2024 - Spring Semester
(Disclaimer: Be advised that some information on this page may not be current due to course scheduling changes.
Please view either the UH Class Schedule page or your Class schedule in myUH for the most current/updated information.)
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GRADUATE COURSES - SPRING 2024
This schedule is subject to changes. Please contact the Course Instructor for confirmation.
Course |
Section |
Course Title |
Course Day/Time |
Rm # |
Instructor |
Math 4309 | 12220 | Mathematical Biology | MW, 2:30—4PM, (F2F) | S 101 | R. Azevedo |
Math 4322 | 15443 | Introduction to Data Science and Machine Learning | TTh, 11:30AM—1PM, (F2F) | SEC 102 | C. Poliak |
Math 4323 | 14927 | Data Science and Statistical Learning | MWF, 10—11AM, (F2F) | SEC 103 | W. Wang |
Math 4332/6313 | 11140 | Introduction to Real Analysis II | TTh, 8:30—10AM, (F2F) | S 207 | B. Bodmann |
Math 4351 | 19769 | Calculus on Manifolds | TTh, 2:30—4PM, (F2F) | F 162 | Y. Wu |
Math 4362 | 14344 | Theory of Differential Equations and Nonlinear Dynamics | MWF, 9—10AM, (F2F) | SEC 201 | G. Jaramillo |
Math 4364-01 | 13069 | Intro. to Numerical Analysis in Scientific Computing | MW, 4—5:30PM, (F2F) | SEC 105 | T.W. Pan |
Math 4364-02 | 17730 | Intro. to Numerical Analysis in Scientific Computing | Asynch./on-campus exams | Online | J. Morgan |
Math 4365 | 12608 | Numerical Methods for Differential Equations | TTh, 10—11:30AM, (F2F) | SW 219 | Min Wang |
Math 4370 | N/A | Mathematics for Physicists - cancelled | N/A | N/A | N/A |
Math 4377/6308 | 12846 | Advanced Linear Algebra I | TTh, 11:30AM—1PM, (F2F) | S 102 | A. Quaini |
Math 4378/6309 | 11141 | Advanced Linear Algebra II | TTh, 11:30AM—1PM, (F2F) | CBB 106 | A. Mamonov |
Math 4380 | 11142 | A Mathematical Introduction to Options | MW, 1—2:30PM, (F2F) | AH 301 | M. Papadakis |
Math 4389 | 11143 | Survey of Undergraduate Mathematics | TTh, 1—2:30PM, (F2F) | F 154 | D. Blecher |
Course |
Section |
Course Title |
Course Day & Time |
Instructor |
Math 5330 | 11601 | Abstract Algebra |
(Asynch./on-campus exams) | A. Haynes |
Math 5332 | 11150 | Differential Equations |
(Asynch./on-campus exams) | G. Etgen |
Math 5334 | 19701 | Complex Analysis | (Asynch./on-campus exams) | S. Ji |
Math 5344 | 19702 | Intro. to Scientific Computing | (Asynch./on-campus exams) | J. Morgan |
Math 5350 | 19703 | Intro. to Differential Geometry | (Asynch./on-campus exams) | M. Ru |
Math 5385 | 15455 | Statistics | (Asynch./on-campus exams) | TBD |
Course |
Section |
Course Title |
Course Day & Time |
Rm # |
Instructor |
Math 6303 | 11151 | Modern Algebra II | TTh, 1—2:30PM | S 101 | M. Kalantar |
Math 6308 | 12847 | Advanced Linear Algebra I | TTh, 11:30AM—1PM | S 102 | A. Quaini |
Math 6309 | 11643 | Advanced Linear Algebra II | TTh 11:30AM—1PM | CBB 106 | A. Mamonov |
Math 6313 | 11642 | Introduction to Real Analysis | TTh, 10—11:30AM | F 162 | B. Bodmann |
Math 6321 | 11156 | Theory of Functions of a Real Variable | MWF, 9—10AM | S 101 | V. Climenhaga |
Math 6361 | 20465 | Applicable Analysis | TTh, 1—2:30PM | S 119 | D. Onofrei |
Math 6367 | 19704 | Optimization Theory | TTh, 11:30AM—1PM | SEC 201 | J. He |
Math 6371 | 11157 | Numerical Analysis | TTh, 10—11:30AM | S 102 | L. Cappanera |
Math 6377 | 19705 | Mathematics of Machine Learning | TTh 1—2:30PM | AH 301 | R. Azencott |
Math 6383 | 11158 | Statistics | MW, 4—5:30PM | S 102 | M. Jun |
Math 6397 | 19706 | Computation & Math Methods in Data Science | MW, 4—5:30PM | F 162 | A. Mang |
Math 6397 | 19707 | Applied & Computational Topology | TTh, 2:30—4PM | S 202 | W. Ott |
Math 6397 | 19708 | Quantum Information and Computation | MWF, 11AM—Noon | F 154 | A. Vershynina |
Math 6397 | 19709 | Stochastic Process | MW, 1—2:30PM | S 202 | I. Timofeyev |
Math 6397 | 20173 | Bayesian Statistics | MW, 2:30—4PM | SEC 202 | Y. Niu |
Math 6397 | 25618 | Image Processing Methods | MWF, 10—11AM | AH 204 | N. Charon |
Math 7321 | 18187 | Functional Analysis | TBD | TBD | TBD |
Math 7326 | 17738 | Dynamical Systems | MWF, 11AM—Noon | S 101 | M. Nicol |
Math 7352 | 25834 | Riemannian Geometry | TBD | TBD | TBD |
Course |
Section |
Course Title |
Course Day & Time |
Rm # |
Instructor |
Math 6315 | 14773 | Masters Tutorial: Internship | TBD | N/A | C. Poliak |
Math 6359 | 14771 | Applied Statistics & Multivariate Analysis | F, 1—3PM | CBB 104 | C. Poliak |
Math 6359 | 15462 | Applied Statistics & Multivariate Analysis | F, 1—3PM (synch. online) | N/A | C. Poliak |
Math 6373 | 14772 | Deep Learning and Artificial Neural Networks | MW, 1—2:30PM (F2F) | F 162 | D. Labate |
Math 6381 | 14970 | Information Visualization | F, 3—5PM | CBB 104 | D. Shastri |
Math 6381 | 17066 | Information Visualization | F, 3—5PM (synch. online) | N/A | D. Shastri |
Math 6397 | 19750 | Case Studies In Data Analysis | W, 5:30—8:30PM | S 202 | L. Arregoces |
Math 6397 | 19739/20173 | Bayesian Statistics | MW, 2:30—4PM | SEC 202 | Y. Niu |
Math 6397 | 20174 | Financial & Commodity Markets | W, 5:30—8:30PM | AH 301 | J. Ryan |
-------------------------------------------Course Details-------------------------------------------------
SENIOR UNDERGRADUATE COURSES
Math 4309 - Mathematical Biology |
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Prerequisites: | |
Text(s): | Required texts: A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, Sarah P. Otto and Troy Day; (2007, Princeton University Press) ISBN-13:9780691123448 Reference texts: (excerpts will be provided)
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Description: |
Catalog description: Topics in mathematical biology, epidemiology, population models, models of genetics and evolution, network theory, pattern formation, and neuroscience. Students may not receive credit for both MATH 4309 and BIOL 4309. |
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Prerequisites: | MATH 3325 or MATH 3336 and three additional hours at the MATH 3000-4000 level. |
Text(s): | Intro to Statistical Learning, Gareth James, 9781461471370 |
Description: | Introduction to basic concepts, results, methods, and applications of graph theory. |
Math 4322 - Introduction to Data Science and Machine Learning
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Prerequisites: | MATH 3339 |
Text(s): | Intro to Statistical Learning, Gareth James, 9781461471370 |
Description: |
Theory and applications for such statistical learning techniques as linear and logistic regression, classification and regression trees, random forests, neutral networks. Other topics might include: fit quality assessment, model validation, resampling methods. R Statistical programming will be used throughout the course. |
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Math 4323 - Data Science and Statistical Learning
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Prerequisites: | MATH 3339 |
Text(s): | Intro to Statistical Learning, Gareth James, 9781461471370 |
Description: | Theory and applications for such statistical learning techniques as maximal marginal classifiers, support vector machines, K-means and hierarchical clustering. Other topics might include: algorithm performance evaluation, cluster validation, data scaling, resampling methods. R Statistical programming will be used throughout the course. |
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Math 4332/6313 - Introduction to Real Analysis II
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Prerequisites: | MATH 4331 or consent of instructor |
Text(s): | Real Analysis with Real Applications | Edition: 1; Allan P. Donsig, Allan P. Donsig; ISBN: 9780130416476 |
Description: |
Further development and applications of concepts from MATH 4331. Topics may vary depending on the instructor's choice. Possibilities include: Fourier series, point-set topology, measure theory, function spaces, and/or dynamical systems. |
Math 4335 - Partial Differential Equations I
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Prerequisites: | MATH 3331, or equivalent, and three additional hours of 3000-4000 level Mathematics. |
Text(s): | TBA |
Description: |
Initial and boundary value problems, waves and diffusions, reflections, boundary values, Fourier series. |
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Math 4351 - Calculus on Manifolds
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Prerequisites: | MATH 2415 and six additional hours of 3000-4000 level Mathematics. |
Text(s): | TBA |
Description: |
Differential forms in R^n (particularly R^2 and integration, the intrinsic theory of surfaces through differential forms, the Gauss-Bonnet theorem, Stokes’ theorem, manifolds, Riemannian metric and curvature. Other topics at discretion of instructor. |
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Math 4362 - Theory of Differential Equations an Nonlinear Dynamics
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Prerequisites: | MATH 3331, or equivalent, and three additional hours of 3000-4000 level Mathematics. |
Text(s): | Nonlinear Dynamics and Chaos (2nd Ed.) by Strogatz. ISBN: 978-0813349107 |
Description: |
ODEs as models for systems in biology, physics, and elsewhere; existence and uniqueness of solutions; linear theory; stability of solutions; bifurcations in parameter space; applications to oscillators and classical mechanics. |
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Math 4364 (13069) - Introduction to Numerical Analysis in Scientific Computing
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Prerequisites: |
MATH 3331 and COSC 1410 or equivalent or consent of instructor. Instructor's Prerequisite Notes: 1. MATH 2331, In depth knowledge of Math 3331 (Differential Equations) or Math 3321 (Engineering Mathematics) 2. Ability to do computer assignments in FORTRAN, C, Matlab, Pascal, Mathematica or Maple. |
Text(s): |
Instructor's notes |
Description: |
Catalog Description: Root finding, interpolation and approximation, numerical differentiation and integration, numerical linear algebra, numerical methods for differential equations. Instructor's 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 finite-difference approximation to a two-points boundary value problem. This is an introductory course and will be a mix of mathematics and computing. |
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Math 4364 (17730)- Introduction to Numerical Analysis in Scientific Computing
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Prerequisites: |
MATH 3331 and COSC 1410 or equivalent or consent of instructor. Instructor's Prerequisite Notes: 1. MATH 2331, In depth knowledge of Math 3331 (Differential Equations) or Math 3321 (Engineering Mathematics) 2. Ability to do computer assignments in FORTRAN, C, Matlab, Pascal, Mathematica or Maple. |
Text(s): |
Numerical Analysis (9th edition), by R.L. Burden and J.D. Faires, Brooks-Cole Publishers, ISBN:9780538733519 |
Description: |
Catalog Description: Root finding, interpolation and approximation, numerical differentiation and integration, numerical linear algebra, numerical methods for differential equations. Instructor's 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 finite-difference approximation to a two-points boundary value problem. This is an introductory course and will be a mix of mathematics and computing. |
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Math 4365 - Numerical Methods for Differential Equations
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Prerequisites: | MATH 3331, or equivalent, and three additional hours of 3000–4000 level Mathematics. |
Text(s): | TBA |
Description: | Numerical differentiation and integration, multi-step and Runge-Kutta methods for ODEs, finite difference and finite element methods for PDEs, iterative methods for linear algebraic systems and eigenvalue computation. |
Math 4370 - Mathematics for Physicists
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Prerequisites: | MATH 2415, and MATH 3321 or MATH 3331 |
Text(s): | TBD |
Description: | Vector calculus, tensor analysis, partial differential equations, boundary value problems, series solutions to differential equations, and special functions as applied to junior-senior level physics courses. |
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Math 4377/6308 - Advanced Linear Algebra I
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Prerequisites: | MATH 2331 or equivalent, and three additional hours of 3000–4000 level Mathematics. |
Text(s): | Linear Algebra | Edition: 4; Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; ISBN: 9780130084514 |
Description: |
Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors. Additional Notes: This is a proof-based course. It will cover Chapters 1-4 and the first two sections of Chapter 5. Topics include systems of linear equations, vector spaces and linear transformations (developed axiomatically), matrices, determinants, eigenvectors and diagonalization. |
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Math 4378/6309 - Advanced Linear Algebra II
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Prerequisites: | MATH 4377 |
Text(s): | Linear Algebra, Fourth Edition, by S.H. Friedberg, A.J Insel, L.E. Spence,Prentice Hall, ISBN 0-13-008451-4; 9780130084514 |
Description: |
Similarity of matrices, diagonalization, Hermitian and positive definite matrices, normal matrices, and canonical forms, with applications. Instructor's Additional notes: This is the second semester of Advanced Linear Algebra. I plan to cover Chapters 5, 6, and 7 of textbook. These chapters cover Eigenvalues, Eigenvectors, Diagonalization, Cayley-Hamilton Theorem, Inner Product spaces, Gram-Schmidt, Normal Operators (in finite dimensions), Unitary and Orthogonal operators, the Singular Value Decomposition, Bilinear and Quadratic forms, Special Relativity (optional), Jordan Canonical form. |
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Math 4380 - A Mathematical Introduction to Options | |
Prerequisites: | MATH 2433 and MATH 3338. |
Text(s): | An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation | Edition: 1; Desmond Higham; 9780521547574 |
Description: | Arbitrage-free pricing, stock price dynamics, call-put parity, Black-Scholes formula, hedging, pricing of European and American options. |
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Math 4389 - Survey of Undergraduate Mathematics | |
Prerequisites: | MATH 3330, MATH 3331, MATH 3333, and three hours of 4000-level Mathematics. |
Text(s): | Instructor notes |
Description: | A review of some of the most important topics in the undergraduate mathematics curriculum. |
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MATH 5330 - Abstract Algebra
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Prerequisites: | Graduate standing. |
Text(s): |
Abstract Algebra , A First Course by Dan Saracino. Waveland Press, Inc. ISBN 0-88133-665-3 |
Description: |
Groups, rings and fields; algebra of polynomials, Euclidean rings and principal ideal domains. Does not apply toward the Master of Science in Mathematics or Applied Mathematics. Other Notes: This course is meant for students who wish to pursue a Master of Arts in Mathematics (MAM). Please contact me in order to find out whether this course is suitable for you and/or your degree plan. Notice that this course cannot be used for MATH 3330, Abstract Algebra. |
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MATH 5332 - Differential Equations
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Prerequisites: | Graduate standing. MATH 5331. |
Text(s): | The text material is posted on Blackboard Learn, under "Content". |
Description: |
First-order equations, existence and uniqueness theory; second and higher order linear equations; Laplace transforms; systems of linear equations; series solutions. Theory and applications emphasized throughout. Applies toward the Master of Arts in Mathematics degree; does not apply toward the Master of Science in Mathematics or the Master of Science in Applied Mathematics degrees. |
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Prerequisites: | Graduate standing. MATH 5333 or consent of instructor. |
Text(s): | TBA |
Description: |
Complex numbers, holomorphic functions, linear transformations, Cauchy integral theorem and residue theorem |
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Prerequisites: | Graduate standing. Math 2331 linear algebra or equivalent. |
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 finite-difference approximation to a two-points boundary value problem. This is an introductory course and will be a mix of mathematics and computing. |
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Prerequisites: | Graduate standing. MATH 2433, or consent of instructor. |
Text(s): | TBA |
Description: |
Curves, arc-length, curvature, Frenet formula, surfaces, first and second fundamental forms, Guass’ theorem egregium, geodesics, minimal surfaces. Does not apply toward the Master of Science in Mathematics or Applied Mathematics. |
MATH 5341 - Mathematical Modeling
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Prerequisites: | Graduate standing. Three semesters of calculus or consent of instructor. |
Text(s): | TBD |
Description: |
Proportionality and geometric similarity, empirical modeling with multiple regression, discrete dynamical systems, differential equations, simulation and optimization. Computing assignments require only common spreadsheet software and VBA programming. |
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MATH 5385 - Statistics
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Prerequisites: | Graduate standing |
Text(s): | Two semesters of calculus and one semester of linear algebra or consent of instructor. |
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., R or Matlab) will be given. Applies toward the Master of Arts in Mathematics degree; does not apply toward Master of Science in Mathematics or the Master of Science in Applied Mathematics degrees. |
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MATH 6303 - Modern Algebra II
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Prerequisites: |
Graduate standing. MATH 4333 or MATH 4378 Additional Prerequisites: students should be comfortable with basic measure theory, groups rings and fields, and point-set topology |
Text(s): |
No textbook is required. |
Description: |
Topics from the theory of groups, rings, fields, and modules. Additional Description: This is primarily a course about analysis on topological groups. The aim is to explain how many of the techniques from classical and harmonic analysis can be extended to the setting of locally compact groups (i.e. groups possessing a locally compact topology which is compatible with their algebraic structure). In the first part of the course we will review basic point set topology and introduce the concept of a topological group. The examples of p-adic numbers and the Adeles will be presented in detail, and we will also spend some time discussing SL_2(R). Next we will talk about characters on topological groups, Pontryagin duality, Haar measure, the Fourier transform, and the inversion formula. We will focus on developing details in specific groups (including those mentioned above), and applications to ergodic theory and to number theory will be discussed. |
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MATH 6308 - Advanced Linear Algebra I
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Prerequisites: | Graduate standing. MATH 2331 and a minimum of 3 semester hours transformations, eigenvalues and eigenvectors. |
Text(s): | Linear Algebra | Edition: 4; Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; ISBN: 9780130084514 |
Description: |
Transformations, eigenvalues and eigenvectors. Additional Notes: This is a proof-based course. It will cover Chapters 1-4 and the first two sections of Chapter 5. Topics include systems of linear equations, vector spaces and linear transformations (developed axiomatically), matrices, determinants, eigenvectors and diagonalization. |
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MATH 6309 - Advanced Linear Algebra II
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Prerequisites: | Graduate standing and MATH 6308 |
Text(s): | Linear Algebra, Fourth Edition, by S.H. Friedberg, A.J Insel, L.E. Spence,Prentice Hall, ISBN 0-13-008451-4; 9780130084514 |
Description: | Similarity of matrices, diagonalization, hermitian and positive definite matrices, canonical forms, normal matrices, applications. An expository paper or talk on a subject related to the course content is required. |
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MATH 6313 - Introduction to Real Analysis II
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Prerequisites: | Graduate standing and MATH 6312. |
Text(s): | Kenneth Davidson and Allan Donsig, “Real Analysis with Applications: Theory in Practice”, Springer, 2010; or (out of print) Kenneth Davidson and Allan Donsig, “Real Analysis with Real Applications”, Prentice Hall, 2001. |
Description: | Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals. An expository paper or talk on a subject related to the course content is required. |
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MATH 6321 - Theory of Functions of a Real Variable
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Prerequisites: |
Graduate standing. MATH 4332 or consent of instructor. Instructor's Prerequisite Notes: MATH 6320 |
Text(s): |
Primary (Required): Real Analysis for Graduate Students, Richard F. Bass Supplementary (Recommended): Real Analysis: Modern Techniques and Their Applications, Gerald Folland (2nd edition); ISBN: 9780471317166. |
Description: |
Lebesque measure and integration, differentiation of real functions, functions of bounded variation, absolute continuity, the classical Lp spaces, general measure theory, and elementary topics in functional analysis. Instructor's Additional Notes: Math 6321 is the second course in a two-semester sequence intended to introduce the theory and techniques of modern analysis. The core of the course covers elements of functional analysis, Radon measures, elements of harmonic analysis, the Fourier transform, distribution theory, and Sobolev spaces. Additonal topics will be drawn from potential theory, ergodic theory, and the calculus of variations. |
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Prerequisites: |
Graduate standing. MATH 3334, MATH 3338 or MATH 3339, and MATH 4378. Students must be in the Statistics and Data Science, MS Program |
Text(s): |
While lecture notes will serve as the main source of material for the course, the following book constitutes a great reference: - ”Statistics and Data Analysis from Elementary to Intermediate” by Tamhane, Ajit and Dunlop, Dorothy ISBN: 0137444265 |
Description: |
Linear models, loglinear models, hypothesis testing, sampling, modeling and testing of multivariate data, dimension reduction. < Course syllabus > |
MATH 6361 - Applicable Analysis
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Prerequisites: |
Graduate standing. |
Text(s): |
Speak to the instructor for textbook information. |
Description: |
Solvability of finite dimensional, integral, differential, and operator equations, contraction mapping principle, theory of integration, Hilbert and Banach spaces, and calculus of variations. |
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MATH 6367 - Optimization Theory
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Prerequisites: | Graduate standing. MATH 4331 and MATH 4377. |
Text(s): |
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Description: |
Constrained and unconstrained finite dimensional nonlinear programming, optimization and Euler-Lagrange equations, duality, and numerical methods. Optimization in Hilbert spaces and variational problems. Euler-Lagrange equations and theory of the second variation. Application to integral and differential equations. Additional Description: This course consists of two parts. The first part is concer- ned with an introduction to Stochastic Linear Programming (SLP) and Dynamic Programming (DP). As far as DP is concerned, the course focuses on the theory and the appli- cation of control problems for linear and nonlinear dynamic systems both in a deterministic and in a stochastic frame- work. Applications aim at decision problems in finance. In the second part, we deal with continuous-time systems and optimal control problems in function space with em- phasis on evolution equations. |
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MATH 6371 - Numerical Analysis
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Prerequisites: | Graduate standing. |
Text(s): | Numerical Mathematics (Texts in Applied Mathematics), 2nd Ed., V.37, Springer, 2010. By A. Quarteroni, R. Sacco, F. Saleri. ISBN: 9783642071010 |
Description: | Ability to do computer assignments. Topics selected from numerical linear algebra, nonlinear equations and optimization, interpolation and approximation, numerical differentiation and integration, numerical solution of ordinary and partial differential equations. |
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Prerequisites: | Graduate standing. Probability/Statistic and linear algebra or consent of instructor. Students must be in Master’s in Statistics and Data Science program. |
Text(s): | TBA |
Description: | Artificial neural networks for automatic classification and prediction. Training and testing of multi-layers perceptrons. Basic Deep Learning methods. Applications to real data will be studied via multiple projects. |
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Prerequisites: | Graduate standing.Linear Algebra, Real Analysis (MATH 4331-4332), Probability. |
Text(s): | TBA- Please contact the instructor |
Descriptions: |
Catalog Description: (this description is currently not accurate. Please use the instructor's description below) Instructor's Description (contents of this course have been modified since last year): Lectures F2F & online via Microsoft Teams. Focus on understanding key algorithms for Automatic Learning . Emphasis on mathematical concepts but not on proving theorems. Applications of Machine Learning techniques to real data sets, through homeworks projects. Instructor's Pre-requisites: Basic linear algebra, probability, statistics (all at undergraduate level). |
Prerequisites: | Graduate standing. MATH 6320 or consent of instructor. |
Text(s): | TBA |
Description: | Random variables, conditional expectation, weak and strong laws of large numbers, central limit theorem, Kolmogorov extension theorem, martingales, separable processes, and Brownian motion. |
MATH 6383 - Statistics
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Prerequisites: | Graduate standing. MATH 3334, MATH 3338 and MATH 4378. |
Text(s): |
Recommended Text: John A. Rice : Mathematical Statistics and Data Analysis, 3rd editionBrooks / Cole, 2007. ISBN-13: 978-0-534-39942-9. Reference Texts: |
Description: |
Catalog Description: A survey of probability theory, probability models, and statistical inference. Includes basic probability theory, stochastic processes, parametric and nonparametric methods of statistics. |
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MATH 6397 (19706) - Computation & Math Methods in Data Science
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Prerequisites: | Graduate standing. TBA |
Text(s): |
TBA |
Instructor's Description: |
TBA |
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MATH 6397 (19707) - Applied & Computational Topology
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Prerequisites: | Graduate standing. TBA |
Text(s): |
TBA |
Instructor's Description: | TBA |
MATH 6397 (19708) - Quantum Information and Computation
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Prerequisites: | Graduate standing. |
Text(s): |
Recommended: - M.Nielsen, I.Chuang, "Quantum computation and quantum information", Cambridge university press, 2010 |
Description: |
During the course we will cover the basics of quantum mechanics (qubits, gates, channels), universal quantum computation, quantum teleportation and other protocols, basics of quantum error-correction, and quantum algorithms (Shor's algorithm, Grover's algorithm). We will practice some of the protocols on the open access quantum computer chip made available online. No knowledge of quantum mechanics, computer science or information theory is needed. Knowledge of linear algebra and the basics of probability and complex numbers are required |
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Prerequisites: | Graduate standing. Graduate Probability |
Text(s): | The main book for the class – “Stochastic Methods A Handbook for the Natural and Social Sciences” by C. Gardiner |
Description: |
This class will cover Continuous-Time Markov Chains (first half) and Brownian Motion/Stochastic Differential Equations (second half). The first half is more relevant to math biology and application of queueing theory, the second half is also relevant for mathematical finance. We will consider math bio applications in the first half and financial applications in the second half. |
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Prerequisites: | Graduate standing. Graduate Probability. |
Text(s): |
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Description: |
This is an introductory course on Bayesian statistics for graduate students. The course introduces the Bayesian paradigm and focus on Bayesian modeling, computation, and inference. We first convey the ideology of Bayesian statistics which is a particular approach to statistical inference that differs philosophically and operationally from the classic frequentist approach. We then define Bayesian inference and discuss its advantages. Detailed applications are illustrated using some classical models, including binomial, Poisson, univariate normal, multivariate normal model, and linear regression. We go through each step of building Bayesian hierarchical models and apply Bayes’ theorem to derive posterior distributions. To inference on posterior distributions, MCMC algorithm is introduced as a modern method of approximating posteriors |
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Prerequisites: | Graduate standing. TBA |
Text(s): | TBA |
Description: |
TBA |
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Prerequisites: | Graduate standing. TBA |
Text(s): | TBA |
Description: |
TBA |
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Prerequisites: | Graduate standing. TBA - |
Text(s): | TBA |
Description: |
TBA |
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MATH 7321 - Functional Analysis- TBD
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Prerequisites: | Graduate standing. MATH 7320 or instructor consent |
Text(s): | W. Rudin, Functional Analysis, 2nd edition, McGraw Hill, 1991 |
Description: | Catalog Description: This course is part of a two semester sequence covering the main results in functional analysis, including Hilbert spaces, Banach spaces, and linear operators on these spaces. Instructor's Description: This is a continuation of what was discussed in 7320. The second semester will mostly be a more technical development of the theory of linear operators on Hilbert space and related subjects, including topics relevant in quantum theory, such as positivity and states. Some of the main topics covered include: Banach algebras and the Gelfand transform. C*-algebras and the functional calculus for normal operators. The spectral theorem for normal operators. Trace, Hilbert-Schmidt, and Schatten classes. |
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Prerequisites: | Graduate standing. MATH 6320 |
Text(s): | TBD |
Description: | Catalog Description: Ergodic theory, topological and symbolic dynamics, statistical properties, infinite-dimensional dynamical systems, random dynamical systems, and themodynamic formalism. Instructor's Description: TBA |