:30PM  SW 423  M. Ru 
Course 
Class #  Course Title  Course Day & Time  Rm #  Instructor 
Math 6359  23928  Applied Statistics & Multivariate Analysis  Fr, 1—3PM  CBB 214  C. Poliak 
Math 6373  23929  Deep Learning & Artificial Neural Networks  MW, 1—2:30PM  SEC 202  R. Azencott/W. Wang 
Math 6381  29756  Information Visualization  Fr, 3—5PM  CBB 214  D. Shastri 
Math 6387  23937  Biomedical Data Analysis & Computing  MW, 4—5:30PM  AH 15  W. Fu 
Math 6388  24083  Genome Data Analysis  MW, 2:30—4PM  SW 423  R.Meisel/W. Wang 
Math 6397  23898  Selected Topics in Mathematics  We, 5:30—8:30PM  SEC 103  L. Arregoces 
Course Details
SENIOR UNDERGRADUATE COURSES
Math 4309 (15605)  Mathematical Biology 

Prerequisites:  
Text(s):  A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by Sarah P. Otto and Troy Day; ISBN13:9780691123448 
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 4315 (20638)  Graph Theory w/Applications


Prerequisites:  Either MATH 3330 or MATH 3336 and three additional hours of 30004000 level Mathematics 
Text(s):  TBA 
Description: 
Introduction to basic concepts, results, methods, and applications of graph theory. Additional Description: How does information propagate between friends and acquaintances on social media? How do diseases spread, and when do epidemics start? How should we design power grids to avoid failures, and systems of roads to optimize traffic flow? These questions can be addressed using network theory . Students in the course will develop a sound knowledge of the basics of graph theory, as well as some of the computational tools used to address the questions above. Course topics include basic structural features of networks, generative models of networks, centrality, random graphs, clustering, and dynamical processes on graphs. 
<< back to top >>
Math 4323 (28786)  Data Science and Statistical Learning


Prerequisites:  MATH 3339 
Text(s):  TBA 
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. 
<< back to top >>
Math 4332 (12497)  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 4351 (TBD)  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 GaussBonnet 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 4362 (21796)  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. 
<< back to top >>
Math 4364 (18290) 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:  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. 
<< back to top >>
Math 4364 (22419) 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:  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. 
<< back to top >>
Math 4365 (16883)  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, multistep and RungeKutta 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 (17674)  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. 
<< back to top >>
Math 4378 (12498)  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. 
<< back to top >>
Math 4380 (12499)  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. 
<< back to top >>
Math 4389 (12500)  Survey of Undergraduate Mathematics  
Prerequisites:  MATH 3330, MATH 3331, MATH 3333, and three hours of 4000level Mathematics. 
Text(s):  Instructor will use his own notes 
Description:  A review of some of the most important topics in the undergraduate mathematics curriculum. 
<< back to top >>
<< back to top >>
ONLINE GRADUATE COURSES
<< back to top >>
MATH 5330 (13701)  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. 
<< back to top >>
MATH 5332 (12513)  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 5344 (22571)  Introduction to Scientific Computing w/Excel


Prerequisites:  Graduate standing and three semesters of Calculus.
MATH 2331, In depth knowledge of Math 3331 (Differential Equations) or Math 3321 (Engineering Mathematics) (see the description for more prerequisite details) 
Text(s):  Numerical Analysis (9th edition), by R.L. Burden and J.D. Faires, BrooksCole Publishers, 9780538733519 
Description: 
The students in this online section will be introduced to topics in scientific computing, including numerical solutions to nonlinear equations, numerical differentiation and integration, numerical solutions of systems of linear equations, least squares solutions and multiple regression, numerical solutions of nonlinear systems of equations, numerical optimization, numerical solutions to discrete dynamical systems, and numerical solutions to initial value problems and boundary value problems. Computations in this course will primarily be illustrated directly in an Excel spreadsheet, or via VBA programming, but students who prefer to do their computations using Matlab, Julia, Python or some other programming language are also welcome. For students who want to do their computing in Excel, there will be tutorials associated with the use of Excel, and programming in VBA. Students who decide to use Excel are expected to have access and basic familiarity with Excel, but they are not expected to know advanced spreadsheet functionality or have programming experience with VBA. Students will not be tested over Excel or VBA, and students using Matlab, Julia or Python will also receive some help materials. 
<< back to top >>
MATH 5397 (23376)  Data Science and Mathematics


Prerequisites: 
Graduate standing. Notice: This course belongs to the group IV. Applied Math,which meets the requirement for MA degree. Students must submit a general petition to count this course towards the Applied Math requirement for the MA degree. 
Text(s): 
Lecture Notes will be provided 
Description:  Instructor's Course description: In this course, we introduce basics for data science with their mathematical proofs or details. The purpose of this course is to allow the students for further study or research in this area, or have basic skills to work in industry, or able to organize extracurricular activities (on data science) in high schools. The course will have the following sections:

<< back to top >>
MATH 5397 (23377)  Dynamical Systems


Prerequisites: 
Graduate standing. Three semesters of Calculus or consent of instructor. Basic knowledge of ODE's is helpful, but not required. Notice: This course belongs to the group IV. Applied Math,which meets the requirement for MA degree. Students must submit a general petition to count this course towards the Applied Math requirement for the MA degree. 
Text(s): 
Steven H. Strogatz: Nonlinear Dynamics and Chaos (with Applications to Physics, Biology, Chemistry, and Engineering) Second Edition, 2014. Print ISBN: 9780813349107 
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), onedimensional ODE's and their bifurcations; twodimensional ODE's (linear case, limit cycles and the PoincareBendixson 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 or Python code. 
<< back to top >>
GRADUATE COURSES
<< back to top >>
MATH 6303 (12517)  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. 
<< back to top >>
MATH 6308 (17675)  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. 
<< back to top >>
MATH 6308 (TBD)  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 (13850)  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. 
<< back to top >>
MATH 6313 (13848)  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. 
<< back to top >>
MATH 6321 (12532)  Theory of Functions of a Real Variable II


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. 
<< back to top >>
MATH 6327 (23390)  Partial Differential Equations


Prerequisites: 
Graduate standing. MATH 4331 
Text(s): 
There is no prescribed text and other texts that may be of interest include some material from E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol IIA, Springer, and chapter 7 of L. C. Evans, Partial Differential Equations, American Math.Society. Handouts for some background material will be provided. 
Description: 
Course Description: 
<< back to top >>
MATH 6359 (23928)  Applied Statistics and Multivariate 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: 
Linear models, loglinear models, hypothesis testing, sampling, modeling and testing of multivariate data, dimension reduction. 
<< back to top >>
MATH 6361 (13851)  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, WileyInterscience 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 >>
<< back to top >>
MATH 6367 (12533)  Optimization Theory


Prerequisites:  Graduate standing. MATH 4331 and MATH 4377. 
Text(s): 
 D.P. Bertsekas; Dynamic Programming and Optimal Con trol, Vol. I, 4th Edition. Athena Scientific, 2017, ISBN10: 1886529434  J.R. Birge and F.V. Louveaux; Introduction to Stochastic Programming. Springer, New York, 1997, ISBN: 038798217 
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. 
<< back to top >>
MATH 6371 (12534)  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 (23929)  Deep Learning and Artificial Neural Networks


Prerequisites:  Graduate standing. Probability/Statistic and linear algebra or consent of instructor. Students must be in the Statistics and Data Science, MS Program. 
Text(s): 
Speak to the instructor for textbook information. 
Description: 
Artificial neural networks for automatic classification and prediction. Training and testing of multilayers perceptrons. Basic Deep Learning methods. Applications to real data will be studied via multiple projects. 
<< back to top >>
MATH 6374 (23391)  Numerical Partial Differential Equations


Prerequisites:  Graduate standing. Instructor's prerequisite: Undergraduate courses on partial differential equations and numerical analysis 
Text(s): 
None 
Description: 
Upon completion of the course,students will be able to apply Finite Difference,Finite Volume and Finite Element methods for the numerical solution of elliptic and parabolic partial differential equations. 
<< back to top >>
MATH 6378 (30507)  Basic Scientific Computing


Prerequisites:  Graduate standing. 
Text(s): 
Speak to the instructor for textbook information. 
Description: 
Speak to the instructor for the course description. 
<< back to top >>
MATH 6381 (29756)  Information Visualization


Prerequisites:  Graduate standing. Students must be in the Statistics and Data Science, MS Program 
Text(s): 
Speak to the instructor for textbook information. 
Description: 
The course presents comprehensive introduction to information visualization and thus, provides the students with necessary background for visual representation and analytics of complex data. The course will cover topics on design strategies, techniques to display multidimensional information structures, and exploratory visualization tools. 
<< back to top >>
MATH 6383 (12535)  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. 
<< back to top >>
MATH 6385 (20639)  ContinuousTime Models in Finance


Prerequisites:  Graduate Standing. MATH 6384 
Text(s): 
Primary Text: The Heston Model and Its Extensions in Matlab and C#, by Fabrice Douglas Rouch, Wiley, 2013. Supplementary Text: Arbitrage Theory in Continuous Time, 3rd edition, by Tomas Bjork, Oxford University Press, 2009. 
Description: 
Stochastic calculus, Brownian motion, change of measures, Martingale representation theorem, pricing financial derivatives whose underlying assets are equities, foreign exchanges, and fixed income securities, singlefactor and multifactor HJM models, and models involving jump diffusion and mean reversion. Additional Description: The course is an introduction to continuoustime models in finance. We use the stochastic volatility model of Heston as the principal paradigm and choose Fourier transform and its variants as the tools for pricing. We introduce stochastic calculus, Brownian motion, Levy processes, change of measures, martingale ans semimartingale and the notion of time change of a stochastic process. We then apply these ideas in pricing financial derivatives whose underlying assets are equities, foreign exchanges, and fixed income securities. The use of MATLAB is expected. 
MATH 6387 (23937)  Biomedical Data Analysis and Computing


Prerequisites: 
Graduate standing. Linear algebra, probability, statistics, or consent of instructor. Students must be in the Statistics and Data Science, MS Program 
Text(s): 
Speak to the instructor for textbook information. 
Description: 
Longitudinal data and correlated data analysis, growthcurve models, mixed effects models, correlation structure, analysis of timetoevent data, hazard and survival functions, KaplanMeier estimate, logrank test. 
<< back to top >>
MATH 6388 (24083)  Genome Data Analysis


Prerequisites: 
Graduate standing. Linear algebra, probability, statistics, or consent of instructor. Students must be in the Statistics and Data Science, MS Program 
Text(s): 
Speak to the instructor for textbook information. 
Description: 
Estimation of allele frequency, HardyWeinberg equilibrium, testing on differentially expressed genes, multiple comparison. 
<< back to top >>
MATH 6395 (23392)  Number Theory


Prerequisites: 
Graduate standing. 
Text(s):  Speak to the instructor for textbook information. 
Description: 
TBA 
<< back to top >>
MATH 6397 (23394)  TBD


Prerequisites: 
Graduate standing. 
Text(s):  TBD 
Description: 
TBD 
<< back to top >>
MATH 6397 (23396)  Quantum Computation Theory


Prerequisites:  Graduate standing. Instructor's Prerequisites: Linear Algebra, Basics of Probability, Basics of Functional Analysis. It will not be expected that you know any quantum mechanics, computer science, of information theory. 
Text(s): 
 Lecture notes will be provided to you every class. You do not need to purchase either of these books. I can recommend any additional books if you request it, which you may borrow from my office. 
Description: 
Course Overview: During the course we aim to cover the following topics: 
<< back to top >>
MATH 6397 (23898)  Selected Topics in Math


Prerequisites: 
Graduate standing. Students must be in the Statistics and Data Science, MS Program 
Text(s): 
TBA 
Description:  Case Studies in Data Analysis: Apply multiple techniques for exploratory data analysis, visualize and understand the data using Inferential Statics, Descriptive Statistics, and probability Distributions. 
<< back to top >>
MATH 6397 (28397)  Mathematics of Machine Learning


Prerequisites:  Graduate standing. Instructor's Prerequisite: Students attending this course are expected to have a solid background in linear algebra, undergraduate real analysis (MATH 43314332) and basic probability. 
Text(s):   There is no official textbook.  I will select material from: "Support Vector Machines", by Ingo Steinwart and Andreas Christmann, Springer 2008; "Learning Theory: An Approximation Theory Viewpoint" by F Cucker and D. Zhou, Cambrigde 2007; "Learning with Kernels", by B Schlkopf and A. Smola, The MIT Pres 2001  Notes and reference papers will be provided by the instructor. 
Description: 
Machine Learning refers to a set of methods designed to extract information from data with the goal to make predictions or perform various types of decisions. This area has witnessed a remarkable growth during the last decade as machine learning is central to the development of intelligent systems and the analysis of massive and complex data found in science or social media. Machine learning algorithms currently enable systems such as Siri, the Google self driving car, or PathAI for medical diagnostics. 
<< back to top >>
MATH 7352 (23397)  Riemannian Geometry


Prerequisites:  Graduate standing. 
Text(s):  Differential Geometry and Topology: With a View to Dynamical Systems" by Keith Burns and Marian Gidea. (CRC Press, 2005). ISBN: 9781584882534 
Description: 
Course Description: Differentiable Manifolds, tangent space, tangent bundle, vector bundle, Riemannian metric, connections, curvature, completeness geodesics, Jacobi fields, spaces of constant curvature, and comparison theorems. Additional Description: This course is an introduction to the theory of smooth manifolds, with an emphasis on their geometry. The first third of the course will cover the basic definitions and examples of smooth manifolds, smooth maps, tangent spaces, and vector fields. Later in the semester we will use Euclidean, spherical, and hyperbolic geometry to introduce the notion of a Riemannian metric; we will study parallel transport, geodesics, the exponential map, and curvature. Other topics will include Lie theory and differential forms, including exterior differentiation and Stokes theorem. 