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: Linear algebra, including canonical forms, infinite-dimensional vector spaces, tensor products, and multilinear algebra. Group theory including group actions and representations.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC W303 MW      1:00PM - 2:15PM Raman Parimala 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
MATH550 Functional Analysis Credits: 3
Content: An introduction to concepts and applications including: metric and normed spaces, Hilbert and Banach spaces, linear operators and functionals, compactness in metric and normed spaces, Fredholm's solvability theory, spectral theory, calculus in metric and normed spaces, selected applications.
Texts: TBA
Assessments: TBA
Prerequisites: Math 511, Math 512.
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E408 MW      11:30AM - 12:45PM David Borthwick 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
MATH579R Seminar in Analysis Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
      
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