Fall 2020
(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: UH plans to deliver classes this fall in the following three instructional modes:
Hyflex: courses have a safe number of students facetoface in a socially distanced classroom, with lectures being livestreamed to allow additional students to participate in the class remotely. Lectures are also recorded for viewing by students online later if necessary, with additional course materials posted online that can be accessed anytime. These courses are displayed with a Meeting Time in the class schedule.
Synchronous Online: courses have NO FacetoFace classes but do meet at a particular day and time in a virtual classroom. All course materials are available online and virtual lectures may be recorded to provide additional flexibility for students to view them later. These courses are displayed as “Online” with a Meeting Time in the class schedule.
Asynchronous Online: courses have NO FacetoFace classes or virtual meeting times. All course materials are available online anytime. These courses are displayed as “Online” with NO Meeting Time in the schedule.
GRADUATE COURSES  FALL 2020
Course  Section  Course Title  Course Day & Time  Rm #  Instructor 
Math 4310  19894  Biostatistics  Online  Online  A. Török 
Math 4320  13147  Intro to Stochastic Processes  TuTh, 2:30—4PM  Online  Online  W. Ott 
Math 4322  20046  Introduction to Data Science and Machine Learning  TuTh, 11:30AM—1PM  Online  Online  C. Poliak 
Math 4323  26382  Data Science and Statistical Learning  MWF, Noon—1PM  Online  Online  W. Wang 
Math 4331  15671  Introduction to Real Analysis I  MWF, 11AM—Noon  Online  Online  A. Vershynina 
Math 4335  17727  Partial Differential Equations I  Online  Online  W. Fitzgibbon/J. Morgan 
Math 4339  20275  Multivariate Statistics  TuTh, 1—2:30PM  Online  Online  C. Poliak 
Math 4350  21332  Differential Geometry I  MW, 1—2:30PM  Online  Online  M. Ru 
Math 4364  16353  Introduction to Numerical Analysis in Scientific Computing 
MW, 4—5:30PM  Online  Online  TW. Pan 
Math 4364  21330  Introduction to Numerical Analysis in Scientific Computing 
Online  Online  Y. Kuznetsov 
Math 4366  17014  Numerical Linear Algebra  Online  Online  J. He 
Math 4377  15673  Advanced Linear Algebra I  MWF, Noon—1PM  Online  Online  A. Mamonov 
Math 4388  14603  History of Mathematics  Online  Online  S. Ji 
Math 4389  14031  Survey of Undergraduate Mathematics  MW, 1—2:30PM  Online  Online  M. Almus 
Math 4397  21953  Math Methods for Physics  MW, 2:30—4PM  Online  Online 
L. Wood 
Course  Section  Course Title  Course Day & Time  Instructor 
Math 5331  14246  Linear Algebra with Applications  Online  K. Kaiser 
Math 5333  14831  Analysis  Online  G. Etgen 
Math 5382  21959  Probability  Online  I. Timofeyev 
Math 5397  21333  Partial Differential Equations  Online  J. Morgan 
Course  Section  Course Title  Course Day & Time  Rm #  Instructor 
Math 6302  13148  Modern Algebra I  Online  Online  G. Heier 
Math 6308  15674  Advanced Linear Algebra I  MWF, Noon—1PM  Online  Online  A. Mamonov 
Math 6312  15672  Introduction to Real Analysis  MWF, 11AM—Noon  Online  Online  A. Vershynina 
Math 6320  13175  Theory of Functions of a Real Variable  MWF, 11AM—Noon  Online  Online  D. Blecher 
Math 6320  28138  Theory of Functions of a Real Variable  MWF, 11AM—Noon  Hyflex  SEC 204  D. Blecher 
Math 6322  21335  Func. Complex Variable  MWF, 10—11AM  Online  Online  S. Ji 
Math 6342  13176  Topology  MWF, 9—10AM  Online  Online  V. Climenhaga 
Math 6360  13736  Applicable Analysis  MWF, 9—10AM  Online  Online  G. Jaramillo 
Math 6366  13177  Optimization Theory  MWF, 10—11AM  Online  Online  A. Mang 
Math 6370  13178  Numerical Analysis  TuTh, 8:30—10AM Online  Online  A. Quaini 
Math 6382  17936  Probability and Statistics  TuTh, 10—11:30AM  Online  Online  M. Nicol 
Math 6384  17730  Discrete Time Model in Finance  TuTh, 2:30—4PM  Online  Online  E. Kao 
Math 6397  21336  Stochastic Models in Biology  MW, 2:30—4PM  Online  Online  K. Josic 
Math 6397  21337  Computational Inverse Problems  MW, 1—2:30PM  Online  Online  A. Mang 
Math 6397  21338  Statistical Computing  Online  Online  W. Fu 
Math 6397  21339  High Dimensional Measures & Geometry  TuTh, 10—11:30AM  Online  Online  B. Bodmann 
Math 6397  21960  Applied and Computational Probability  Online  Online  I. Timofeyev 
Math 6397  30076  Spatial Statistics  MW, 4—5:30PM  Online  Online  M. Jun 
Math 7320  21334  Functional Analysis  TuTh, 1—2:30PM  Online  Online  M. Kalantar 
MSDS Courses (MSDS Students Only)
Course  Section  Course Title  Course Day & Time  Rm #  Instructor 
Math 6350  19912  Statistical Learning and Data Mining  MW, 1—2:30PM  Online  Online  R. Azencott 
Math 6357  20271  Linear Models & Design of Experiments  MW, 4—5:30PM  Online  Online  W. Wang 
Math 6357  28141  Linear Models & Design of Experiments  MW, 4—5:30PM  Hyflex  SEC 201  W. Wang 
Math 6358  18147  Probability Models and Statistical Computing  Friday, 1—3PM  Online  Online  C. Poliak 
Math 6358  28142  Probability Models and Statistical Computing  Friday, 1—3PM  Hyflex  SEC 101  C. Poliak 
Math 6380  20633  Programming Foundation for Data Analytics  Friday, 3—5PM  Online  Online  D. Shastri 
Math 6397  TBD  Topics in Financial Machine Learning/Analytics in Commodity & Financial Markets  TBD  TBD  TBD 
SENIOR UNDERGRADUATE COURSES
Math 4310 Biostatistics: 19894 (Online)


Prerequisites:  MATH 3339 and BIOL 3306 
Text(s):  "Biostatistics: A Foundation for Analysis in the Health Sciences, Edition (TBD), by Wayne W. Daniel, Chad L. Cross. ISBN: (TBD) 
Description:  Statistics for biological and biomedical data, exploratory methods, generalized linear models, analysis of variance, crosssectional studies, and nonparametric methods. Students may not receive credit for both MATH 4310 and BIOL 4310. 
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Math 4320  Intro to Stochastic Processes


Prerequisites:  MATH 3338 
Text(s): 
An Introduction to Stochastic Modeling" by Mark Pinsky, Samuel Karlin. Academic Press, Fourth Edition. 
Description: 
We study the theory and applications of stochastic processes. Topics include discretetime and continuoustime Markov chains, Poisson process, branching process, Brownian motion. Considerable emphasis will be given to applications and examples. 
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Math 4322  Introduction to Data Science and Machine Learning


Prerequisites:  MATH 3339 
Text(s): 
While lecture notes will serve as the main source of material for the course, the following book constitutes a great reference: 
Description: 
Course will deal with theory and applications for such statistical learning techniques as linear and logistic regression, classification and regression trees, random forests, neural networks. Other topics might include: fit quality assessment, model validation, resampling methods. R Statistical programming will be used throughout the course. Learning Objectives: By the end of the course a successful student should: Supervised and unsupervised learning. Regression and classification. 
Math 4323  Introduction to Data Science and Machine 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 4331  Introduction to Real Analysis I


Prerequisites:  MATH 3333. In depth knowledge of Math 3325 and Math 3333 is required. 
Text(s):  Real Analysis, by N. L. Carothers; Cambridge University Press (2000), ISBN 9780521497565 
Description: 
This first course in the sequence Math 43314332 provides a solid introduction to deeper properties of the real numbers, continuous functions, differentiability and integration needed for advanced study in mathematics, science and engineering. It is assumed that the student is familiar with the material of Math 3333, including an introduction to the real numbers, basic properties of continuous and differentiable functions on the real line, and an ability to do epsilondelta proofs. Topics: Open and closed sets, compact and connected sets, convergence of sequences, Cauchy sequences and completeness, properties of continuous functions, fixed points and the contraction mapping principle, differentiation and integration. 
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Math 4335  Partial Differential Equations I


Prerequisites: 
MATH 3331 or equivalent, and three additional hours of 30004000 level Mathematics. Previous exposure to Partial Differential Equations (Math 3363) is recommended. 
Text(s): 
"Partial Differential Equations: An Introduction (second edition)," by Walter A. Strauss, published by Wiley, ISBN13 9780470054567 
Description: 
Description:Initial and boundary value problems, waves and diffusions, reflections, boundary values, Fourier series. Instructor's Description: will cover the first 6 chapters of the textbook. See the departmental course description. 
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Math 4339 (20275)  Multivariate Statistics


Prerequisites: 
MATH 3349 
Text(s): 
 Applied Multivariate Statistical Analysis (6th Edition), Pearson. Richard A. Johnson, Dean W. Wichern. ISBN: 9780131877153 (Required)  Using R With Multivariate Statistics (1st Edition). Schumacker, R. E. SAGE Publications. ISBN: 9781483377964 (recommended) 
Description: 
Course Description: Multivariate analysis is a set of techniques used for analysis of data sets that contain more than one variable, and the techniques are especially valuable when working with correlated variables. The techniques provide a method for information extraction, regression, or classification. This includes applications of data sets using statistical software. Course Objectives:
Course Topics:

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Math 4350 (21332)  Differential Geometry I


Prerequisites: 
MATH 2433 and six additional hours of 30004000 level Mathematics. 
Text(s):  Instructor's notes will be provided 
Description: 
Curves in the plane and in space, global properties of curves and surfaces in three dimensions, the first fundamental form, curvature of surfaces, Gaussian curvature and the Gaussian map, geodesics, minimal surfaces, Gauss’ Theorem Egregium, The Codazzi and Gauss Equations, Covariant Differentiation, Parallel Translation. 
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Math 4364 (16353)  Introduction to Numerical Analysis in Scientific Computing


Prerequisites: 
MATH 3331 and COSC 1410 or equivalent. (2017—2018 Catalog) MATH 3331 or MATH 3321 or equivalent, and three additional hours of 30004000 level Mathematics (2018—2019 Catalog) *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, 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 4364 (21330)  Introduction to Numerical Analysis in Scientific Computing


Prerequisites: 
MATH 3331 and COSC 1410 or equivalent. (2017—2018 Catalog) MATH 3331 or MATH 3321 or equivalent, and three additional hours of 30004000 level Mathematics (2018—2019 Catalog) *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, 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 4377 (15673)  Advanced Linear Algebra I


Prerequisites:  MATH 2331, or equivalent, and a minimum of three semester hours of 30004000 level Mathematics. 
Text(s):  Linear Algebra, 4th Edition, by S.H. Friedberg, A.J Insel, L.E. Spence,Prentice Hall, ISBN 0130084514 
Description: 
Catalog Description: Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors. Instructor's Description: The course covers the following topics: vector spaces, subspaces, linear combinations,systems of linear equations, linear dependence and linear independence, bases and dimension,linear transformations, null spaces, ranges, matrix rank, matrix inverse and invertibility,determinants and their properties, eigenvalues and eigenvectors, diagonalizability. 
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Math 4388  History of Mathematics


Prerequisites:  MATH 3333 
Text(s):  No textbook is required. Instructor notes will be provided 
Description:  This course is designed to provide a collegelevel experience in history of mathematics. Students will understand some critical historical mathematics events, such as creation of classical Greek mathematics, and development of calculus; recognize notable mathematicians and the impact of their discoveries, such as Fermat, Descartes, Newton and Leibniz, Euler and Gauss; understand the development of certain mathematical topics, such as Pythagoras theorem, the real number theory and calculus. Aims of the course: To help students to understand the history of mathematics; to attain an orientation in the history and philosophy of mathematics; to gain an appreciation for our ancestor's effort and great contribution; to gain an appreciation for the current state of mathematics; to obtain inspiration for mathematical education, and to obtain inspiration for further development of mathematics. Online course is taught through Blackboard Learn, visit http://www.uh.edu/webct/ for information on obtaining ID and password. The course will be based on my notes. Homework and Essays assignement are posted in Blackboard Learn. There are four submissions for homework and essays and each of them covers 10 lecture notes. The dates of submission will be announced. All homework and essays, handwriting or typed, should be turned into PDF files and be submitted through Blackboard Learn. Late homework is not acceptable. There is one final exam in multiple choice. Grading: 35% homework, 45% projects, 20 % Final exam. 
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Math 4389  Survey of Undergraduate Mathematics


Prerequisites:  MATH 3331, MATH 3333, and three hours of 4000level Mathematics. 
Text(s):  No textbook is required. Instructor notes will be provided 
Description:  A review of some of the most important topics in the undergraduate mathematics curriculum. 
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Math 4397 (21953)  Selected Topics in Mathematics


Prerequisites: 
Catalog Prerequisite: MATH 3333 or consent of instructor. 
Text(s): 

Description: 
Course Content:

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ONLINE GRADUATE COURSES
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MATH 5331 (14246)  Linear Algebra with Applications


Prerequisites: 
Graduate standing. 
Text(s): 
Linear Algebra Using MATLAB, Selected material from the text Linear Algebra and Differential Equations Using Matlab by Martin Golubitsky and Michael Dellnitz) 
Description: 
Software: Scientific Note Book (SNB) 5.5 (available through MacKichan Software, http://www.mackichan.com/) Syllabus: Chapter 1 (1.1, 1.3, 1.4), Chapter 2 (2.12.5), Chapter 3 (3.13.8), Chapter 4 (4.14.4), Chapter 5 (5.15.2, 5.456), Chapter 6 (6.16.4), Chapter 7 (7.17.4), Chapter 8 (8.1) Project: Applications of linear algebra to demographics. To be completed by the end of the semester as part of the final. Course Description: Solving Linear Systems of Equations, Linear Maps and Matrix Algebra, Determinants and Eigenvalues, Vector Spaces, Linear Maps, Orthogonality, Symmetric Matrices, Spectral Theorem Students will also learn how to use the computer algebra portion of SNB for completing the project. Homework: Weekly assignments to be emailed as SNB file. There will be two tests and a Final. Grading: Tests count for 90% (25+25+40), HW 10% 
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MATH 5333 (14831)  Analysis


Prerequisites:  Graduate standing and two semesters of Calculus. 
Text(s):  Analysis with an Introduction to Proof  Edition: 5, Steven R. Lay, 9780321747471 
Description:  A survey of the concepts of limit, continuity, differentiation and integration for functions of one variable and functions of several variables; selected applications. 
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MATH 5382 (21959)  Probability


Prerequisites:  Graduate Standing. Instructor's prerequisite: Calculus 3 (multidimensional integrals), very minimal background in Probability. 
Text(s): 
Sheldon Ross, A First Course in Probability (10th Edition) 
Description: 
This course is for students who would like to learn about Probability concepts; I’ll assume very minimal background in probability. Calculus 3 (multidimensional integrals) is the only prerequisite for this class. This class will emphasize practical aspects, such as analytical calculations related to conditional probability and computational aspects of probability. No measuretheoretical concepts will be covered in this class. This is class is intended for students who want to learn more practical concepts in probability. This class is particularly suitable for Master students and nonmath majors. 
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MATH 5397 (21333)  Partial Differential Equations


Prerequisites:  Graduate standing 
Text(s): 
Required Text: Walter A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons 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 on August 24, 2020. 
Description: 
Course Material: The primary goal of this course is to provide a conceptual introduction to the basic ideas encountered in partial differential equations, the techniques for analyzing these equations, and the ideas associated with the context of physical applications. The secondary goal is to expose students to Matlab methods for approximating the solutions to Partial Differential Equations. Students are not expected to have any previous experience with Matlab, and the software is free for all UH students. In addition to reading the text book, students will have access to weekly posted notes and videos associated with the course material. 
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GRADUATE COURSES
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MATH 6302 (13148)  Modern Algebra I


Prerequisites:  Graduate standing. 
Text(s): 
Required Text: Abstract Algebra by David S. Dummit and Richard M. Foote, ISBN: 9780471433347 This book is encyclopedic with good examples and it is one of the few books that includes material for all of the four main topics we will cover: groups, rings, field, and modules. While some students find it difficult to learn solely from this book, it does provide a nice resource to be used in parallel with class notes or other sources. 
Description:  We will cover basic concepts from the theories of groups, rings, fields, and modules. These topics form a basic foundation in Modern Algebra that every working mathematician should know. The Math 63026303 sequence also prepares students for the department’s Algebra Preliminary Exam. 
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MATH 6308 (15674) Advanced Linear Algebra I


Prerequisites: 
Catalog Prerequisite: Graduate standing, MATH 2331 and a minimum of 3 semester hours transformations, eigenvalues and eigenvectors. Instructor's Prerequisite: MATH 2331, or equivalent, and a minimum of three semester hours of 30004000 level Mathematics. 
Text(s):  Linear Algebra, Fourth Edition, by S.H. Friedberg, A.J Insel, L.E. Spence,Prentice Hall, ISBN 0130084514 
Description: 
Catalog Description: An expository paper or talk on a subject related to the course content is required. Instructor's Description: The course covers the following topics: vector spaces, subspaces, linear combinations,systems of linear equations, linear dependence and linear independence, bases and dimension,linear transformations, null spaces, ranges, matrix rank, matrix inverse and invertibility,determinants and their properties, eigenvalues and eigenvectors, diagonalizability. 
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MATH 6312 (15672)  Introduction to Real Analysis


Prerequisites: 
Graduate standing and MATH 3334. In depth knowledge of Math 3325 and Math 3333 is required. 
Text(s):  Real Analysis, by N. L. Carothers; Cambridge University Press (2000), ISBN 9780521497565 
Description: 
This first course in the sequence Math 43314332 provides a solid introduction to deeper properties of the real numbers, continuous functions, differentiability and integration needed for advanced study in mathematics, science and engineering. It is assumed that the student is familiar with the material of Math 3333, including an introduction to the real numbers, basic properties of continuous and differentiable functions on the real line, and an ability to do epsilondelta proofs. Topics: Open and closed sets, compact and connected sets, convergence of sequences, Cauchy sequences and completeness, properties of continuous functions, fixed points and the contraction mapping principle, differentiation and integration. 
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MATH 6320 Theory Functions of a Real Variable [Hyflex]: 13175 (Online) & 28138 (FacetoFace)


Prerequisites:  Graduate standing and Math 4332 (Introduction to real analysis). 
Text(s):  Real Analysis: Modern Techniques and Their Applications  Edition: 2, by: Gerald B. Folland, G. B. Folland. ISBN: 9780471317166 
Description:  Math 6320 / 6321 introduces students to modern real analysis. The core of the course will cover measure, Lebesgue integration, differentiation, absolute continuity, and L^p spaces. We will also study aspects of functional analysis, Radon measures, and Fourier analysis. 
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MATH 6322 (21335)  Func. Complex Variable


Prerequisites: 
Graduate Standing. Math 3333 or consent of instructor. 
Text(s): 
No textbook required. Lecture notes provided. 
Description: 
This course is an introduction to complex analysis. It will cover the theory of holomorphic functions, Cauchy theorem and Cauchy integral formula, residue theorem, harmonic and subharmonic functions, and other topics 
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MATH 6342 (13176)  Topology


Prerequisites:  Graduate standing and MATH 4331 and MATH 4337. 
Text(s): 
(Required) Topology, A First Course, J. R. Munkres, Second Edition, PrenticeHall Publishers. 
Description: 
Catalog Description: Pointset topology: compactness, connectedness, quotient spaces, separation properties, Tychonoff’s theorem, the Urysohn lemma, Tietze’s theorem, and the characterization of separable metric spaces Instructor's Description: Topology is a foundational pillar supporting the study of advanced mathematics. It is an elegant subject with deep links to algebra and analysis. We will study general topology as well as elements of algebraic topology (the fundamental group and homology theories). 
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MATH 6350 (19912)  Statistical Learning and Data Mining


Prerequisites:  Graduate Standing and must be in the MSDS Program. Undergraduate Courses in basic Linear Algebra and basic descriptive Statistics 
Text(s): 
Recommended text: Reading assignments will be a set of selected chapters extracted from the following reference text:

Description: 
Summary: A typical task of Machine Learning is to automatically classify observed "cases" or "individuals" into one of several "classes", on the basis of a fixed and possibly large number of features describing each "case". Machine Learning Algorithms (MLAs) implement computationally intensive algorithmic exploration of large set of observed cases. In supervised learning, adequate classification of cases is known for many training cases, and the MLA goal is to generate an accurate Automatic Classification of any new case. In unsupervised learning, no known classification of cases is provided, and the MLA goal is Automatic Clustering, which partitions the set of all cases into disjoint categories (discovered by the MLA). This MSDSfall 2019 course will successively study : 1) Quick Review (Linear Algebra) : multi dimensional vectors, scalar products, matrices, matrix eigenvectors and eigenvalues, matrix diagonalization, positive definite matrices 2) Dimension Reduction for Data Features : Principal Components Analysis (PCA) 3) Automatic Clustering of Data Sets by Kmeans algorithmics 3) Quick Reviev (Empirical Statistics) : Histograms, Quantiles, Means, Covariance Matrices 4) Computation of Data Features Discriminative Power 5) Automatic Classification by Support Vector Machines (SVMs) Emphasis will be on concrete algorithmic implementation and testing on actual data sets, as well as on understanding importants concepts.

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MATH 6357 Linear Models and Design of Experiments [Hyflex]: 20271 (Online) & 28141 (FacetoFace)


Prerequisites:  Graduate Standing and must be in the MSDS Program. MATH 2433, MATH 3338, MATH 3339, and MATH 6308 
Text(s): 
Required Text: ”Neural Networks with R” by G. Ciaburro. ISBN: 9781788397872 
Description:  Linear models with LS estimation, interpretation of parameters, inference, model diagnostics, oneway and twoway ANOVA models, completely randomized design and randomized complete block designs. 
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MATH 6358 Probability Models and Statistical Computing [Hyflex]: 18147 (Online) and 28142 (FacetoFace)


Prerequisites:  Graduate Standing and must be in the MSDS Program. MATH 3334, MATH 3338 and MATH 4378 
Text(s): 

Description: 
Course Description: Probability, independence, Markov property, Law of Large Numbers, major discrete and continuous distributions, joint distributions and conditional probability, models of convergence, and computational techniques based on the above. Topics Covered:
Software Used:

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MATH 6360 (13736)  Applicable Analysis


Prerequisites:  Graduate standing and MATH 4331 or equivalent. 
Text(s): 
J.K. Hunter and B. Nachtergaele, Applied Analysis, World Scientific, (2005). ISBN: 9789812705433 A.W. Naylor and G.R. Sell, Linear Operator Theory in Engineering and Science, Springer. ISBN: 9780387950013 
Description:  This course treats topics related to the solvability of various types of equations, and also of optimization and variational problems. The first half of the semester will concentrate on introductory material about norms, Banach and Hilbert spaces, etc. This will be used to obtain conditions for the solvability of linear equations, including the Fredholm alternative. The main focus will be on the theory for equations that typically arise in applications. In the second half of the course the contraction mapping theorem and its applications will be discussed. Also, topics to be covered may include finite dimensional implicit and inverse function theorems, and existence of solutions of initial value problems for ordinary differential equations and integral equations 
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MATH 6366 (13177)  Optimization Theory


Prerequisites: 
Graduate standing and MATH 4331 and MATH 4377 Students are expected to have a good grounding in basic real analysis and linear algebra. 
Text(s): 
"Convex Optimization", Stephen Boyd, Lieven Vandenberghe, Cambridge University Press, ISBN: 9780521833783 (This text is available online. Speak to the instructor for more details) 
Description:  The focus is on key topics in optimization that are connected through the themes of convexity, Lagrange multipliers, and duality. The aim is to develop a analytical treatment of finite dimensional constrained optimization, duality, and saddle point theory, using a few of unifying principles that can be easily visualized and readily understood. The course is divided into three parts that deal with convex analysis, optimality conditions and duality, computational techniques. In Part I, the mathematical theory of convex sets and functions is developed, which allows an intuitive, geometrical approach to the subject of duality and saddle point theory. This theory is developed in detail in Part II and in parallel with other convex optimization topics. In Part III, a comprehensive and uptodate description of the most effective algorithms is given along with convergence analysis. 
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MATH 6370  Numerical Analysis: 13178


Prerequisites:  Graduate standing. Students should have knowledge in Calculus and Linear Algebra. 
Text(s):  Numerical Mathematics (Texts in Applied Mathematics), 2nd Ed., V.37, Springer, 2010. By A. Quarteroni, R. Sacco, F. Saleri. ISBN: 9783642071010 
Description:  The course introduces to the methods of scientific computing and their application in analysis, linear algebra, approximation theory, optimization and differential equations. The purpose of the course to provide mathematical foundations of numerical methods, analyse their basic properties (stability, accuracy, computational complexity) and discuss performance of particular algorithms. This first part of the twosemester course spans over the following topics: (i) Principles of Numerical Mathematics (Numerical wellposedness, condition number of a problem, numerical stability, complexity); (ii) Direct methods for solving linear algebraic systems; (iii) Iterative methods for solving linear algebraic systems; (iv) numerical methods for solving eigenvalue problems; (v) nonlinear equations and systems, optimization. 
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MATH 6380 (20633)  Programming Foundation for Data Analytics


Prerequisites: 
Graduate Standing and must be in the MSDS Program. Instructor prerequisites: The course is essentially selfcontained. The necessary material from statistics and linear algebra is integrated into the course. Background in writing computer programs is preferred but not required. 
Text(s): 

Description: 
Instructor's Description: The course provides essential foundations of Python programming language for developing powerful and reusable data analysis models. The students will get handson training on writing programs to facilitate discoveries from data. The topics include data import/export, data types, control statements, functions, basic data processing, and data visualization. 
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MATH 6382 (17936)  Probability and Statistics


Prerequisites:  Graduate standing and MATH 3334, MATH 3338 and MATH 4378. 
Text(s): 
Recommended Texts : Review of Undergraduate Probability: Complementary Texts for further reading: 
Description: 
General Background (A). Measure theory (B). Markov chains and random walks (C). 
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MATH 6384 Discrete Time Models in Finance: 17730


Prerequisites:  Graduate standing and MATH 6382. 
Text(s): 
Introduction to Mathematical Finance: Discretetime Models, by Stanley Pliska, Blackwell, 1997. ISBN: 9781557869456 
Description:  The course is an introduction to discretetime models in finance. We start with singleperiod securities markets and discuss arbitrage, riskneutral probabilities, complete and incomplete markets. We survey consumption investment problems, meanvariance portfolio analysis, and equilibrium models. These ideas are then explored in multiperiod settings. Valuation of options, futures, and other derivatives on equities, currencies, commodities, and fixedincome securities will be covered under discretetime paradigms. 
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MATH 6397 (21336)  Stochastic Models in Biology


Prerequisites: 
Graduate standing. Instructor's prerequisite: Two semesters of calculus, undergraduate probability, some knowledge of differential equations and linear algebra 
Text(s): 
There is no required textbook, but the following will be useful as references:

Description: 
Instructor's description: In this course we will apply the theory of probability and stochastic processes to models of biological systems. Students taking the course should be comfortable with multivariate calculus, differential equations, linear algebra, as well as undergraduate level probability (I will not assume familiarity with measure theory). Computational component: Python There will be several computational challenges that will require the use of Python. There are numerous helpful tutorials to help you get started. I will also offer some suggestions in a separate note. Please use the Jupyter environment, as it makes the presentation a lot easier to follow. 
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MATH 6397 (TBD)  Topics in Financial Machine Learning/Analytics in Commodity & Financial Markets


Prerequisites: 
Graduate Standing and must be in the MSDS Program. 
Text(s): 
Much of the material is drawn from these works:

Description: 
This is an applied data analysis course focusing on financial and economic data. We will cover various kinds of analyses common in the field and, as much as possible, use multiple approaches to each case in order to demonstrate the strengths, weaknesses, and advantages of each technique. This is not intended to be a programming course. There are many examples done in R and you are welcome to use that language. If you are, or aspire to be a strong Python programmer, you are welcome to use that language also. Proficiency in basic probability and linear algebra is assumed. By the end of the course you may find your skills in those areas strengthened as well. The goals for the course are to familiarize students with common types of economic and financial data, some of the statistical properties of this kind of data which usually involves time series, and to equip everyone with a thorough enough understanding of the techniques available for them to make the best decision on the approach to take in an analysis depending on the nature of the data and the specific purpose of the study. 
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MATH 6397 (21337)  Computational Inverse Problems


Prerequisites:  Graduate standing. Instructor's prerequisite: Credit for or concurrent enrollment in MATH 4331 and MATH 4377/4378, or consent of instructor. Students are expected to have a good grounding in basic real analysis and linear algebra. Basic knowledge about optimization theory (MATH 6366/6367) is helpful but not required. 
Text(s): 
No particular textbook is required, but several good references for various topics related to inverse problems

Description: 
Instructor's Description: Inverse problems are paramount importance and can be found in virtually all scientific disciplines with applications ranging from medicine, geophysics, to engineering. In many of these applications the forward or simulation problem, i.e., the solution of an underlying mathematical model to yield outputs given some inputs, is already a challenging task. Many applications require us to go beyond evaluating forward operators; we have to address what is often the ultimate goal: prediction and decisionmaking. This requires us to tackle mathematical challenges that comprise, and, therefore, are more difficult than the forward problem. One example is the solution of inverse problems. Here, we seek model inputs (or parameters) so that the output of the forward model matches observational data. 
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MATH 6397 (21338)  Statistical Computing


Prerequisites:  Graduate standing. Instructor's prerequisite: Two years of Calculus, Math 2331 Linear Algebra, and undergraduate probability and statistics (concepts), or equivalent, or approval by instructor. 
Text(s):  Recommended books: Textbook: Maria Rizzo: Statistical Computing with R (Chapman & Hall/CRC The R Series) 2007. ISBN13: 9781584885450 ISBN10: 1584885459 Edition: 1st References:

Description:  This course is designed for graduate students who have been exposed to basic probability and statistics and would like to learn more advanced statistical computing techniques in modeling data. The selected topics will include basic sampling techniques from known probability distributions, Monte Carlo estimation and testing, bootstrapping, permutation methods for testing, shrinkage model and variable selection with the Lasso, Treebased methods and other statistical learning, such as the RandomForests, etc. The instructor reserves the right to exclude certain topics from the textbook and add other topics not covered in the textbook. 
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MATH 6397  High Dimensional Measures and Geometry: 21339


Prerequisites:  Graduate standing. Instructor's prerequisite: A course on Probability and a graduatelevel course on Analysis. 
Text(s): 
Texts (recomm.): The materials will be collected from the following recommended monographs.
Topics papers:

Description:  This course covers many aspects of the phenomenon that functions of small oscillation become nearly constant in highdimensional spaces. This principle, developed by Milman for Banach spaces, has applications in geometry, probability and statistics, functional analysis, discrete mathematics and even in quantum information theory and complexity theory. In an introductory part, some interesting features of Boolean cubes and Euclidean balls in high dimensions will be discussed. We will also see how integration with respect to a suitable Gaussian measure and with respect to the surface measure of the sphere are more and more indistinguishable in high dimensions. The probabilistic aspects of the concentration of measure phenomenon start with the traditional laws of large numbers for independent random variables and random processes. When reformulated in a geometric fashion, this allows to find more general versions of this phenomenon. We will even establish a version of the central limit theorem for matrices! In the final part of the course, we will discuss applications ranging from compressed sensing and machine learning to quantum information theory. 
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MATH 6397  Applied and Computational Probability: 21960


Prerequisites:  Graduate standing. Calculus 3 (multidimensional integrals), very minimal background in Probability. 
Text(s):  Sheldon Ross, A First Course in Probability (10th Edition) 
Description:  This course is for students who would like to learn about Probability concepts; I’ll assume very minimal background in probability. Calculus 3 (multidimensional integrals) is the only prerequisite for this class. This class will emphasize practical aspects, such as analytical calculations related to conditional probability and computational aspects of probability. No measuretheoretical concepts will be covered in this class. This is class is intended for students who want to learn more practical concepts in probability. This class is particularly suitable for Master students and nonmath majors. 
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MATH 6397  Spatial Statistics: 30076


Prerequisites:  Graduate standing and MATH 6382 
Text(s): 
Lectures will be based on lecture notes provided by the instructor. Recommended Texts:

Description:  This is a graduate level course (multidisciplinary, for Master as well as PhD students) that gives a general overview of the field of spatial and spatiotemporal statistics. Students will learn concepts and statistical methods for real data with spatial and temporal dependence. Course material will be applied in nature although some discussion on theory and technical contents will be given (will be kept at minimal level). Students will learn to analyze spatial and spatiotemporal data, mainly using R and thus some programming experience with R, or similar languages such as matlab is necessary. Various real data application examples will be given during lectures. Students will learn to make prediction in space and time based on the analysis results of spatial and spatiotemporal data. There will be a semesterlong project (could be team or individual, depending on enrollment) on real applications, and they are welcome to work on data that come from their own graduate research (as long as they are appropriate for spatial or spatiotemporal analysis). Statistical Software: R (http://rproject.org) 
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MATH 7320 Functional Analysis: 21334


Prerequisites:  Graduate standing. Instructor's Prerequisite: MATH 6308, Math 6320, and Math 6342, or the approval of the instructor. For this course, you need to have a strong background in real analysis and linear algebra, and a good background in measure theory and topology 
Text(s):  A Course in Functional Analysis by John B. Conway, Second Edition. 
Description:  Instructor's Description: Banach spaces, Hilbert spaces, linear operators on Hilbert spaces, weak topologies. 
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