Graduate catalog 2018 - 2019, Mathematics

Note: The class catalog is published every two years. Courses listed in the catalog may not be offered in a given term. For class offerings for each semester please click on the "Offerings" links.
MATH 511: Analysis ICredits: 3− Description
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.
MATH 512: Analysis IICredits: 3− Description
Content: Topics will include: Measure and integration theory on the real line as well as on a general measure space, Bounded linear functionals on L^p spaces. If time permits, Sobolev spaces and Fourier transforms will be introduced.
Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
MATH 515: Numerical Analysis ICredits: 3− Description
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.
Particulars: Excellent background in linear algebra is assumed. Some knowledge of computer architectures, programming and elementary numerical analysis is highly desirable.
MATH 516: Numerical Analysis IICredits: 3− Description
Content: This course covers fundamental concepts of numerical analysis and scientific computing. Material includes numerical methods for curve fitting (interpolation, splines, least squares), differentiation, integration, and differential equations. It is assumed that students have a strong background in numerical linear algebra.
Prerequisites: Math 515, undergraduate course work in multivariable calculus and ordinary differential equations. An undergraduate course in numerical analysis would help, but is not absolutely essential.
MATH 521: Algebra ICredits: 3− Description
Content: Linear algebra, including canonical forms, infinite-dimensional vector spaces, tensor products, and multilinear algebra. Group theory including group actions and representations.
Particulars: Text: A.W. Knapp, "Basic algebra", Birkhauser, 2006.
MATH 522: Algebra IICredits: 3− Description
Content: Continuation of 521. Topics: Modules, especially modules over a principal ideal domain, fields, Galois theory, representation of finite groups, Commutative algebra.
Prerequisites: Math 521.
MATH 523: Commutative Algebra & GeometryCredits: 3− Description
MATH 528: Algebraic Number TheoryCredits: 3− Description
MATH 531: Graph Theory ICredits: 3− Description
MATH 532: Graph Theory IICredits: 3− Description
MATH 535: Combinatorics ICredits: 3− Description
MATH 545: Introduction to Differential Geometry ICredits: 3− Description
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.
Particulars: Open to undergraduates with permission of the instructor.
MATH 546: Intro. to Differential Geometry IICredits: 3− Description
Content: An introduction to Riemannian geometry and global analysis. Topics to be covered: Manifolds, Riemannian metrics, Connections, Curvature; Geodesics, Convexity, Topics in Global Analysis.
MATH 547: Differential TopologyCredits: 3− Description
MATH 550: Functional AnalysisCredits: 3− Description
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.
Prerequisites: Math 511, Math 512.
MATH 557: Partial Differential Equations ICredits: 3− Description
MATH 577R: Seminar in CombinatoricsCredits: 3− Description
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.
MATH 578R: Seminar in AlgebraCredits: 1 - 9− Description
Content: Research topics in algebra of current interest to faculty and students.
MATH 579R: Seminar in AnalysisCredits: 3− Description
MATH 590: Teaching SeminarCredits: 3− Description
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.
MATH 788: Topics in AlgebraCredits: 3− Description
MATH 789: Topics in AnalysisCredits: 3− Description
MATH 789R: Topics in Analysis: Numerical Methods for Deep LearningCredits: 3− Description