Fall 2023
(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 08/24/23)
GRADUATE COURSES  FALL 2023
SENIOR UNDERGRADUATE COURSES
Course 
Section 
Course Title 
Course Day/Time 
Rm # 
Instructor 
Math 431001  15299  Biostatistics  MWF, 11AM—Noon (F2F)  AH 301  D. Labate 
Math 432001  11542  Intro. To Stochastic Processes  TTh, 10—11:30AM (F2F)  SEC 202  I. Timofeyev 
Math 432202  16022  Intro. to Data Science and Machine Learning  TTh, 11:30AM—1PM (F2F)  SEC 104  C. Poliak 
Math 432301  15980  Data Science and Statistical Learning  TTh, 10—11:30AM (F2F)  SEC 104  W. Wang 
Math 433102  12923  Introduction to Real Analysis I  TTh, 1—2:30PM (F2F)  S 207  B. Bodmann 
Math 433501  14363  Partial Differential Equations I  MWF, 9—10AM (F2F)  AH 301  G. Jaramillo 
Math 433902  15445  Multivariate Statistics  TTh, 1—2:30PM (F2F)  CBB 214  C. Poliak 
Math 436401  13320  Intro. to Numerical Analysis in Scientific Computing  MW, 4—5:30PM (F2F)  SEC 204  T. Pan 
Math 436402  15767  Intro. to Numerical Analysis in Scientific Computing  MWF, 10—11AM (F2F)  F 154  Yunhui He 
Math 437701  12925  Advanced Linear Algebra I  TTh, 11:30AM—1PM (F2F)  F 154  A. Mamonov 
Math 438301  26029  Number Theory and Cryptography  MW, 1—2:30PM (F2F)  S 207  M. Ru 
Math 438801  12329  History of Mathematics  Asynchronous/On Campus Exams  N/A  S. Ji 
Math 438901  11980  Survey of Undergraduate Mathematics  TTh, 2:30—4PM (F2F)  S 114  N. Leger 
Math 439701  20652  Intro to Mathematical Neuroscience  TTh, 11:30AM—1PM (F2F)  CBB 214  K. Josic 
GRADUATE ONLINE COURSES
Course 
Section 
Course Title 
Course Day & Time 
Instructor 
Math 531001  18200  History of Mathematics  Asynchronous/Oncampus Exams; Online  S. Ji 
Math 533101  20623  Linear Algebra w/Applications  Asynchronous/Oncampus Exams; Online  G. Etgen 
Math 533301  18195  Analysis  Asynchronous/Oncampus Exams; Online  S. Ji 
Math 538201  15828  Probability  Asynchronous/Oncampus Exams; Online  A. Török 
GRADUATE COURSES
Course 
Section 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 630201  11543  Modern Algebra I  TTh, 1—2:30PM  S 102  M. Kalantar 
Math 630804  12926  Advanced Linear Algebra I  TTh, 11:30AM—1PM  F 154  Mamonov 
Math 631202  12924  Introduction to Real Analysis  TTh, 1—2:30PM  S 207  B Bodmann 
Math 632001  11570  Theory of Functions of a Real Variable  MWF, 9—10AM  S 101  V. Climenhaga 
Math 632201  18196  Function Complex Variable  WF, 1—2:30PM  S 101  M. Nicol 
Math 632601  18196  Partial Differential Equations  TTh, 10—11:30AM  S 207  M. Perepelitsa 
Math 634201  11571  Topology  TTh, 2:30—4PM  S 119  W. Ott 
Math 636001  16955  Applicable Analysis  TTh, 1—2:30PM  S 202  D. Onofrei 
Math 636601  11572  Optimization Theory  MW, 4—5:30PM  S 132  A. Mang 
Math 637001  11573  Numerical Analysis  MWF, 10—11AM  S 101  Cappanera 
Math 637401  20627  Numerical Partial Differential Equations  MW, 1—2:30PM  AH 301  A. Quaini 
Math 638202  14433  Probability  TTh, 2:30—4PM  S 101  R. Azencott 
Math 639701  20629  Intro to Mathematical Neuroscience  TTh, 11:30AM—1PM  CBB 214  K. Josic 
Math 639702  20631  Numerical Linear Algebra  TTh, 4—5:30PM  AH 301  A. Mamonov 
Math 639703 / Math 639704  20632 / 21040  Statistical Analysis Computation  TTh, 11:30AM—1PM  S 101  M. Jun 
Math 639705  25011  Selected Topics in Math  MW, 5:30—8:30PM  S 119  C. Poliak 
Math 732001  18198  Functional Analysis  TTh, 10—11:30AM  S 202  D. Blecher 
Math 735001  20633  Geometry of Manifolds  TTh, 1—2:30PM  S 101  G. Heier 
MSDS Courses
Course 
Section 
Course Title 
Course Day & Time 
Rm # 
Instructor 
Math 635001  15306  Statistical Learning and Data Mining  MW, 1—2:30PM (F2F)  SEC 202  J. Ryan 
Math 635701  15443  Linear Models & Design of Experiments  MW, 2:30—4PM (F2F)  SEC 203  W. Wang 
Math 635802  14558  Probability Models and Statistical Computing  F, 1—3PM (F2F)  CBB 214  C. Poliak 
Math 635803  17383  Probability Models and Statistical Computing  F, 1—3PM, Synchronous/Oncampus Exams  N/A  C. Poliak 
Math 638001  15567  Programming Foundation for Data Analytics  F, 3—5PM (F2F)  CBB 214  D. Shastri 
Math 638002  17382  Programming Foundation for Data Analytics  F, 3—5PM, Synchronous/Oncampus Exams  N/A  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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Math 4320  Intro to Stochastic Processes


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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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): 
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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Math 4339  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 436401 (13320)  Introduction to Numerical Analysis in Scientific Computing


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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Math 436402 (15767)  Introduction to Numerical Analysis in Scientific Computing


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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Math 4377  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. 
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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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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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. 
Math 4397 (20652)  Intro to Computational Neurosciences


Prerequisites: 
Math 4397 Prerequisites: MATH 3333. Instructor's prerequisites: 
Text(s): 

Description:  Information theory is the scientific study of the quantification, storage, and communication of digital information. It has been widely used in the communication and cryptography in our daily life. In last several decades, motivated by quantum computation, quantum information theory has been a rapid growing area studying how information can be processed, transmit and stored in quantum mechanics system. The aim of this course is to give a minimal introduction to both classical and quantum information theory in a unified manner. We will start with some basics in Shannon’s classical information theory and then study their counterpart in quantum mechanics model. After that, we will focus on the quantum side and covers some selected topics such as entanglement, Bell’s inequality, Shor's algorithm, Quantum Teleportation and Superdense coding, etc. 
Math 4397 (TBD)  Selected Topics in Mathematics


Prerequisites:  MATH 3333 or consent of instructor. 
Text(s):  No textbook is required. Instructor notes will be provided 
Description:  Selected topics in Mathematics 
ONLINE GRADUATE COURSES
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. 
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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GRADUATE COURSES
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MATH 6302  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  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  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


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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MATH 6342  Topology


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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MATH 6350  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


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


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:

MATH 6360  Applicable Analysis  
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.

MATH 6366  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


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. 
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. 
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 639701 (20629)  Intro to Computational Neurosciences


Prerequisites: 
Graduate standing. 
Text(s): 
TBA 
Description: 
TBA 
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Math 639702 (20631)  Numerical Linear Algebra


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