Fall 2019
GRADUATE COURSE FALL 2019
Course  Section  Course Title  Course Day & Time  Rm #  Instructor 
Math 4310  26074  Biostatistics  TuTh, 1—2:30pm  MH 140  D. Labate 
Math 4320  16736  Intro to Stochastic Processes  MWF, 10—11am  SEC 103  I. Timofeyev 
Math 4322  27531  Introduction to Data Science and Machine Learning  MWF, 11am—Noon  SEC 102  A. Skripnikov 
Math 4331  19930  Introduction to Real Analysis I  TuTh, 8:30—10am  F 154  B. Bodmann 
Math 4335  22583  Partial Differential Equations I  MWF, 9—10am  CBB 214  G. Jaramillo 
Math 4339  28362  Multivariate Statistics  (online)  (online)  J. Morgan 
Math 4339  28373  Multivariate Statistics  TuTh, 1—2:30pm  ARC 402  C. Poliak 
Math 4364  20801  Introduction to Numerical Analysis in Scientific Computing 
MW, 4—5:30pm  SEC 104  TW. Pan 
Math 4366  21616  Numerical Linear Algebra  TuTh, 11:30am1pm  SW 229  J. He 
Math 4377  19933  Advanced Linear Algebra I  TuTh, 10—11:30am  F 154  A. Vershynina 
Math 4383  25435  Number Theory and Cryptopgraphy  MW, 1—2:30pm  AH 12  M. Ru 
Math 4388  18566  History of Mathematics  (online)  (online)  S. Ji 
Math 4389  17781  Survey of Undergraduate Mathematics  MW, 12:30pm  SEC 202  M. Almus 
Math 4397  27370  Mathematical Methods for Physics  MW, 2:30—4pm  CBB 124 
L. Wood 
Course  Section  Course Title  Course Day & Time  Instructor 
Math 5331  18067  Linear Algebra with Applications  Arrange (online course)  K. Kaiser 
Math 5333  18856  Analysis  Arrange (online course)  G. Etgen 
Math 5383  25706  Number Theory  Arrange (online course)  M. Ru 
Math 5385  17472  Statistics  Arrange (online course)  J. Morgan 
Course  Section  Course Title  Course Day & Time  Rm #  Instructor 
Math 6302  16741  Modern Algebra I  TuTh, 11:30am—1pm  SW 2019  M. Kalantar 
Math 6308  19935  Advanced Linear Algebra I  TuTh, 8:30am—10am  F 154  A. Vershynina 
Math 6308  TBA  Advanced Linear Algebra I  TBA  TBA  TBA 
Math 6312  19931  Introduction to Real Analysis  TuTh, 8:30—10am  F 154  B. Bodmann 
Math 6320  16770  Theory of Functions of a Real Variable  TuTH, 1—2:30pm  CAM 101  W. Ott 
Math 6326  28709  Partial Differential Equations  TuTh, 11:30am—1pm  SEC 105  G. Auchmuty 
Math 6342  16771  Topology  MWF, 10—11am  CBB 214  D. Blecher 
Math 6360  17453  Applicable Analysis  TuTh, 2:30—4pm  AH 208  A. Mamonov 
Math 6366  16772  Optimization Theory  MWF, Noon—1pm  AH 301  A. Mang 
Math 6370  16773  Numerical Analysis  MW, 4—5:30pm  CBB 214  M. Olshanskiy 
Math 6382  22891  Probability and Statistics  TuTh, 10—11:30am  AH 301  M. Nicol 
Math 6384  22588  Discrete Time Model in Finance  TuTh, 2:304pm  SW 423  E. Kao 
Math 6395  25708  Spectral & Operator Theory  MWF, 9—10am  CBB 120  A. Czuron 
Math 7326  25412  Dynamical Systems  MWF, Noon—1pm  AH 202  V. Climenhaga 
Math 7396  25411  Preconditioned Iterative Methods for Large Scale Problems  MW, 1—2:30pm  CBB 214  Y. Kuznetsov 
MSDS Courses (MSDS Students Only)
Course  Section  Course Title  Course Day & Time  Rm #  Instructor 
Math 6350  26102  Statistical Learning and Data Mining  MW, 1—2:30pm  CBB 214  R. Azencott 
Math 6357  28361  Linear Models & Design of Experiments  MW, 4—5:30pm  SEC 202  W. Wang 
Math 6358  23164  Probability Models and Statistical Computing  Fr, 1—3:00pm  AH 301  C. Poliak 
Math 6380  29420  Programming Foundation for Data Analytics  Fr, 3—5pm  SEC 202  D. Shastri 
Math 6397  26096  Topics in Financial Machine Learning/Analytics in Commodity & Financial Markets  W, 5:30—8:30pm  AH 204  D. Zimmerman 
SENIOR UNDERGRADUATE COURSES
Math 4310  Biostatistics


Prerequisites:  MATH 3339 and BIOL 3306 
Text(s):  "Biostatistics: A Foundation for Analysis in the Health Sciences, Eleventh Edition, by Wayne W. Daniel, Chad L. Cross. ISBN: 9781119496700 
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. 
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Math 4331  Introduction to Real Analysis


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 (28362)  Multivariate Statistics


Prerequisites: 
MATH 3349 
Text(s): 

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:

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Math 4339 (28373)  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 4364 (20801)  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 (19933)  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 4383 (25435)  Number Theory and Cryptography


Prerequisites:  MATH 3330 or MATH 3336 
Text(s): 
Instructor Notes. Recommended texts:

Description: 
Catalog 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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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 (27370)  Mathematical Methods for Physics


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  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  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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TBD


Prerequisites:  TBD 
Text(s): 
TBD 
Description: 
TBD 
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MATH 5383  Number Theory


Prerequisites:  Graduate standing 
Text(s):  Instructor's lecture notes. The reference book will be "Beginning Number Theory" by Neville Robbins, second Edition. 
Description:  Number theory is a subject that has interested people for thousand of years. This course is a onesemester long graduate course on number theory. Topics to be covered include divisibility and factorization, linear Diophantine equations, congruences, applications of congruences, solving linear congruences, primes of special forms, the Chinese Remainder Theorem, multiplicative orders, the Euler function, primitive roots, quadratic congruences, and introduction to cryptography . There'll be no specific prerequisites beyond basic algebra and some ability in reading and writing mathematical proofs. 
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MATH 5385  Statistics (17472)


Prerequisites:  Graduate standing. 
Text(s): 

Description:  Data collection and types of data, descriptive statistics, probability, estimation, model assessment, regression, analysis of categorical data, analysis of variance. Computing assignments using a prescribed software package (e.g., EXCEL, Minitab) will be given. 
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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 (19935) 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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MATH 6326  Partial Differential Equations


Prerequisites: 
Graduate Standing and MATH 4331. 
Text(s): 
Required: The instructor will provide notes on much of the material for the course and there is no prescribed text. Recommended Texts: The course will cover the material in the first three chapters of ”Hilbert Space Methods in Partial Differential Equations” by Ralph E. Showalter (Dover or free online) and some of the text ”Elliptic Equations: An Introductory Course”,by Michel Chipot, Birkhauser, 2009. The Universitext ”Functional Analysis, Sobolev Spaces and Partial Differential Equations” by Haim Brezis, Springer 2011 provides a thorough treatment of the functional analysis used. These three texts may be good reference texts for the material treated in the course. 
Description: 
Course Outline: This course will provide an introduction to the modern theory of elliptic partial differential equations using Sobolev space methods. The prerequisite is competence in multivariable calculus and real analysis. Ideally a student should have done well in M6320 21 and having a working knowledge of Lebesgue integration and some Fourier analysis. The basic constructions of linear analysis in Hilbert and Banach spaces will be assumed known. 
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MATH 6342  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  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: Introduction to Statistical Learning w/Applications in R, by James , Witten, Hastie, Tibshirani (This book is freely available online). ISBN: 9781461471370 
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. 
Text(s): 
TBA 
Description:  TBA 
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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:

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MATH 6360  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  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. 
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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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MATH 6382  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 Model in Finance


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 6395 (25708)  Spectral & Operator Theory


Prerequisites: 
Graduate standing. Instructor's prerequisites: TBA 
Text(s): 
TBA 
Description: 
Description: May be repeated with approval of chair. Instructor's description: TBA 
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MATH 6397 (26096)  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 7326 (25412)  Dynamical Systems


Prerequisites:  Graduate standing. Instructor's prerequisite: Undergraduate real analysis (Math 43314332 or equivalent) and undergraduate differential equations (Math 3331 or equivalent), or consent of instructor.Â Some background in measure theory and graduate level ODE would be helpful, but will not be assumed, and any relevant notions from these areas will be introduced as they appear. 
Text(s):  There is no required textbook. A The more indepth arguments in the course will largely be drawn from the primary literature (references will be provided) or from the book "Onedimensional dynamics" by Wellington de Melo and Sebastian van Strien, which is out of print but available free in pdf form from the second author's website: http://wwwf.imperial.ac.uk/~svanstri/ Some of the history of the subject is discussed in "Chaos: Making a New Science" by James Gleick, ISBN: 9780143113454, and an undergraduatelevel introduction to some of the topics is given in "Nonlinear Dynamics and Chaos" by Steven Strogatz ISBN: 9780813349107, so these books are worth looking at and I will draw from both to some extent, but neither is required for this course. 
Description: 
Catalog Description: 
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TBD TBD


Prerequisites:  Graduate standing. 
Text(s):  
Description: 
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MATH 7396  Preconditioned Iterative Methods for Large Scale Problems


Prerequisites:  Graduate standing. Instructor's Prerequisite: Graduate Course on Numerical Analysis 
Text(s):  None 
Description:  Instructor's Description: Finite Element, Finite Volume, and Finite Difference discretizations of partial differential equations result in large scale systems of linear algebraic equations with sparse illconditioned matrices. Preconditioned iterative methods are the only way for efficient solution of such systems. The course consists in four major parts. In the first part, we recall basic information on preconditioned Conjugate Gradient and Generalized Minimal Residual methods. In the second part, we describe properties of matrices arising from discretizations of differential problems. The third part is devoted to several major approaches for designing of efficient preconditioners based on Domain Decomposition and Fictitious Domain algorithms. Finally, we consider applications of preconditioned Iterative methods for solving of steadystate and timedependent diffusion and convectiondiffusion problems. 
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