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 | | 000 | MSC: E408 | TuTh 10:00am - 11:15am | Shanshuang Yang | max 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 | | 000 | MSC: E406 | TuTh 1:00pm - 2:15pm | James Nagy | max 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 | | 000 | MSC: E406 | MWF 9:35am - 10:25am | Suresh Venapally | max 16 | | MATH 535: Combinatorics I | Credits: 4 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | 000 | MSC: E406 | MW 11:45am - 1:00pm | Ron Gould | max 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 | | 000 | MSC: W306 | MWF 10:40am - 11:30am | David Borthwick | max 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 | | 000 | MSC: E406 | TuTh 11:30am - 12:45pm | Michele Benzi | max 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 | | 000 | MSC: W303 | F 4:00pm - 5:00pm | Dwight Duffus | max 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 | | 000 | MSC: W306 | W 3:00pm - 4:00pm | Raman Parimala | max 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 | | 000 | MSC: W306 | W 12:50pm - 1:40pm | Alessandro Veneziani | max 30 | | 001 | MSC: W301 | Tu 4:00pm - 5:00pm | Vladimir Oliker | max 30 | | MATH 597R: Directed Study | Credits: 1 - 12 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | 0ONO | | | Ken Ono | max 999 | | DUFF | MSC: ----- | | Dwight Duffus | max 999 | | GOUL | MSC: Other | | Ron Gould | max 999 | | NAGY | MSC: ----- | | James Nagy | max 999 | | VENE | MSC: ----- | | Alessandro Veneziani | max 999 | | YANG | MSC: ----- | | Shanshuang Yang | max 999 | | MATH 772: Numerical Partial Differential Equations | Credits: 4 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | 000 | MSC: E408 | TuTh 2:30pm - 3:45pm | Alessandro Veneziani | max 16 | | MATH 787R: Topics in Combinatorics: Hypergraphs | Credits: 4 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | 000 | MSC: E408 | TuTh 8:30am - 9:45am | Vojtech Rodl | max 16 | | MATH 788R: Topics in Algebra: Stacks | Credits: 4 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | 000 | MSC: E408 | TuTh 1:00pm - 2:15pm | David Zureick-Brown | max 16 | | MATH 797R: Directed Study | Credits: 1 - 12 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | BENZ | MSC: ----- | | Michele Benzi | max 999 | | BORT | MSC: ----- | | David Borthwick | max 999 | | GARI | MSC: ----- | | Skip Garibaldi | max 999 | | NAGY | MSC: ----- | | James Nagy | max 999 | | RAMA | MSC: Other | | Raman Parimala | max 999 | | RODL | MSC: ----- | | Vojtech Rodl | max 999 | | VENE | MSC: ----- | | Alessandro Veneziani | max 999 | | MATH 799R: Dissertation Research | Credits: 1 - 12 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA | | BENZ | MSC: ----- | | Michele Benzi | max 999 | | BORT | MSC: ----- | | David Borthwick | max 999 | | GOUL | MSC: ----- | | Ron Gould | max 999 | | NAGY | MSC: ----- | | James Nagy | max 999 | | OLIK | MSC: ----- | | Vladimir Oliker | max 999 | | ONO | MSC: ----- | | Ken Ono | max 999 | | RAMA | MSC: ----- | | Raman Parimala | max 999 | | RODL | MSC: ----- | | Vojtech Rodl | max 999 | | VENE | MSC: ----- | | Alessandro Veneziani | max 999 | | YANG | MSC: ----- | | Shanshuang Yang | max 999 |
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