2024  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.)
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GRADUATE COURSES  SPRING 2024
This schedule is subject to changes. Please contact the Course Instructor for confirmation.
(UNDER CONSTRUCTION  1/16/24)
Course 
Section 
Course Title 
Course Day/Time 
Rm # 
Instructor 
Math 4309  12220  Mathematical Biology  MW, 2:30—4PM, (F2F)  S 101  R. Azevedo 
Math 4322  15443  Introduction to Data Science and Machine Learning  TTh, 11:30AM—1PM, (F2F)  SEC 102  C. Poliak 
Math 4323  14927  Data Science and Statistical Learning  MWF, 10—11AM, (F2F)  SEC 103  W. Wang 
Math 4332/6313  11140  Introduction to Real Analysis II  TTh, 8:30—10AM, (F2F)  S 207  B. Bodmann 
Math 4351  19769  Calculus on Manifolds  TTh, 2:30—4PM, (F2F)  F 162  Y. Wu 
Math 4362  14344  Theory of Differential Equations and Nonlinear Dynamics  MWF, 9—10AM, (F2F)  SEC 201  G. Jaramillo 
Math 436401  13069  Intro. to Numerical Analysis in Scientific Computing  MW, 4—5:30PM, (F2F)  SEC 105  T.W. Pan 
Math 436402  17730  Intro. to Numerical Analysis in Scientific Computing  Asynch./oncampus exams  Online  J. Morgan 
Math 4365  12608  Numerical Methods for Differential Equations  TTh, 10—11:30AM, (F2F)  SW 219  Min Wang 
Math 4370  N/A  Mathematics for Physicists  cancelled  N/A  N/A  N/A 
Math 4377/6308  12846  Advanced Linear Algebra I  TTh, 11:30AM—1PM, (F2F)  S 102  A. Quaini 
Math 4378/6309  11141  Advanced Linear Algebra II  TTh, 11:30AM—1PM, (F2F)  CBB 106  A. Mamonov 
Math 4380  11142  A Mathematical Introduction to Options  MW, 1—2:30PM, (F2F)  AH 301  M. Papadakis 
Math 4389  11143  Survey of Undergraduate Mathematics  TTh, 1—2:30PM, (F2F)  F 154  D. Blecher 
Course 
Section 
Course Title 
Course Day & Time 
Instructor 
Math 5330  11601  Abstract Algebra 
(Asynch./oncampus exams)  A. Haynes 
Math 5332  11150  Differential Equations 
(Asynch./oncampus exams)  G. Etgen 
Math 5334  19701  Complex Analysis  (Asynch./oncampus exams)  S. Ji 
Math 5344  19702  Intro. to Scientific Computing  (Asynch./oncampus exams)  J. Morgan 
Math 5350  19703  Intro. to Differential Geometry  (Asynch./oncampus exams)  M. Ru 
Math 5385  15455  Statistics  (Asynch./oncampus exams)  TBD 
Course 
Section 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 6303  11151  Modern Algebra II  TTh, 1—2:30PM  S 101  M. Kalantar 
Math 6308  12847  Advanced Linear Algebra I  TTh, 11:30AM—1PM  S 102  A. Quaini 
Math 6309  11643  Advanced Linear Algebra II  TTh 11:30AM—1PM  CBB 106  A. Mamonov 
Math 6313  11642  Introduction to Real Analysis  TTh, 10—11:30AM  F 162  B. Bodmann 
Math 6321  11156  Theory of Functions of a Real Variable  MWF, 9—10AM  S 101  V. Climenhaga 
Math 6361  20465  Applicable Analysis  TTh, 1—2:30PM  S 119  D. Onofrei 
Math 6367  19704  Optimization Theory  TTh, 11:30AM—1PM  SEC 201  J. He 
Math 6371  11157  Numerical Analysis  TTh, 10—11:30AM  S 102  L. Cappanera 
Math 6377  19705  Mathematics of Machine Learning  TTh 1—2:30PM  AH 301  R. Azencott 
Math 6383  11158  Statistics  MW, 4—5:30PM  S 102  M. Jun 
Math 6397  19706  Computation & Math Methods in Data Science  MW, 4—5:30PM  F 162  A. Mang 
Math 6397  19707  Applied & Computational Topology  TTh, 2:30—4PM  S 202  W. Ott 
Math 6397  19708  Quantum Information and Computation  MWF, 11AM—Noon  F 154  A. Vershynina 
Math 6397  19709  Stochastic Process  MW, 1—2:30PM  S 202  I. Timofeyev 
Math 6397  25618  Image Processing Methods  MWF, 10—11AM  AH 204  N. Charon 
Math 7321  18187  Functional Analysis  TBD  TBD  TBD 
Math 7326  17738  Dynamical Systems  MWF, 11AM—Noon  S 101  M. Nicol 
Math 7352  25834  Riemannian Geometry  TBD  TBD  TBD 
Course 
Section 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 6315  14773  Masters Tutorial: Internship  TBD  N/A  C. Poliak 
Math 6359  14771  Applied Statistics & Multivariate Analysis  F, 1—3PM  CBB 104  C. Poliak 
Math 6359  15462  Applied Statistics & Multivariate Analysis  F, 1—3PM (synch. online)  N/A  C. Poliak 
Math 6373  14772  Deep Learning and Artificial Neural Networks  MW, 1—2:30PM (F2F)  F 162  D. Labate 
Math 6381  14970  Information Visualization  F, 3—5PM  CBB 104  D. Shastri 
Math 6381  17066  Information Visualization  F, 3—5PM (synch. online)  N/A  D. Shastri 
Math 6397  19750  Case Studies In Data Analysis  W, 5:30—8:30PM  S 202  L. Arregoces 
Math 6397  19739/20173  Bayesian Statistics  MW, 2:30—4PM  SEC 202  Y.Niu 
Math 6397  20174  Financial & Commodity Markets  W, 5:30—8:30PM  AH 301  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 4332/6313  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 (13069)  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): 
Instructor's notes 
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 (17730) 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 4377/6308  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 4378/6309  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. 
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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: 
Firstorder equations, existence and uniqueness theory; second and higher order linear equations; Laplace transforms; systems of linear equations; series solutions. Theory and applications emphasized throughout. 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. 
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Prerequisites:  Graduate standing. MATH 5333 or consent of instructor. 
Text(s):  TBA 
Description: 
Complex numbers, holomorphic functions, linear transformations, Cauchy integral theorem and residue theorem 
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Prerequisites:  Graduate standing. Math 2331 linear algebra or equivalent. 
Text(s):  Instructor's notes 
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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Prerequisites:  Graduate standing. MATH 2433, or consent of instructor. 
Text(s):  TBA 
Description: 
Curves, arclength, curvature, Frenet formula, surfaces, first and second fundamental forms, Guass’ theorem egregium, geodesics, minimal surfaces. Does not apply toward the Master of Science in Mathematics or Applied Mathematics. 
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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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): 
While lecture notes will serve as the main source of material for the course, the following book constitutes a great reference:  ”Statistics and Data Analysis from Elementary to Intermediate” by Tamhane, Ajit and Dunlop, Dorothy ISBN: 0137444265 
Description: 
Linear models, loglinear models, hypothesis testing, sampling, modeling and testing of multivariate data, dimension reduction. < Course syllabus > 
MATH 6361  Applicable Analysis


Prerequisites: 
Graduate standing. 
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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Prerequisites:  Graduate standing. Probability/Statistic and linear algebra or consent of instructor. Students must be in Master’s in Statistics and Data Science program. 
Text(s):  TBA 
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. 
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Prerequisites:  Graduate standing.Linear Algebra, Real Analysis (MATH 43314332), Probability. 
Text(s):  TBA Please contact the instructor 
Descriptions: 
Catalog Description: (this description is currently not accurate. Please use the instructor's description below) Instructor's Description (contents of this course have been modified since last year): Lectures F2F & online via Microsoft Teams. Focus on understanding key algorithms for Automatic Learning . Emphasis on mathematical concepts but not on proving theorems. Applications of Machine Learning techniques to real data sets, through homeworks projects. Instructor's Prerequisites: Basic linear algebra, probability, statistics (all at undergraduate level). 
Prerequisites:  Graduate standing. MATH 6320 or consent of instructor. 
Text(s):  TBA 
Description:  Random variables, conditional expectation, weak and strong laws of large numbers, central limit theorem, Kolmogorov extension theorem, martingales, separable processes, and Brownian motion. 
MATH 6383  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 (19706)  Computation & Math Methods in Data Science


Prerequisites:  Graduate standing. TBA 
Text(s): 
TBA 
Instructor's Description: 
TBA 
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MATH 6397 (19707)  Applied & Computational Topology


Prerequisites:  Graduate standing. TBA 
Text(s): 
TBA 
Instructor's Description:  TBA 
MATH 6397 (19708)  Quantum Information and Computation


Prerequisites:  Graduate standing. 
Text(s): 
Recommended:  M.Nielsen, I.Chuang, "Quantum computation and quantum information", Cambridge university press, 2010 
Description: 
During the course we will cover the basics of quantum mechanics (qubits, gates, channels), universal quantum computation, quantum teleportation and other protocols, basics of quantum errorcorrection, and quantum algorithms (Shor's algorithm, Grover's algorithm). We will practice some of the protocols on the open access quantum computer chip made available online. No knowledge of quantum mechanics, computer science or information theory is needed. Knowledge of linear algebra and the basics of probability and complex numbers are required 
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Prerequisites:  Graduate standing. Graduate Probability 
Text(s):  The main book for the class – “Stochastic Methods A Handbook for the Natural and Social Sciences” by C. Gardiner 
Description: 
This class will cover ContinuousTime Markov Chains (first half) and Brownian Motion/Stochastic Differential Equations (second half). The first half is more relevant to math biology and application of queueing theory, the second half is also relevant for mathematical finance. We will consider math bio applications in the first half and financial applications in the second half. 
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Prerequisites:  Graduate standing. TBA 
Text(s):  TBA 
Description: 
TBA 
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Prerequisites:  Graduate standing. TBA 
Text(s):  TBA 
Description: 
TBA 
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Prerequisites:  Graduate standing. TBA 
Text(s):  TBA 
Description: 
TBA 
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Prerequisites:  Graduate standing. TBA  
Text(s):  TBA 
Description: 
TBA 
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MATH 7321  Functional Analysis TBD


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 