All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
The first part, provides a brief overview of the containers, strings, streams, input/output, and the numeric library of the C++ standard library. For linear algebra, we will look into Blaze which is an open-source, high-performance C++ math library for dense and sparse arithmetic.
The second part will solve computational mathematics problems based-on the the previous introduced features of the C++ standard library.
The third part will focus on the parallel features provided by the C++ standard library. Here, the implemented computational problems in the second part of the course will be parallized using the C++ standard library for parallelism and concurrency.
Since programming skills can only be improved by doing, there will be weekly programming exercises and a small project. After this course students have a basic overview of the C++ standard library to solve efficiently computational mathematics problems without using low-level C/C++.
The goal of this course is to give a gentle introduction to some basic properties of classical hypergeometric functions, finite field analogues of hypergeometric functions, and their connection to hypergeometric type abelian varieties. In the later part of the semester, we will discuss some recent developments related to different versions of hypergeometric functions, and advanced topics, depending on audiences' interests.
Modern algebraic geometry is based on the fundamental notion of a scheme. This course will give an introduction to schemes and their geometry, with particular emphasis on motivating the definitions and constructions and providing many examples. Time permitting, we will use this machinery to discuss some concrete classical problems in intersection theory and enumerative geometry.
We will mostly follow the book by Folland. We will also hand out notes as needed. There are several other very good books on analysis and measure theory:
These techniques form an important core skill set for research in elliptic and parabolic PDE, as well as a valuable springboard when studying many other evolution equations derived from physical models. We will focus on linear elliptic equations and equations of fluid mechanics (and possibly of viscoelasticity) as prototypes for this analysis.
Proposed Course Topics:
This course will provide a comprehensive introduction to the basic theory of matroids. This will include discussions of the basic definitions and examples, duality theory, and certain fundamental substructures of matroids. Particular emphasis will be given to matroids that arise from graphs and from matrices.
This is an excellent class to take if you are interested in topics like symplectic geometry, algebraic geometry from a Kahler manifold perspective, hyperbolic geometry and geometric group theory, symplectic and contact topology, Lagrangian and Legendrian sub manifolds, mirror symmetry, analysis on manifolds, gauge theory, path integrals and Chern-Simons theory, representation varieties, L^2-cohomology, and, of course, the mathematics behind general relativity. We won’t cover these topics, but this class will make them significantly easier to learn and put them into a larger context if you are currently learning them.