MATH 511: Analysis I  Credits: 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 II  Credits: 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 411412 sequence or the equivalent. 
MATH 515: Numerical Analysis I  Credits: 3  − Description 
Content: Course will cover fundamental parts of
numerical linear algebra including matrix factorizations,
solution of linear systems and leastsquares problems,
the calculation of eigenvalues and eigenvectors, and
basic notions on
iterative methods for largescale 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 II  Credits: 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 I  Credits: 3  − Description 
Content: Linear algebra, including canonical forms, infinitedimensional 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 II  Credits: 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 & Geometry  Credits: 3  − Description 

MATH 528: Algebraic Number Theory  Credits: 3  − Description 

MATH 531: Graph Theory I  Credits: 3  − Description 

MATH 532: Graph Theory II  Credits: 3  − Description 

MATH 535: Combinatorics I  Credits: 3  − Description 

MATH 545: Introduction to Differential Geometry I  Credits: 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 3space to illustrate key concepts. Particulars: Open to undergraduates with permission of the instructor. 
MATH 546: Intro. to Differential Geometry II  Credits: 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 Topology  Credits: 3  − Description 

MATH 550: Functional Analysis  Credits: 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 I  Credits: 3  − Description 

MATH 577R: Seminar in Combinatorics  Credits: 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 Algebra  Credits: 1  9  − Description 
Content: Research topics in algebra of current interest to faculty and students. 
MATH 579R: Seminar in Analysis  Credits: 3  − Description 

MATH 590: Teaching Seminar  Credits: 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 Algebra  Credits: 3  − Description 

MATH 789: Topics in Analysis  Credits: 3  − Description 

MATH 789R: Topics in Analysis: Numerical Methods for Deep Learning  Credits: 3  − Description 
