MATH 512: Analysis II | Credits: 3 | − Description | − Sections |
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. Texts: Real Analysis by Royden
ISBN: 9780024041517 Assessments: TBA Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent. |

000 | MSC: E406 | MW 8:30am - 9:45am | Shanshuang Yang | max 16 |

MATH 516: Numerical Analysis II | Credits: 3 | − Description | − Sections |
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. Texts: Numerical Mathematics by Quarteroni, Sacco and Saleri ISBN: 9783540346586 Assessments: TBA 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.
Prerequisites: This is a "hands on" course and students will be required to demonstrate their understanding of the concepts
through programming assignments in MATLAB/Octave (help will be given for the novice programmer). |

000 | MSC: W302 | MW 1:00pm - 2:15pm | Alessandro Veneziani | max 16 |

MATH 522: Algebra II | Credits: 3 | − Description | − Sections |
Content: Continuation of 521. Topics: Modules, especially modules over a principal ideal domain, fields, Galois theory, representation of finite groups, Commutative algebra. Texts: Galois Theory by Stewart ISBN: 9781482245820 Assessments: TBA Prerequisites: Math 521. |

000 | MSC: E406 | MW 11:30am - 12:45pm | Suresh Venapally | max 16 |

MATH 544: Algebraic Topology II | Credits: 3 | − Description | − Sections |
Content: Singular, simplicial and cellular homology, long exact sequences in homology, Mayer-Vietoris sequences, excision, Euler characteristic, degrees of maps, Borsuk-Ulam theorem, Lefschetz fixed point theorem, cohomology, universal coefficient theorem, the cup product, Poincare duality Texts: Algebraic Topology by Hatcher ISBN: 9780521795401 Assessments: TBA Prerequisites: TBA |

000 | MSC: E406 | TuTh 11:30am - 12:45pm | David Zureick-Brown | max 16 |

MATH 545: Introduction to Differential Geometry I | Credits: 3 | − Description | − Sections |
Content: TBA Texts: Riemannian Manifolds: An Introduction to Curvature by Lee ISBN: 9780387983226 Assessments: TBA Prerequisites: TBA |

000 | MSC: W306 | MW 10:00am - 11:15am | David Borthwick | max 20 |

MATH 577R: Seminar in Combinatorics | Credits: 3 | − 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: W301 | M 4:00pm - 4:50pm | Dwight Duffus | max 30 |

MATH 578R: Seminar in Algebra | Credits: 3 | − Description | − Sections |
Content: Research topics in algebra of current interest to faculty and students. Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W304 | Tu 4:00pm - 4:50pm | Victoria Powers | max 30 |

001 | MSC: W301 | W 4:00pm - 5:00pm | David Zureick-Brown | max 20 |

MATH 579R: Seminar in Analysis | Credits: 1 - 9 | − Description | − Sections |
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W306 | F 1:00pm - 1:50pm | James Nagy | max 30 |

001 | MSC: W302 | Tu 4:00pm - 4:50pm | Vladimir Oliker | max 20 |

MATH 590: Teaching Seminar | Credits: 3 | − Description | − Sections |
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. Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E406 | F 2:00pm - 2:50pm | Bree Ettinger | max 15 |

MATH 597R: Directed Study | Credits: 1 - 9 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

00P | | | Faculty (TBA) | max 999 |

MATH 599R: Master's Thesis Research | Credits: 1 - 9 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

00P | MSC: ----- | | Faculty (TBA) | |

MATH 787R: Topics in Combinatorics | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E408 | TuTh 10:00am - 11:15am | Vojtech Rodl | max 16 |

MATH 788R: Topics in Algebra: Algebraic Groups | Credits: 3 | − Description | − Sections |
Content: The course will consist of the following distinct components :
1. Structure theory of reductive groups over algebraically closed fields : Overview of objects and notions such as tori, solvable groups, Lie algebras, Jordan decomposition. Conjugacy of Borel subgroups and maximal tori, root systems, Bruhat decomposition, representation and classification of semi simple groups in terms of root systems.
2. Galois cohomology of linear algebraic groups : Classical groups and algebras with involutions, Steinberg's theorem, dimension two fields and Serre's conjecture, cohomological invariants and a discussion on some open questions in this area. Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E408 | MW 1:00pm - 2:15pm | Raman Parimala | max 16 |

MATH 789R: Topics in Analysis: Bayesian Inverse Problems and Uncertainty Qualification | Credits: 3 | − Description | − Sections |
Content: This special topics course introduces basic concepts as well as more recent advances in Bayesian methods for solving inverse problems. Motivated by real-world applications, we will contrast the frequentists and the Bayesian approach to inverse problems and emphasize the role of regularization/priors. Also, we will explore sampling techniques used for uncertainty quantification. Texts: Somersalo and Calvetti, An Introduction to Bayesian Scientific Computing, Springer, 2007
Kaipio and Somersalo, Statistical and Computational Inverse Problems, Springer 2004 Assessments: TBA Prerequisites: TBA |

000 | MSC: E406 | MW 3:00pm - 4:15pm | Lars Ruthotto | max 16 |

MATH 797R: Directed Study | Credits: 1 - 9 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

00P | | | Faculty (TBA) | |

MATH 799R: Dissertation Research | Credits: 1 - 9 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

00P | | | Faculty (TBA) | |