Graduate classes, Spring 2018, Mathematics

MATH 512: Analysis IICredits: 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: TBA
Assessments: TBA
Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
1MSC: W302MW 8:30am - 9:45amShanshuang Yang
MATH 516: Numerical Analysis IICredits: 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: TBA
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).
1MSC: W306MW 11:30am - 12:45pmAlessandro Veneziani
MATH 522: Algebra IICredits: 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: TBA
Assessments: TBA
Prerequisites: Math 521.
1MSC: E406TuTh 2:30pm - 3:45pmRaman Parimala
MATH 528: Algebraic Number TheoryCredits: 3− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
1MSC: E406MW 11:30am - 12:45pmJohn Duncan
MATH 532: Graph Theory IICredits: 3− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
1MSC: E406MW 2:30pm - 3:45pmHao Huang
MATH 546: Intro. to Differential Geometry IICredits: 3− Description− Sections
Content: An introduction to Riemannian geometry and global analysis. Topics to be covered: Manifolds, Riemannian metrics, Connections, Curvature; Geodesics, Convexity, Topics in Global Analysis.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
1MSC: E408TuTh 11:30am - 12:45pmVladimir Oliker
MATH 550: Functional AnalysisCredits: 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: A. Bressan, Lecture Notes on Functional Analysis. With Application to Partial Differential Equations, Graduate Studies in Mathematics 143, American Mathematical Society, Providence, RI, 2013.
Assessments: TBA
Prerequisites: Math 511, Math 512.
1MSC: E406TuTh 10:00am - 11:15amMichele Benzi
MATH 577R: Seminar in CombinatoricsCredits: 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
1MSC: W303M 4:00pm - 4:50pmDwight Duffus
MATH 578R: Seminar in AlgebraCredits: 1 - 9− Description− Sections
Content: Research topics in algebra of current interest to faculty and students.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
1MSC: W304Tu 4:00pm - 4:50pmDavid Zureick-Brown
MATH 579R: Seminar in AnalysisCredits: 3− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
1MSC: W301F 2:00pm - 2:50pmLars Ruthotto
2MSC: W301Tu 4:00pm - 5:00pmVladimir Oliker
MATH 590: Teaching SeminarCredits: 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
1MSC: W306F 11:00am - 11:50amBree Ettinger
MATH 788: Topics in AlgebraCredits: 3− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
1MSC: E408TuTh 10:00am - 11:15amDavid Zureick-Brown
MATH 789R: Topics in Analysis: Numerical Methods for Deep LearningCredits: 3− Description− Sections
Content: This course provides students with the mathematical background needed to analyze and further develop numerical methods at the heart of deep learning. The course briefly reviews current trends in machine learning, classification, and in particular deep neural networks. Mathematical techniques covered in this class include numerical optimization, numerical differential equations, optimal control.
Texts: Homework and additional course material will be made available using Canvas.
Assessments: TBA
Prerequisites: In order to succeed in this class, students need to have a solid background in multivariate calculus and linear algebra and some programming experience in MATLAB, Julia, or Python. In addition, students are also expected to have experience or skills in either numerical analysis (optimization, partial differential equations) or machine learning (e.g., CS534, CS584, or similar).
1MSC: W302WF 11:30am - 12:45pmLars Ruthottomax 10