Graduate classes, Spring 2018, Mathematics
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: TBA Assessments: TBA Prerequisites: Students are expected to have the background of Math 411412 sequence or the equivalent.  1  MSC: W302  MW 8:30am  9:45am  Shanshuang Yang   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: 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).  1  MSC: W306  MW 11:30am  12:45pm  Alessandro Veneziani   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: TBA Assessments: TBA Prerequisites: Math 521.  1  MSC: E406  TuTh 2:30pm  3:45pm  Raman Parimala   MATH 528: Algebraic Number Theory  Credits: 3  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  1  MSC: E406  MW 11:30am  12:45pm  John Duncan   MATH 532: Graph Theory II  Credits: 3  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  1  MSC: E406  MW 2:30pm  3:45pm  Hao Huang   MATH 546: Intro. to Differential Geometry II  Credits: 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  1  MSC: E408  TuTh 11:30am  12:45pm  Vladimir Oliker   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: 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.  1  MSC: E406  TuTh 10:00am  11:15am  Michele Benzi   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  1  MSC: W303  M 4:00pm  4:50pm  Dwight Duffus   MATH 578R: Seminar in Algebra  Credits: 1  9  − Description  − Sections 
Content: Research topics in algebra of current interest to faculty and students. Texts: TBA Assessments: TBA Prerequisites: TBA  1  MSC: W304  Tu 4:00pm  4:50pm  David ZureickBrown   MATH 579R: Seminar in Analysis  Credits: 3  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  1  MSC: W301  F 2:00pm  2:50pm  Lars Ruthotto   2  MSC: W301  Tu 4:00pm  5:00pm  Vladimir Oliker   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  1  MSC: W306  F 11:00am  11:50am  Bree Ettinger   MATH 788: Topics in Algebra  Credits: 3  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  1  MSC: E408  TuTh 10:00am  11:15am  David ZureickBrown   MATH 789R: Topics in Analysis: Numerical Methods for Deep Learning  Credits: 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).  1  MSC: W302  WF 11:30am  12:45pm  Lars Ruthotto  max 10 
