MATH 511: Analysis I | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

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

MATH 515: Numerical Analysis I | Credits: 3 | − Description | − Sections |
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. Texts: A. Bjorck, Numerical Methods in Matrix Computations.
Texts in Applied Mathematics 59, Springer, 2015. Assessments: TBA Prerequisites: Excellent background in linear algebra is assumed.
Some knowledge of computer architectures, programming
and elementary numerical analysis is
highly desirable. |

000 | MSC: E408 | TuTh 2:30pm - 3:45pm | Michele Benzi | max 16 |

MATH 521: Algebra I | Credits: 3 | − Description | − Sections |
Content: Linear algebra, including canonical forms, infinite-dimensional vector spaces, tensor products, and multilinear algebra. Group theory including group actions and representations. Texts: TBA Assessments: TBA |

000 | MSC: E406 | MW 10:00am - 11:15am | Suresh Venapally | max 16 |

MATH 543: Algebraic Topology I | Credits: 3 | − Description | − Sections |
Content: Homotopy theory, the fundamental group, free products of groups with amalgamation, Van Kampen's Theorem, covering spaces, classification of surfaces, classifying spaces, higher homotopy groups Texts: TBA Assessments: TBA |

000 | MSC: E408 | MW 1:00pm - 2:15pm | Suresh Venapally | max 16 |

MATH 550: Functional Analysis | Credits: 3 | − Description | − Sections |
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. Texts: Barbara D. MacCluer: Elementary Functional Analysis.
Graduate Texts in Mathematics, Springer, New York, 2008.
Avner Friedman: Foundations of Modern Analysis. Dover, New York, 1982. Assessments: TBA Prerequisites: Math 511, Math 512. |

000 | MSC: E408 | TuTh 10:00am - 11:15am | Michele Benzi | max 16 |

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 |

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 |

000 | MSC: W304 | Tu 4:00pm - 4:50pm | Ken Ono | max 30 |

MATH 579R: Seminar in Analysis | Credits: 1 - 9 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W302 | F 1:00pm - 1:50pm | James Nagy | max 30 |

001 | MSC: W301 | Tu 4:00pm - 4:50pm | Vladimir Oliker | max 30 |

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

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

BENZ | | | Michele Benzi | max 0 |

GOUL | | | Ron Gould | max 0 |

NAGY | | | James Nagy | max 999 |

ONO | | | Ken Ono | max 999 |

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

00P | | | David Zureick-Brown | max 999 |

MATH 771: Numerical Optimization | Credits: 3 | − Description | − Sections |
Content: This course will provide students with an overview of state-of-the-art numerical methods for solving unconstrained, large-scale optimization problems. Algorithm development will be emphasized, including efficient and robust implementations. In addition, students will be exposed to state-of-the-art software that can be used to solve optimization problems. Texts: TBA Assessments: TBA Prerequisites: Mathematics 511-512, 515-516. |

000 | MSC: E406 | MW 1:00pm - 2:15pm | Lars Ruthotto | max 16 |

MATH 787R: Topics in Combinatorics: Hypergraphs | Credits: 3 | − Description | − Sections |
Content: The course will have two components:
(1) A series of lectures on the basics of order theory, including an introduction to finite and infinite partially ordered sets and lattices, topics from combinatorics/set systems such as Sperner theory, uses of ordering to study classes of graphs, digraphs and other relational systems.
The length of time spent on this will depend upon the backgrounds and interests of participants.
(2) Focus on topics from "Graphs and Homomorphisms" by Hell and Nesetril, particularly the lattice of graph types ordered by homomorphism. There will be time spent on recent papers motivated by the Hedetniemi Conjecture, diverse notions of chromatic number [fractional, circular], etc. A set of coherently organized papers will be made available to participants before the beginning of the seminar. The emphasis will be on several open problems [of varying degrees of accessibility]. Texts: TBA Assessments: TBA Prerequisites: The introductory sequence in combinatorics and basic knowledge of group theory and graph theory will be assumed. |

000 | MSC: E406 | TuTh 10:00am - 11:15am | Vojtech Rodl | max 16 |

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

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

RAMA | | | Raman Parimala | max 999 |

ZURE | | | David Zureick-Brown | max 999 |

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

00P- | | | Michele Benzi | max 999 |

NAGY | | | James Nagy | max 999 |

ONO | | | Ken Ono | max 999 |

RODL | | | Vojtech Rodl | max 999 |

VENA | | | Suresh Venapally | max 999 |

VENE | | | Alessandro Veneziani | max 999 |

ZURE | | | David Zureick-Brown | max 999 |