Methods of solving first and second order differential equations, applications, systems of equations, series solutions, existence theorems, numerical methods, and partial differential equations.
Probability as a mathematical system, random variables and their distributions, limit theorems, statistical inference, estimation, decision theory and testing hypotheses.
Topics to be selected from counting techniques, mathematical logic, set theory, data structures, graph theory, trees, directed graphs, algebraic structures, Boolean algebra, lattices, and optimization of discrete processes.
This course explores the mathematical foundations of algorithms used in the field of Data Science, typically taken after a course in mathematical statistics. It includes the study of classification and regression techniques, robust regression, decision trees, support vector machines, neural networks, cross-validation techniques, forecasting models, and Topological data analysis. The course includes a data-driven project that requires the student to propose a question and gather, clean, and analyze data to present a response to a real-world problem.
The history of mathematics from ancient to modern times. The mathematicians, their times, their problems, and their tools. Major emphasis on the development of geometry, algebra, and calculus.
A review of Euclidean geometry, an examination of deficiencies in Euclidean geometry, and an introduction to non-Euclidean geometrics. Axiomatic structure and methods of proof are emphasized.
A survey of the classical algebraic structures taking an axiomatic approach. Deals with the theory of groups and rings and associated structures, including subgroups, factor groups, direct sums of groups or rings, quotient rings, polynomical rings, ideals, and fields.
An introduction to topological structures from point-set, differential, algebraic, and combinatorial points of view. Topics include continuity, connectedness, compactness, separation, dimension, homeomorphism, homology, homotopy, and classification of surfaces.
This course develops the logical foundations underlying the calculus of real-valued functions of a single real variable. Topics include limits, continuity, uniform continuity, derivatives and integrals, sequences and series of numbers and functions, convergence, and uniform convergence.
A study of the concepts of calculus for functions with domain and range in the complex numbers. The concepts are limits, continuity, derivatives, integrals, sequences, and series. Topics include Cauchy-Riemann equations, analytic functions, contour integrals, Cauchy integral formulas, Taylor and Laurent series, and special functions.