Mathematics

This course offers a study of the basic concepts of discrete mathematics: graphs, vertex and adjacency relations; trees; existence of Euler and Hamiltonian paths; graph coloring; pairings. It explores ways to perform software modeling and resolution of routing optimization, interconnection, and assignment problems.

This course discussed classical solution methods for first order equations. After this, linear equations of higher order with constant coefficients and first order systems are studied. Power series solutions are introduced for linear equations with variable coefficients. The last part of the course focuses on general theorems about existence and uniqueness. These theorems are important since most differential equations lack explicit solutions.

This course introduces students to techniques and tools in modern analysis which have important uses in a variety of areas of analysis, including the study of partial differential equations and Fourier analysis. Students achieve this in the context of linear analysis, introducing normed linear, inner product spaces and their completions, Banach and Hilbert spaces. The structure and geometry of these spaces are studied as well as continuous linear operators acting on them. 

This course covers mathematics relating to differential equations. Topics include ordinary differential equations, systems of differential equations, Laplace transformations and applications, partial differential equations separable solutions, plane waves solutions, Bessel's Equation, Legendre's equation, dynamic systems and boundary eigenvalue problems. Techniques for solving differential equations are used in the context of application to fields of engineering.

This course offers an introduction to probability theory for students with knowledge of elementary calculus. The course covers not only the mathematics of probability theory but works through diverse examples to illustrate the wide scope of applicability of probability, such as in engineering and computing, social, and management sciences. Topics covered include counting methods, sample space and events, axioms of probability, conditional probability, independence, random variables, discrete and continuous distributions, joint and marginal distributions, conditional distribution, independence of random variables, expectation, conditional expectation, moment generating function, central limit theorem, and weak law of large numbers.