Mathematics

This course provides a study of finite mathematical structures that are widely used in computer science. Topics include logic, number theory, methods of proof, sequences, mathematical induction, recursion, functions, probability, etc.

This course covers first- and second-order ordinary differential equations and their applications and modeling. Topics include direction fields, separable and non-homogeneous ODEs, integrating factors, Bernoulli equations, and Euler-Cauchy equations. Additional topics include power series method, Legendre Polynomials, Frobenius method, and Bessel functions. The course also provides a brief overview of linear algebra topics to assist with matrix eigenvalue problems and basics of linear systems. Other topics include Laplace transforms with related topics, such as inverse, s-shifting, derivatives, integrals, Heaviside function, t-shifting, convolution, integral equations, and solving system of ODEs.

The course covers the following: Microscopic properties of networks: adjacency matrix, vertex degree, clustering coefficient, measures of node centrality and node similarity.  Macroscopic properties of networks: degree distributions, graph modularity, and assortativity. Processes on networks: voter model, diffusion process, random walk on a graph, PageRank, and spectral distribution. Random graphs: Erdos-Renyi ensemble, graphs with a prescribed degree distribution, giant components and percolation transition.  

This is a first course on the theory and applications of numerical approximation techniques. It looks at how in practice mathematically formulated problems are solved using computers, and how computational errors are analyzed and tackled. Major topics covered include computational errors, direct method for systems of linear equations, interpolation and approximation, numerical integration, and use of MATLAB software.

An introduction to probability with a view toward applications. Topics include mathematical models for random phenomena, random variables, expectation, the common discrete and continuous distribution with applications, joint distributions, conditional distributions and expectation, independence, monent generating functions, laws of large numbers and the central limit theorem, sample and population, sample distributions, concept of estimation for population parameters, and linear regression and correlation.

Textbook: Thomas Haslwanter, "AN INTRODUCTION TO STATISTICS WITH PYTHON"