2024 - Spring Semester - University of Houston
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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.

(UNDER CONSTRUCTION - 1/16/24)

 

SENIOR UNDERGRADUATE COURSES 

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



GRADUATE ONLINE COURSES 

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

 

GRADUATE COURSES 
 

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  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

 

MSDS Courses (MSDS Students Only)

 

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

Prerequisites:

MATH 3331 and BIOL 3306 or consent of instructor.

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)

  • An Introduction to Systems Biology, 2/e, U. Alon (an excellent, recently updated text on the “design principles of biological circuits”)
  • Random Walks in Biology, H.C. Berg (a classic introduction to the applicability of diffusive processes and the Reynolds number at the cellular scale)
  • Mathematical Models in Biology, L. Edelstein-Keshet (a systematic development of discrete, continuous, and spatially distributed biological models)
  • Nonlinear Dynamics and Chaos, S.H. Strogatz (a very readable introduction to phase-plane analysis and bifurcation theory in dynamical systems with an emphasis on visual thinking; contains numerous applications in biology)
  • Thinking in Systems, D.H. Meadows (a lay introduction to control systems and analyzing parts-to-whole relationships, their organizational principles, and sensitivity in their design)
  • Adaptive Control Processes: A Guided Tour, R. Bellman (a classic, more technical introduction to self-regulating systems, feedback control, decision processes, and dynamic programming)
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.

Instructor's description: An introduction to mathematical methods for modeling biological dynamical systems. This course will survey canonical models of biological systems using the mathematics of calculus, differential equations, logic, matrix theory, and probability.

Applications will span several spatial orders-of-magnitude, from the microscopic (sub-cellular), to the mesoscopic (multi-cellular tissue and organism) and macroscopic (population-level: ecological, and epidemiological) scales. Specific applications will include biological-signaling diffusion, enzyme kinetics, genetic feedback networks, population dynamics, neuroscience, and the dynamics of infectious diseases. Optional topics (depending on schedule and student interest) may be chosen from such topics as: game theory, artificial intelligence and learning, language processing, economic multi-agent modeling, Turing systems, information theory, and stochastic simulations.

The course will be taught from two complementary perspectives:
(1) critical analysis of biological systems’ modeling using applicable mathematical tools, and
(2) a deeper understanding of mathematical theory, illustrated through biological applications.

Relevant mathematical theory for each course section will be reviewed from first principles, with an emphasis on bridging abstract formulations to practical modeling techniques and dynamical behavior prediction.

The course will include some programming assignments, to be completed in Matlab or Python programming languages (available free through UH Software and public domain, respectively). However, advanced programming techniques are not required, and resources for introduction to these languages will be provided.

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Math 4315 - Graph Theory with Applications
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
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
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
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
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
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
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
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 DescriptionRoot 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
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 DescriptionRoot 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
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
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
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
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 3330MATH 3331MATH 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.

 


ONLINE GRADUATE COURSES

<< back to Grad Online>>
MATH 5330 - Abstract Algebra
Prerequisites: Graduate standing. 
Text(s):

Abstract Algebra , A First Course by Dan Saracino. Waveland Press, Inc. ISBN 0-88133-665-3
(You can use the first edition. The second edition contains additional chapters that cannot be covered in this course.)

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. 

<< back to Grad Online >>
MATH 5332 - Differential Equations
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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MATH 5334 - Complex Analysis
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

 

<< back to Grad Online >>
MATH 5344 - Introduction to Scientific Computing
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.

 

<< back to Grad Online >>
MATH 5350 - Introduction to Differential Geometry
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
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
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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GRADUATE COURSES

  

MATH 6303 - Modern Algebra II
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.

  
<< back to Grad >>
MATH 6308 - Advanced Linear Algebra I
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.

 

  

<< back to Grad >>
MATH 6309 - Advanced Linear Algebra II 
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
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
Prerequisites:

Graduate standingMATH 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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MATH 6359 (14771/15462)- Applied Statistics & Multivariate Analysis
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
- ”Applied Multivariate Statistics with R”, by Daniel Zelterman, ISBN: 9783319140926
- ”Applied Multivariate Statistical Analysis, sixth edition”, by Richard A. Johnson and Dean W. Wichern, published by Pearson.
- Rstudio: Make sure to download R and RStudio (which can’t be installed without R) before the course starts. Use the link R download to download R frst, then RStudio download to download it from the mirror appropriate for your platform.

Description:

Linear models, loglinear models, hypothesis testing, sampling, modeling and testing of multivariate data, dimension reduction.

< Course syllabus >

 

 

 

MATH 6361 - Applicable Analysis
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
Prerequisites: Graduate standing. MATH 4331 and MATH 4377.
Text(s):
  •  D.P. Bertsekas; Dynamic Programming and Optimal Con- trol, Vol. I, 4th Edition. Athena Scientific, 2017, ISBN-10: 1-886529-43-4
  • J.R. Birge and F.V. Louveaux; Introduction to Stochastic Programming. Springer, New York, 1997, ISBN: 0-387-98217-
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
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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MATH 6373 (14772) - Deep Learning and Artificial Neural Networks
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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MATH 6377 - Numerical Analysis
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). 

 

 

MATH 6381 (14970/17066) - Information Visualization
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
Prerequisites: Graduate standingMATH 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:

-P. MuCullagh and J.A. Nelder: Generealized Linear Models, 2nd ed. 1999 Chapman Hall/CRC. ISBN: 978-0412317606

-Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining, Timothy J. Robinson, Generalized Linear Models: with Applications in Engineering and the Sciences, 2nd ed. Wiley, 2010. ISBN: 978-0-470-45463-3.

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.

Instructor's Description: This course is designed for graduate students who have been exposed to basic probability and statistics and would like to learn more advanced statistical theory and techniques in modelling data of various types, including continuous, binary, counts and others. The selected topics will include basic probability distributions, likelihood function and parameter estimation, hypothesis testing, regression models for continuous and categorical response variables, variable selection methods, model selection, large sample theory, shrinkage models, ANOVA and some recent advances

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MATH 6397 (19706) - Computation & Math Methods in Data Science
Prerequisites: Graduate standing. TBA
 Text(s):

 TBA

 Instructor's Description:

 TBA

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MATH 6397 (19707) - Applied & Computational Topology
Prerequisites: Graduate standing. TBA
Text(s):

 TBA

Instructor's Description:  TBA

 
MATH 6397 (19708) - Quantum Information and Computation
Prerequisites:  Graduate standing
Text(s):

 Recommended:

- M.Nielsen, I.Chuang, "Quantum computation and quantum information", Cambridge university press, 2010
- M.Wilde, "From Classical to Quantum Shannon Theory" arXiv:1106.1445

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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MATH 6397 (19709) - Stochastic Process
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.

This is an applied class where we will consider various topics for Continuous-Time Markov Chains (CTMC) and Stochastic Differential Equations (SDEs) driven by Brownian motion (diffusions). There are many books on CTMC. We will mostly use notes for the first half. The book is more relevant for the second half of the class. It is very applied, this is one of the most applied books on stochastic processes.

The goal of this class is to cover main background material and consider various applications. However, we will not concentrate on proofs and often consider examples that explain mathematical concepts in the context of a particular example and can be generalized to other cases. In particular, we will consider applications to biology and finance (especially in the second half on stochastic differential equations). We will discuss numerical methods for stochastic processes, but this is not a computational class, no computational assignments will be given.

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MATH 6397 (19739/20173) - Bayesian Statistics
Prerequisites:  Graduate standing. TBA
Text(s):  TBA
Description:

 TBA

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MATH 6397 (19750) - Case Studies In Data Analysis
Prerequisites:  Graduate standing. TBA
Text(s):  TBA
Description:

 TBA

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MATH 6397 (25618) - Image Processing Methods
Prerequisites:  Graduate standing. TBA
Text(s):  TBA
Description:

 TBA

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MATH 6397 (20174) - Financial & Commodity Markets
Prerequisites:  Graduate standing. TBA -
Text(s):  TBA
Description:

 TBA

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MATH 7321 - Functional Analysis- TBD
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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MATH 7326 - Dynamical Systems
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

 

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