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Course Day & Time

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Instructor

Course/Section

Class #

Course Title

Course Day & Time

Rm#

Instructor

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.)

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. 

Course 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.

Instructor's Prerequisite Notes: MATH 6320

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.

While lecture notes will serve as the main source of material for the course, the following book constitutes a great reference:

• 鈥漇tatistics and Data Analysis from Elementary to Intermediate鈥� by Tamhane, Ajit and Dunlop, Dorothy ISBN: 0137444265
• 鈥滱pplied Multivariate Statistics with R鈥�, by Daniel Zelterman, ISBN: 9783319140926
• 鈥滱pplied Multivariate Statistical Analysis, sixth edition鈥�, by Richard A. Johnson and Dean W. Wichern, published by Pearson.
• Rstudio: Make sure to download R and RStudio (which can鈥檛 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.

• Peter Hoff (2009). A first course in Bayesian statistical methods. Springer
• Brian J. Reich & Sujit K. Ghosh (2019). Bayesian Statistical Methods. CRC Press.
• Christian P. Robert (2007). The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. Springer (2nd Edition).

• 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鈥� theorem to derive posterior distributions.
• To inference on posterior distributions, MCMC algorithm is introduced as a modern method of approximating posteriors