Course Atlas
Graduate MATH Courses
| MATH511 | Analysis I | Credits: 3 | ||
|---|---|---|---|---|
| Content: An introduction to fundamental analytic concepts including: The complex number system, geometry and topology of the complex plane, analytic functions, conformal mappings, complex integration, and singularities. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC E406 | TuTh 10:00AM - 11:15AM | Shanshuang Yang | 18 |
| MATH515 | Numerical Analysis I | Credits: 3 | ||
|---|---|---|---|---|
| Content: Course will cover fundamental parts of numerical linear algebra including matrix factorizations, solution of linear systems and least-squares problems, the calculation of eigenvalues and eigenvectors, and basic notions on iterative methods for large-scale matrix problems. Issues pertaining to conditioning and numerical stability will be thoroughly analyzed. We will also point out and use links to other mathematical and computer science disciplines such as mathematical modelling, computer architectures and parallel computing. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC W303 | MW 10:00AM - 11:15AM | Yuanzhe Xi | 30 |
| MATH521 | Algebra I | Credits: 3 | ||
|---|---|---|---|---|
| Content: Finite groups, Sylow theorems, principal ideal domains and unique factorisation domains, structure theorem for modules over principal ideal domains and consequences in linear algebra, tensor products, symmetric and exterior algebras, the functors Ext and Tor. | ||||
| Texts: D.S. Dummit, R.M Foote, Abstract Algebra, Wiley 2003 | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC W303 | MW 1:00PM - 2:15PM | Parimala Raman | 30 |
| MATH528 | Algebraic Number Theory | Credits: 3 | ||
|---|---|---|---|---|
| Content: The course will cover local fields, local class field theory, and the statements and applications of global class field theory. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC E408 | TuTh 11:30AM - 12:45PM | David Zureick-Brown | 18 |
| MATH531 | Graph Theory I | Credits: 3 | ||
|---|---|---|---|---|
| Content: The course will cover some fundamental concepts in structural and extremal graph theory, including matchings, connectivity, graph planarity, graph colorings, flows, minors and topological minors, Hamiltonian cycles and paths, Ramsey Theory, and Szemeredi's regularity lemma. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC E406 | MW 2:30PM - 3:45PM | Hao Huang | 18 |
| MATH545 | Introduction to Differential Geometry I | Credits: 3 | ||
|---|---|---|---|---|
| Content: An introduction to Riemannian geometry. The main goal is an understanding of the nature and uses of curvature, which is the local geometric invariant that measures the departure from Euclidean geometry. No previous experience in differential geometry is assumed, and we will rely heavily on pictures of surfaces in 3-space to illustrate key concepts. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC E408 | TuTh 1:00PM - 2:15PM | Vladimir Oliker | 18 |
| MATH577R | Seminar in Combinatorics | Credits: 3 | ||
|---|---|---|---|---|
| Content: The seminar in combinatorics is a research seminar for students and faculty. It runs weekly, and features speakers from outside Emory who come to talk about topics of interest to the Emory faculty. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC E406 | M 4:00PM - 5:00PM | Dwight Duffus | 18 |
| MATH578R | Seminar in Algebra | Credits: 1-9 | ||
|---|---|---|---|---|
| Content: Research topics in algebra of current interest to faculty and students. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC W303 | Tu 4:00PM - 4:50PM | David Zureick-Brown | 20 |
| MATH579R | Seminar in Analysis | Credits: 3 | ||
|---|---|---|---|---|
| Content: TBA | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC W303 | F 2:00PM - 3:00PM | Yuanzhe Xi | 30 |
| 2 | PAIS 220 | Tu 4:00PM - 4:50PM | Vladimir Oliker | 20 |
| MATH590 | Teaching Seminar | Credits: 3 | ||
|---|---|---|---|---|
| Content: This seminar will concentrate on effective teaching techniques in mathematics. Topics included will include: General advice for new TA's. General advice for International TA's. Students will present several practice lectures over different levels of material. They will receive practice on quiz and test preparation. Syllabus information on courses most likely to be taught by new TA's will be supplied. General professional development information will also be included. | ||||
| Texts: TBA | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC E408 | F 11:00AM - 12:00PM | Juan Villeta-Garcia | 6 |
| MATH789 | Topics in Analysis | Credits: 3 | ||
|---|---|---|---|---|
| Content: The use of quantitative methods in traditional and new fields of engineering and science urges the introduction of specific techniques for merging the back- ground knowledge of mathematical and physical models with the foreground knowledge of data, measures and images. This is a critical step for moving from ”simulation” to ”assimilation”, i.e. from a segregated quantitative use of different information to an integrated one. This is expected to reduce the impact of modeling error as well as measurement noise, and to quantify the reliability of the numerical results, in a process that is somehow ”dual” to supervised machine-learning, where models are used to guide the interpretation of data. Diverse methods are available for this aim, ranging from variational deterministic techniques - based on constrained minimization approaches - to stochastic methods, like Kalman filtering, and their combination. The course will cover the most popular techniques and some of their recent customizations. In the second part of the course, a showcase of different applications ranging from the geophysical and environmental fields to human sciences will be presented. The course will be completed by Lab sessions with Matlab and FreeFem++. Introduction to data assimilation, uncertainty quantification and inverse problems. Variational Deterministic Data Assimilation Methods. Lagrange multipliers and their use. Statistical Estimation, Sequential data assimilation, Kalman Filters, Bayesian techniques Advanced methods: model reduction, Proper Orthogonal Decomposition, Ensemble Kalman Filter, Hybrid Methods. Applications and case studies: environment, geophysics, medicine, human sciences | ||||
| Texts: Data Assimilation: Methods, Algorithms, and Applications, M. Asch, M. Bocquet, M. Nodet, SIAM PA 2017 + Additional notes and papers indicated in class. | ||||
| Assessments: TBA | ||||
| Prerequisites: TBA | ||||
| Section | Location | Meeting Time | Instructor | Enrollment (max) |
| 1 | MSC W301 | MW 4:00PM - 5:15PM | Alessandro Veneziani | 30 |