Results for discrete mathematics and algorithms

Introduction to theoretical foundations of discrete mathematics and algorithms. Emphasis on providing mathematical tools for combinatorial optimization, i.e. how to efficiently optimize over large finite sets and reason about the complexity of such problems. Topics include: graph theory, minimum cut, minimum spanning trees, matroids, maximum flow, non-bipartite matching, NP-hardness, approximation algorithms, spectral graph theory, and Laplacian systems. Prerequisites: CS 161 is highly recommended, although not required.

Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements. Prerequisites: MATH 51 and 53.

Introduction to theoretical foundations of discrete mathematics and algorithms. Emphasis on providing mathematical tools for combinatorial optimization, i.e. how to efficiently optimize over large finite sets and reason about the complexity of such problems. Topics include: graph theory, minimum cut, minimum spanning trees, matroids, maximum flow, non-bipartite matching, NP-hardness, approximation algorithms, spectral graph theory, and Laplacian systems. Prerequisites: CS 161 is highly recommended, although not required.