# Graduate classes, Fall 2012, Mathematics

 MATH 511: Analysis I Credits: 4 − Description − Sections
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: John B. Conway, "Functions of one complex variables I", Springer Publishing. ISBN: 3-540-90328-3, 2nd edition.
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 10:00am - 11:15amShanshuang Yangmax 16
 MATH 515: Numerical Analysis I Credits: 4 − Description − Sections
Content: This course covers topics in numerical linear algebra, including: matrix factorizations such as LU, QR and SVD; direct and iterative methods for solving linear systems and least squares problems; numerical approaches to solving eigenvalue problems; problem sensitivity and algorithm stability. A solid theoretical background of algorithms will be balanced with practical implementation issues.
Texts: Gene H. Golub, "Matrix Computations", Johns Hopkins Studies in Mathematical Sciences, 3rd Edition.
Assessments: TBA
Prerequisites: TBA
000MSC: E406TuTh 1:00pm - 2:15pmJames Nagymax 16
 MATH 521: Algebra I Credits: 4 − Description − Sections
Content: An introduction to fundamental algebraic concepts including: Groups, homomorphisms, the action of a group on a set, Sylow theorems, group representations and characters, rings, ring homomorphisms, and basics on commutative rings.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E406MWF 9:35am - 10:25amSuresh Venapallymax 16
 MATH 535: Combinatorics I Credits: 4 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E406MW 11:45am - 1:00pmRon Gouldmax 16
 MATH 550: Functional Analysis Credits: 4 − Description − Sections
Content: An introduction to concepts and applications including: metric and normed spaces. Sobolev spaces, linear operators, and functionals, compactness in metric and normed spaces. Fredholm's solvability theory, spectral theory, calculus in metric and normed spaces, selected application.
Texts: MaaCluer. "Elementary Functional Analysis", Springer Publishing (2009).
Assessments: TBA
Prerequisites: TBA
000MSC: W306MWF 10:40am - 11:30amDavid Borthwickmax 16
 MATH 561: Matrix Analysis Credits: 4 − Description − Sections
Content: Main topics: Eigenvalues and eigenvectors of matrices, invariant subspaces, Schur triangular form, diagonalizable matrices, minimal polynomial, characteristic polynomial, Hamilton-Cayley Theorem, localization of eigenvalues, Gerschgorin's Theorem. Unitary, Hermitian and skew-Hermitian matrices. Normal matrices and the Spectral Theorem. Orthogonalization. Householder matrices and the QR factorization. Moore-Penrose pseudoinverse. Applications to the solution of under- and over-determined systems of linear equations. Other generalized inverses. Applications to data fitting (least-squares approximation). The Singular Value Decomposition. Matrix norms: spectral norm and Frobenius norm. Solution to matrix nearness problems. Applications to signal processing and information retrieval. Jordan canonical form. An algorithmic proof. Powers of matrices. Matrix functions. Applications to systems of differential equations. Bilinear and quadratic forms. Hermitian forms. Congruence. Sylvester's Law of Inertia. Rayleigh's principle. Courant-Fischer Theorem. Positive definite and semidefinite matrices. Applications to statistics (covariance matrices) and numerical analysis (PDE's). Additional topics: Nonnegative matrices. The spectral radius. Positive matrices. Directed graphs. Nonnegative irreducible matrices. Perron-Frobenius Theorem. M-matrices. Applications to probability theory (Markov chains), economics (Leontiev's input-output model), and numerical analysis (iterative methods for linear systems). Structured matrices: circulant, Toeplitz, Hankel, Cauchy, Vandermonde, others. Block generalizations. Applications in signal processing, image processing, and numerical analysis (PDE's, interpolation).
Texts: R. A. Horn and C. R. Johnson, "Matrix Analysis", Cambridge University Press (1985; 1991).
Assessments: TBA
Prerequisites: TBA
000MSC: E406TuTh 11:30am - 12:45pmMichele Benzimax 16
 MATH 577R: Seminar in Combinatorics Credits: 4 − Description − Sections
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
000MSC: W303F 4:00pm - 5:00pmDwight Duffusmax 30
 MATH 578R: Seminar in Algebra Credits: 1 - 12 − Description − Sections
Content: Research topics in algebra of current interest to faculty and students.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W306W 3:00pm - 4:00pmRaman Parimalamax 16
 MATH 579R: Seminar in Analysis Credits: 4 − Description − Sections
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W306W 12:50pm - 1:40pmAlessandro Venezianimax 30
001MSC: W301Tu 4:00pm - 5:00pmVladimir Olikermax 30
 MATH 597R: Directed Study Credits: 1 - 12 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
0ONOKen Onomax 999
DUFFMSC: -----Dwight Duffusmax 999
GOULMSC: OtherRon Gouldmax 999
NAGYMSC: -----James Nagymax 999
VENEMSC: -----Alessandro Venezianimax 999
YANGMSC: -----Shanshuang Yangmax 999
 MATH 772: Numerical Partial Differential Equations Credits: 4 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 2:30pm - 3:45pmAlessandro Venezianimax 16
 MATH 787R: Topics in Combinatorics: Hypergraphs Credits: 4 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 8:30am - 9:45amVojtech Rodlmax 16
 MATH 788R: Topics in Algebra: Stacks Credits: 4 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 1:00pm - 2:15pmDavid Zureick-Brownmax 16
 MATH 797R: Directed Study Credits: 1 - 12 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
BENZMSC: -----Michele Benzimax 999
BORTMSC: -----David Borthwickmax 999
GARIMSC: -----Skip Garibaldimax 999
NAGYMSC: -----James Nagymax 999
RAMAMSC: OtherRaman Parimalamax 999
RODLMSC: -----Vojtech Rodlmax 999
VENEMSC: -----Alessandro Venezianimax 999
 MATH 799R: Dissertation Research Credits: 1 - 12 − Description − Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
BENZMSC: -----Michele Benzimax 999
BORTMSC: -----David Borthwickmax 999
GOULMSC: -----Ron Gouldmax 999
NAGYMSC: -----James Nagymax 999