2021  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 2021
This schedule is subject to changes. Please contact the Course Instructor for confirmation.
UNDER CONSTRUCTION
Course  Class # 
Course Title

Course Day & Time  Rm #  Instructor 
Math 4309  17880  Mathematical Biology  MWF, Noon—1PM  Online  J. Winkle 
27551 
Introduction to Data Science and Machine Learning  TuTh, 11:30AM—1PM 
Online 
C. Poliak 

Math 4323 
24854 
Data Science and Statistical Learning  MW, 1—2:30PM  Online  W. Wang 
15104 
Introduction to Real Analysis II  MWF, 11AM—Noon  Online  A. Vershynina  
Math 4351  27576  Differential Geometry II  MW, 1—2:30PM  Online  M. Ru 
Math 4355  27716  Mathematics of Signal Representation  TuTh, 10—11:30AM  Online  D. Labate 
Math 4362  23243  Theory of Differential Equations and Nonlinear Dynamics  Online  Online  V. Climenhaga 
Math 4364  23243  Intro. to Numerical Analysis in Scientific Computing  MW, 4—5:30PM  Online  T. Pan 
Math 4365  19020  Numerical Methods for Differential Equations  TuTh, 11:30AM—1PM  Online  J. He 
19679/19680 
Advanced Linear Algebra I  MWF, 9—10AM  Online  L. Cappanera  
15105/16332 
Advanced Linear Algebra II  MWF, Noon—1PM  Online  A. Mamonov  
Math 4380  15106  A Mathematical Introduction to Options  TuTh, 2:30—4PM  Online  E. Kao 
Math 4389  15107  Survey of Undergraduate Mathematics  MW, 1—2:30PM  Online  M. Almus 
Math 4397  28354 
Mathematical Methods for Physics 
MW, 2:30—4PM 
Online  L. Wood 
Course  Class #  Course Title  Course Day & Time  Instructor 
Math 5330  16204  Abstract Algebra  Arrange (online course)  K. Kaiser 
Math 5332  5332  Differential Equations  Arrange (online course)  G. Etgen 
Math 5350  27370  Intro To Differential Geometry  Arrange (online course)  M. Ru 
Math 5385  27667  Statistics  Arrange (online course)  M. Jun 
Math 5386  27168  Regression & Linear Models  Arrange (online course)  J. Morgan 
Math 5397  27369  Data Science and Mathematics  Arrange (online course)  S. Ji 
Course 
Class #  Course Title  Course Day & Time  Rm #  Instructor 
Math 6303  15122  Modern Algebra II  Online  Online  G. Heier 
Math 6308  19680  Advanced Linear Algebra I  MWF, 9—10AM  Online  L. Cappanera 
Math 6309  16332  Advanced Linear Algebra II  MWF, Noon1PM  Online  A. Mamonov 
Math 6313  16331  Introduction to Real Analysis  MWF, 11AM—Noon  Online  A. Vershynina 
Math 6321  15137  Theory of Functions of a Real Variable  MWF, 11AM—Noon  Online  D. Blecher 
Math 6367  15138  Optimization Theory  MWF, 10—11AM  Online  R. Hoppe 
Math 6371  15139  Numerical Analysis  Online  Online  A. Quaini 
Math 6383  15140  Probability Statistics  TuTh, 10—11:30AM  Online  W. Fu 
Math 6397  27373  Pattern Recognition  TuTh, 10—11:30AM  Online  K. Josic 
Math 6397  27452  Linear Algebra and L from Data  W, 5:30—8:30PM  Online  M. Olshanskii 
Math 6397  27721  Mathematics of Data Science  TuTh, 2:30—4PM  Online  D. Labate 
Math 6397  31150  Differential Geometry  Online  Online  M. Ru 
Math 7321  27374  Functional Analysis  TuTh, 1—2:30PM  Online  M. Kalantar 
Course 
Class #  Course Title  Course Day & Time  Rm #  Instructor 
Math 6359  24286  Applied Statistics & Multivariate Analysis  F, 1—3PM  Hyflex  C. Poliak 
Math 6359  27727  Applied Statistics & Multivariate Analysis  F, 1—3PM  Hyflex  C. Poliak 
Math 6373  24287  Deep Learning and Artificial Neural Networks  MW, 1—2:30PM  Online  R. Azencott 
Math 6381  25006  Information Visualization  F, 3—5PM  Online  D. Shastri 
Math 6397  27650  Case Studies in Data Analysis  MW, 2:30—4PM  Online  L. Arregoces 
Math 6397  27653  Topics in Data Science  MW, 2:30—4PM  Online  C. Poliak 
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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Math 4322  Introduction to Data Science and Machine Learning


Prerequisites:  TBA 
Text(s):  TBA 
Description: 
TBA Additional Description: TBA 
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Math 4323  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. 
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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 4351  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). 
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Math 4355  Mathematics of Signal Representation


Prerequisites:  TBA 
Text(s):  TBA 
Description: 
TBA 
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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  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. 
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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):  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. 
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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 will use his own notes 
Description:  A review of some of the most important topics in the undergraduate mathematics curriculum. 
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Math 4397  Selected Topics in Mathematics  
Prerequisites:  Catalog Prerequisite: MATH 3333 or approval of the instructor. 
Text(s):  TBA 
Description: 
TBA 
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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 5350  Intro To Differential Geometry


Prerequisites:  Graduate standing 
Text(s):  TBA 
Description: 
TBA 
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MATH 5385  Statistics


Prerequisites:  Graduate standing 
Text(s):  TBA 
Description: 
TBA 
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MATH 5386  Regression & Linear Models


Prerequisites:  Graduate standing. Math 5385 (introductory Statistics or an equivalent course), one semester of linear algebra at or above the undergraduate level, and two semesters of calculus. 
Text(s): 
Required Text: Introduction to Linear Regression Analysis, 5th Edition, by Montgomery, Peck and Vining, Wiley 2012. Additional Required Resources: In addition to the textbook, students need a computer with a highspeed internet connection, and the opensource software package R, and R Studio. R Studio can be downloaded free from www.rproject.org . To download it, go to the web site, click on the download link, select your platform (Windows, Mac etc.), select a CRAN (Comprehensive R Archive Network) mirror site in the U.S. and follow the instructions. Downloading and installation are straightforward. RStudio facilitates importing and exporting of data and text files, and makes it easy to integrate R with other applications. It is available at www.rstudio.com , and can be installed after R is installed. 
Description: 
Course Content: Course Site: This course will be hosted on Space (https://space.uh.edu). You will be able to go to this site and access the course beginning January 15, 2021. Resources for Online Learning: The University of Houston is committed to student success, and provides information to optimize the online learning experience through our website at https://uh.edu/poweron. Please visit this website for a comprehensive set of resources, tools, and tips including: obtaining access to the internet and AccessUH, requesting a laptop through the Laptop Loaner Program, using your smartphone as a webcam; and downloading Microsoft Office 365 at no cost. For questions or assistance contact UHOnline@uh.edu. 
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MATH 5397  Data Science and Mathematics


Prerequisites: 
Graduate standing. Note that for a student in the MA program, this course is counted toward the MA degree in the group III "Probability and Statistics" or in the group IV: "Applied Mathematics". 
Text(s): 
No required textbook. Notes will be provided. Online video course: 10:00—11:00 am, Saturday and Sunday by Microsoft Teams. Videos are posted in Microsoft Stream. 
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 allow the students to take higher level courses in data science, or have basic skills to work in industry, or to lay down background to teach related courses, or to organize extracurricular activities in high schools. The course will have the following sections:

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MATH 5397  TBD


Prerequisites: 
Graduate standing. 
Text(s): 
TBD 
Description: 
TBD 
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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 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. 
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MATH 6359 (24286) & (27727)  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. 
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MATH 6367  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. 
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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 6373  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. 
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MATH 6381 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. 
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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 (27373)  Pattern Recognition Machine Learning, Dynamical Systems, and Control


Prerequisites: 
Graduate standing. Instructor prerequisite: Students attending this course are expected to have a solid background in linear algebra, undergraduate real analysis and basic probability. This is class is targeted to graduate students interested in gaining experience in learning modern data analysis techniques, and how to implement them. While neural networks will be mentioned, they will not be the focus of the course. 
Text(s):  Text will be taken from several sources:

Description: 
This is a practical introduction to the mathematical methods that are making the current revolution in datadriven science possible. We will cover select topics in dimensionality reduction, machine learning, dynamics, and control. The emphasis will be on implementing the different methods in Python, following the examples provided in the references. Grades will be primarily based on class participation and project completion. There will be no exams.

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MATH 6397 (27452)  Linear Algebra and L from Data


Prerequisites:  Graduate standing. 
Text(s):  The course is largely based on the 2019 book "Linear algebra and learning from data'' by G.Strang and correlates with the corresponding MIT course. 
Description: 
The course covers fundamental topics and essential tools of linear algebra required to understand and analyze big data. It also reviews basics of optimization for data analysis and corresponding linear algebra. Altogether this introduces a student to some mathematical fundamentals of data science and machine learning. Course Content: Main topics we plan to cover in the course include matrices, matrix factorizations, low rank approximations, SVD and principal components analysis, least square problems and regression, matrix low norm and low rank perturbations, Krylov methods, computing eigenvalues and singular values, interlacing eigenvalues and low rank signals, convexity and Newton method, constrained optimization, saddle point systems, accelerated gradient descent, nonlinear least squares, stochastic Gradient Descent, and some other topics. The class is given in the unsynchronized online mode: the video lectures are uploaded each week and a student has access to them throughout the semester. 
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MATH 6397 (27721)  Mathematics of Data Science: From signal processing to Convolutional Neural Networks


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/required textbook: Material will be selected from the several sources listed below: It includes material on the Curse of Dimensionality and various topics in machine learning. This classical treatise covers a broad range of topics in statistical learning theory and neural networks. 
Description: 
Course Objectives:

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MATH 6397 (27650)  Case Studies in Data Analysis


Prerequisites:  Graduate standing. 
Text(s):  TBA 
Description: 
Apply multiple techniques for exploratory data analysis, visualize and understand the data using Inferential Statics, Descriptive Statistics, and probability Distributions. 
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MATH 6397 (27653)  Topics in Data Science


Prerequisites:  Graduate standing. 
Text(s):  TBA 
Description: 
TBA 
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MATH 6397 (31150)  Differential Geometry


Prerequisites:  Graduate standing. 
Text(s):  Instructor's notes 
Description: 
he basic notions of differential geometry of curves and surfaces in R^3 will be reviewed. Then several selected topics will be covered, including: Connections, holonomy and the GaussBonnet theorem, surface theory with differential forms, calculus of variations and minimal surfaces, introduction to hyperbolic geometry, and abstract surfaces (2D Riemannian manifolds). It will be offered combined with Math. 4351 through asynchronous online 
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MATH 7321  Functional Analysis


Prerequisites:  Graduate standing. 
Text(s):  TBA 
Description: 
TBA 