Fall 2024
(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.)
(Updated 08/07/24)
GRADUATE COURSES  FALL 2024
SENIOR UNDERGRADUATE COURSES
Course/Section 
Class # 
Course Title 
Course Day/Time 
Rm # 
Instructor 
Math 431001  14844  Biostatistics  MWF, 10—11AM  S 102  D. Labate 
Math 431501  21252  Graph Theory with Applications  TTh, 2:30—4PM  S 116  K. Josic 
Math 432001  11469  Intro. To Stochastic Processes  TTh, 11:30AM—1PM  AH 301  W. Ott 
Math 432202  15451  Intro. to Data Science and Machine Learning  TTh, 11:30AM—1PM  SEC 204  C. Poliak 
Math 432301  15420  Data Science and Statistical Learning  MWF, 10—11AM  SEC 104  W. Wang 
Math 433102  12754  Introduction to Real Analysis I  MWF, 9—10AM  SEC 201  M. Nicol 
Math 433501  14029  Partial Differential Equations I  Asynchronous/On Campus Exams  Online  W. Fitzgibbon 
Math 433902  14959  Multivariate Statistics  TTh, 1—2:30PM  SEC 201  C. Poliak 
Math 435001  21272  Differential Geometry I  MW, 1—2:30PM  AH 301  M. Ru 
Math 436401  13125  Intro. to Numerical Analysis in Scientific Computing  MW, 4—5:30PM  SEC 206  T. Pan 
Math 436402  15232  Intro. to Numerical Analysis in Scientific Computing  MWF, 10—11AM  CBB 214  M. Zhong 
Math 436601  21271  Numerical Linear Algebra  TTh, 11:30AM—1PM  SEC 201  J. He 
Math 437704  12756  Advanced Linear Algebra I  TTh, 10—11:30AM  AH 108  G. Heier 
Math 438801  12193  History of Mathematics  Asynchronous/On Campus Exams  N/A  S. Ji 
Math 438901  11873  Survey of Undergraduate Mathematics  MWF, 11AM—Noon  S 114  V. Climenhaga 
GRADUATE ONLINE COURSES
Course/Section 
Class # 
Course Title 
Course Day & Time 
Instructor 
Math 531001  17219  History of Mathematics  Asynchronous/Oncampus Exams; Online  S. Ji 
Math 533101  18216  Linear Algebra w/Applications  Asynchronous/Oncampus Exams; Online  G. Etgen 
Math 533301  17217  Analysis  Asynchronous/Oncampus Exams; Online  S. Ji 
Math 538201  15289  Probability  Asynchronous/Oncampus Exams; Online  A. Török 
Math 539701  21236  Partial Differential Equations  Asynchronous/Oncampus Exams; Online  W. Fitzgibbon 
GRADUATE COURSES
Course/Section 
Class # 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 630201  11470  Modern Algebra I  MWF, 10—11AM  F 154  A. Haynes 
Math 630804  12757  Advanced Linear Algebra I  TTh, 10—11:30AM  AH 108  G. Heier 
Math 631202  12755  Introduction to Real Analysis  MWF, 9—10AM  SEC 201  M. Nicol 
Math 632001  11497  Theory of Functions of a Real Variable  TTh, 11:30AM—1PM  F 154  B. Bodmann 
Math 632201  17218  Function Complex Variable  MWF, 11AM—Noon  F 154  M. Nicol 
Math 632601  18238  Partial Differential Equations  MWF, 9—10AM  F 154  G. Jaramillo 
Math 634201  11498  Topology  MWF, Noon—1PM  S 114  V. Climenhaga 
Math 636001  16277  Applicable Analysis  TTh, 1—2:30PM  S 101  B. Bodmann 
Math 636601  11499  Optimization Theory  TTh, 4—5:30PM  F 154  N. Charon 
Math 637001  11500  Numerical Analysis  TTh, 2:30—4PM  SEC 201  A. Quaini 
Math 637401  18218  Numerical Partial Differential Equations  TTh, 8:30—10AM  F 154  L. Cappanera 
Math 638202  14094  Probability  TTh, 1—2:30PM  F 154  R. Azencott 
Math 639701  21255  Python for scientific computation  TTh, 10—11:30AM  AH 301  I. Timofeyev 
Math 639703  21468  Spatial Statistics  TTh, 1—2:30PM  S 132  M. Jun 
Math 732001  21254  Functional Analysis  TTh, 4—5:30PM  F 162  M. Kalantar 
Math 735001  18221  Geometry of Manifolds  MW, 1—2:30PM  C 118  Y. Wu 
Math 739701  21253  Numerical Linear Algebra Data  TTh, 11:30AM—1PM  S 119  M. Olshanskii 
MSDS Courses
(MSDS Students Only  Contact Ms. Callista Brown for specific class numbers)
CourseSection 
Class # 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 635001  Not shown to students  Statistical Learning and Data Mining  MW, 2:30—4PM  SEC 203  J. Ryan 
Math 635701  Not shown to students  Linear Models & Design of Experiments  MW, 1—2:30PM  SEC 204  W. Wang 
Math 635802/03  Not shown to students  Probability Models and Statistical Computing  F, 1—3PM  CBB 108  C. Poliak 
Math 638001/02  Not shown to students  Programming Foundation for Data Analytics  F, 3—5PM (F2F)/Synchronous/Oncampus Exams  CBB 108  D. Shastri 
SENIOR UNDERGRADUATE COURSES
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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Prerequisites:  MATH 3325 or MATH 3336 and three additional hours at the MATH 30004000 level. 
Text(s):  TBA 
Description:  Introduction to basic concepts, results, methods, and applications of graph theory. 
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Prerequisites:  MATH 3338 
Text(s): 

Description: 
Catalog 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. Instructor's description: This course provides a overview of stochastic processes. We cover Poisson processes, discretetime and continuoustime Markov chains, renewal processes, diffusion process and its variants, marttingales. We also study Markov chain Monte Carlo methods, and regenerative processes. In addition to covering basic theories, we also explore applications in various areas such as mathematical finance. Syllabus can be found here: https://www.math.uh.edu/~edkao/MyWeb/doc/math4320_fall2022_syllabus.pdf 
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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. 
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Prerequisites:  MATH 3339 
Text(s): 
Intro to Statistical Learning. ISBN: 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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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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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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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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Prerequisites:  MATH 2415 and six additional hours of 30004000 level Mathematics. 
Text(s):  TBA 
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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Prerequisites: 
MATH 3331 or MATH 3321 or equivalent, and three additional hours of 30004000 level Mathematics *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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Prerequisites: 
MATH 3331 or MATH 3321 or equivalent, and three additional hours of 30004000 level Mathematics *Ability to do computer assignments in FORTRAN, C, Matlab, Pascal, Mathematica or Maple. 
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: 
MATH 2318, or equivalent, and six additional hours of 30004000 level Mathematics. 
Text(s):  TBA 
Description: 
Conditioning and stability of linear systems, matrix factorizations, direct and iterative methods for solving linear systems, computing eigenvalues and eigenvectors, introduction to linear and nonlinear optimization. 
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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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Prerequisites: 
MATH 3330 and MATH 3336 
Text(s): 
Refer to the instructor's syllabus 
Description: 
Description: Divisibility theory, primes and their distribution, theory of congruences and application in security, integer representations, Fermat’s Little Theorem and Euler’s Theorem, primitive roots, quadratic reciprocity, and introduction to cryptography 
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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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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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Prerequisites: 
MATH 3333 or consent of instructor 
Text(s):  TBD 
Description:  Selected topics in Mathematics 
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Prerequisites:  MATH 3333 or consent of instructor 
Text(s):  TBD 
Description:  Selected topics in Mathematics 
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ONLINE GRADUATE COURSES
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MATH 5310  History of Mathematics


Prerequisites: 
Graduate standing. 
Text(s): 
Instructor's notes 
Description:  Mathematics of the ancient world, classical Greek mathematics, the development of calculus, notable mathematicians and their accomplishments. 
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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) 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. 
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. 
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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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. 
Prerequisites:  Graduate standing. Instructor's prerequisite: TBA 
Text(s):  TBA 
Description:  TBA 
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GRADUATE COURSES
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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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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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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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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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Prerequisites:  Graduate standing and MATH 4331 
Text(s):  TBD 
Description:  Geometry of the complex plane, mappings of the complex plane, integration, singularities, spaces of analytic functions, special function, analytic continuation, and Riemann surfaces. 
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Prerequisites:  Graduate standing and MATH 4331 
Text(s):  • Robert McOwen, "Partial Differential Equations, Methods and Applications", 2nd Ed. (2004) • Lawrence C. Evans, "Partial Differential Equations, Graduate studies in Mathematics 19.2 (1998) 
Description: 
Existence and uniqueness theory in partial differential equations; generalized solutions and convergence of approximate solutions to partial differential systems. This course introduces four main types of partial differential equations: parabolic, elliptic, hyperbolic and transport equations. The focus is on existence and uniqueness theory. Maximum principles and regularity of solutions will be considered. Other concepts that will be explored include weak formulations and weak solutions, distribution theory, fundamental solutions. The course will touch on applications and a brief introduction to numerical methods: finite differences, finite volume, and finite elements. 
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Prerequisites: 
Catalog prerequisite: Graduate standing. MATH 4331. Instructor's prerequisite: Graduate standing. MATH 4331 or consent of instructor 
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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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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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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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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Prerequisites: 
Graduate standing. 
Text(s): 
No obligatory text. Part of the material will be collected from Ken Davidson and Alan Donsig, “Real Analysis with Applications: Theory in Practice”, Springer, 2009. Other sources on Applied Functional Analysis will complement the material.

Description: 
This course covers topics in analysis that are motivated by applications.

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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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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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Prerequisites:  Graduate standing, and MATH 6371 
Text(s):  TBA 
Description:  Finite difference, finite element, collocation and spectral methods for solving linear and nonlinear elliptic, parabolic, and hyperbolic equations and systems with applications to specific problems. 
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MATH 6380  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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Prerequisites: 
Graduate standing and MATH 3334, MATH 3338 and MATH 4378. Instructor's prerequisite: main notions in undergraduate Probability and undergraduate Linear Algebra &familiarity with either Matlab or Python or R (no software initiation in this course) 
Text(s): 
Selected chapters in...

Description: 
Basic Probability Concepts:

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Prerequisites: 
Graduate standing. Math 63706371 
Text(s): 
"DataDriven Science and Engineering: Machine Learning, Dynamical Systems, and Control" 2nd Edition, Steven L. Brunton and J. Nathan Kutz 
Description: 
Instructor's description: The goal of this class is to develop proficiency in implementing numerical methods in Python. In particular, this class will cover implementations of various numerical algorithms from Math 63706371 (Numerical Analysis) and more advanced topics from the book by Brunton and Kutz. Some topics might be taken out of Math 6374 (Numerical PDEs, but no finite elements) and Math 63666367 (Optimization). In addition, we might discuss deep learning and PyTorch if we have enough time and there is enough interest in the class. 
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Prerequisites:  Graduate standing. 
Text(s):  TBA 
Description: 
TBA 
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Prerequisites:  Graduate standing. 
Text(s): 
TBA 
Description: 
TBA 
Prerequisites:  Graduate standing. 
Text(s): 
TBA 
Description: 
TBA 
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Prerequisites:  Graduate standing. MATH 6320 or consent of instructor. 
Text(s): 
Walter Rudin, Functional Analysis, 2nd edition. McGraw Hill, 1991. (Instructor may suggest other tests or have their own typed notes) 
Description: 
Catalog description: Linear topological spaces, Banach and Hilbert spaces, duality, and spectral analysis. Instructor's description: Topics covered in this first part of the course sequence include: Topological vector spaces; Completeness; Convexity; Spectral theory; etc. See Instructor's syllabus for more details. 
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Prerequisites:  Graduate standing. MATH 3431 and MATH 3333 
Text(s): 
TBA 
Description: 
Manifolds and tangent bundles, submanifolds and imbeddings, integral manifolds, triangulation of manifolds, connections and holonomy; Riemannian geometry, surface theory, Morse theory, and Gstructures. 
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Prerequisites:  Graduate standing. MATH 3431 and MATH 3333 
Text(s): 
TBA 
Description: 
Manifolds and tangent bundles, submanifolds and imbeddings, integral manifolds, triangulation of manifolds, connections and holonomy; Riemannian geometry, surface theory, Morse theory, and Gstructures. 