# Special Topics Courses

# Spring 2020

**MA 591-003 and MA 493 Special Topics in Geometry and Topology and their Applications, Radmila Sazdanovic T Th 1:00-2:45 PM**

**MA 591-004 Scientific Programming with Python, Arvind Saibaba, F 1:55-2:45 PM**

**MA 788 Numerical Nonlinear Partial Differential Equations, Alina Chertock, T Th 10:15-11:30 AM, SAS 1108.**

*This course is intended as a review of modern numerical techniques for a vide range of time-dependent partial differential equations. A significant part of the course will be devoted to a variety of applications including compressible and incompressible fluids, flows in rivers and coastal areas, ocean and atmospheric currents, pollutant propagation models, various biological and traffic flow models, and others. The course will be offered as a balanced blend of analysis and computation and should be very useful for students in applied and computational mathematics, engineering and the sciences. The course is designed for students who are familiar with basic concepts of partial differential equations, numerical analysis and scientific programming. Topics include: Finite Difference, Finite Volume and Implicit-Explicit Discretizations; Spectral, Particle and Splitting Methods; Hybrid Eulerian-Lagrangian Numerical Methods, and others. Prerequisites: Numerical analysis, ordinary and partial differential equations, scientific programming (Matlab, Fortran, C, C++, …). It is possible to participate in this class without part of the recommended background but this will require to do a lot of extra reading. Students from all scientific and engineering departments are welcome.*

#### MA 792 Special Topics: Infinite-Dimensional Lie Algebras and Vertex Algebras, Bojko Bakalov, T Th 4:30-5:45 PM 209 Winston Hall

**MA 792 Special Topics: C/C++/Python for Mathematicians, Erich Kaltofen, M W 4:30-5:45 PM SAS 1218**

*The course is intended to cover those 3 widely-used programming languages from a language semantics point-of-view, that is, covering most C and Python language* *constructs (all of C’s memory model) and 75% of the C++ constructs (including C++ templates) with a smattering of the C/C++ standard libraries and selected Phython libraries (NumPy, SciPy). Note that Google internally uses C++ and* *Python for its development and Intel supplies a C compiler with every new processor release. The course covers the Unix “make” command for C (or Latex) selective compilation. The meta “automake” and version management will be mentioned in passing. The relation of a C/Python program and the definition of the mathematical notions “algorithm” and “decidability” will be explained. Prerequisite: an introductory knowledge of (imperative) computer programming (arrays, conditionals, loops, procedures, I/O).*

**MA 796 Schubert Calculus, Ricky Liu, T Th, 3:00-4:15 PM**

# Fall 2019

**MA 591-001 Math Analysis II, Bevin Maultsby, MWF 11:45-12:35**

*Calculus of several variables, topology in n-dimensions, limits, continuity, differentiability, implicit functions, integration. Cross-listed with MA 426.*

**MA 591-002 Fixed income products & analysis, R. Ellson, MW: 8:30-9:45**

**MA 591-003 Topological combinatorics, P. Hersh, MW 1:30-2:45**

*This class will focus on a rich interplay between topology and combinatorics. This will include combinatorial techniques including shellability, discrete Morse theory, and the Quillen Fiber Lemma, among others for computing homotopy type, homology groups and Betti numbers of simplicial complexes and cell complexes. Going in the other direction, we explore how the Mobius function of a partially ordered set is interpreted topologically. We will spend considerable time on hyperplane arrangements and geometric lattices first (from both an enumerative and a topological viewpoint), and then on poset topology more generally later in the semester. Along the way, we will do a quick review of representation theory of the symmetric group, to the extent it will be needed in our study of poset topology. For students who have taken topology and would like to understand things in a very concrete, hands-on way with lots of examples, this course could be useful. It would be helpful (but not absolutely necessary) to have previously taken MA 753; it is not necessary to have previously taken MA 524/724. *

**MA 591-004 Scientific programming with Python, A. Saibaba, F: 1:55-2:45**

**MA 792-001 Algebraic topology II, T. Lidman, MW: 11:45-1:00**

*In this course, we will develop powerful tools for studying algebraic and topological problems by building deep connections between the two areas. Beginning with a development of cohomology and higher homotopy groups, we will be able to characterize when two spaces are homotopy equivalent and also bound the minimal number of relations needed to present a group. From here we will develop more advanced algebraic and topological tools which have applications to topology, geometry, combinatorics, algebraic geometry, representation theory, and more. Potential topics include: cohomology, homotopy theory, group cohomology, vector bundles, characteristic classes, spectral sequences, spectra, K-theory, topology of manifolds. The content will be somewhat guided by the interests of the constituents. Prerequisites: MA 753.*

**MA 793-001 Viscosity solutions, T. Nguyen, MF: 3:00-4:15**

**MA 797-001 Convex optimization methods in data science, P. Combettes, TTh: 10:15-11:30**

**MA 810-001 Foundations of deep learning, M. Haider, M: 4:30-7:15**

*This course will be offered at SAMSI. It will start with a review of standard neural networks, and then progress to modern deep learning, including convolutional neural networks, recursive neural networks, generative adversarial networks, and various kinds of autoencoders. We shall discuss training strategies, architecture search, regularization and quantization.*