MATH 500: Probability | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E406 | TuTh 10:00am - 11:15am | Zoltan Furedi | max 16 |

MATH 511: Analysis I | Credits: 3 | − 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: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W306 | MWF 10:00am - 10:50am | David Borthwick | max 20 |

MATH 515: Numerical Analysis I | Credits: 3 | − 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: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W304 | TuTh 11:30am - 12:45pm | Michele Benzi | max 20 |

MATH 521: Algebra I | Credits: 3 | − 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: E408 | MW 2:30pm - 3:45pm | Raman Parimala | max 16 |

MATH 523: Commutative Algebra and Geometry | Credits: 3 | − Description | − Sections |
Content: This is an introductory course covering topics like affine and projective varieties, Hilbert's Nullstellensatz, morphism and rational maps of varieties, dimension, smoothness, algebraic curves, intersection multiplicity and Bezout's theorem. Topics from commutative algebra like integral extensions, Noether's normalisation lemma and primary decomposition will also be treated simultaneously. Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E408 | MW 11:30am - 12:45pm | Suresh Venapally | max 16 |

MATH 528: Algebraic Number Theory | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E408 | MW 1:00pm - 2:15pm | Ken Ono | max 16 |

MATH 531: Graph Theory I | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E408 | TuTh 8:30am - 9:45am | Zoltan Furedi | max 16 |

MATH 543: Algebraic Topology I | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: E408 | TuTh 11:30am - 12:45pm | Robin Forman | max 16 |

MATH 545: Introduction to Differential Geometry I | Credits: 3 | − Description | − Sections |
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W304 | TuTh 2:30pm - 3:45pm | Vladimir Oliker | 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 Prerequisites: TBA |

000 | MSC: W306 | F 4:00pm - 4:50pm | Dwight Duffus | max 20 |

MATH 577R: Seminar in Combinatorics: Introduction to Complex Networks | Credits: 3 | − Description | − Sections |
Content: Mathematical background. A brief on matrix algebra. A brief on data analysis.
Introduction to networks. History; Basic Definitions; Walks and Paths: Eulerian and Hamiltonian networks, random walks, shortest path distance, Degree Distributions: Poisson, power law, identifying correlations; Graph Connectivity: connected components, cliques; Graph Structures: trees, bipartivity and planarity; Modern Applications.
Adjacency relation in networks. Degree distributions; degree-degree correlations; Spectral properties of networks. Spectrum of the Adjacency Matrix, the Graph Laplacian.
Fragments in complex networks. subgraphs, network motifs, graphlets, closed walks, combinatorics of subgraphs, clustering coefficients, combinatorics of assortativity, network hierarchy, network reciprocity
Matrix functions on networks. exponential adjacency matrix, hyperbolic functions of the adjacency matrix, network entropy and free energy, network communicability, returnability
Centrality measure in networks. A description of the definitions and applications of centralities like degree, Katz, eigenvector, PageRank, subgraph, closeness and betweenness.
Global measures of networks. A description of a few global measures characterising the degree heterogeneity, fractality, and topological classes of networks. Adjacency and distance-based invariants; expansion and network classes; spectral scaling method; network bipartivity
Community structure in networks. Network partition methods; local improvement methods; spectral partittioning; methods based on link centrality; quality criteria; methods based on modularity; the problem of resolution; clustering based on similarity; communities based on communicability; how to find bipartitions in networks.
Random models of networks. Classical random networks; small-world random networks; scale-free networks; random geometric networks. Texts: Estrada, E. The Structure of Complex Networks. Theory and Applications. Oxford University Press, 2011. ISBN: 978-0-19-959175-6 Assessments: TBA Prerequisites: TBA |

001 | MSC: W302 | TuTh 10:00am - 11:15am | Ernesto Estrada | max 20 |

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: W306 | W 4:00pm - 4:50pm | Ken Ono | max 20 |

001 | MSC: E406 | F 1:00pm - 2:00pm | David Zureick-Brown | max 16 |

MATH 579R: Seminar in Analysis | Credits: 3 | − Description | − Sections |
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's Texts: TBA Assessments: TBA Prerequisites: TBA |

000 | MSC: W301 | Tu 4:00pm - 4:50pm | Vladimir Oliker | max 20 |

001 | MSC: W302 | F 12:00pm - 12:50pm | Alessandro Veneziani | max 25 |

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

GOUL | MSC: Other | | Faculty (TBA) | max 999 |

ONO | MSC: ----- | | Faculty (TBA) | max 999 |

RAMA | | | Faculty (TBA) | |

VENE | MSC: ----- | | Faculty (TBA) | max 999 |

ZURE | MSC: ----- | | Faculty (TBA) | max 999 |

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

YANG | | | Faculty (TBA) | |

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

NAGY | MSC: ----- | | Faculty (TBA) | max 999 |

RAMA | MSC: Other | | Faculty (TBA) | max 999 |

RODL | MSC: ----- | | Faculty (TBA) | max 999 |

VENA | MSC: ----- | | Faculty (TBA) | max 999 |

VENE | MSC: ----- | | Faculty (TBA) | max 999 |

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

BENZ | MSC: ----- | | Faculty (TBA) | max 999 |

BORT | MSC: ----- | | Faculty (TBA) | max 999 |

NAGY | MSC: ----- | | Faculty (TBA) | max 999 |

ONO | MSC: ----- | | Faculty (TBA) | max 999 |

RODL | MSC: ----- | | Faculty (TBA) | max 999 |

VENE | MSC: ----- | | Faculty (TBA) | max 999 |

YANG | MSC: ----- | | Faculty (TBA) | max 999 |