The quality of an applied course is measured by how well they can apply the techniques covered in the course to the solution of real problems encountered in their field of study. Consequently, we advocate moving on to new topics only after the students have demonstrated the ability (through testing) to apply the techniques under discussion. In-class consulting sessions, where a case study is presented and the students have the opportunity to diagnose the problem and recommend an appropriate method of analysis, are very helpful in teaching applied regression analysis. This approach is particularly useful in helping students master the difficult topic of model selection and model building and relating questions about the model to real-world questions.
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.
This course content develops the basic statistical techniques used in applied fields like engineering, and the physical and natural sciences. Principal topics include point and interval estimation; tests of hypotheses. Applications include one-way classification data and chi-square tests. This course act as a gateway to other higher-level statistical courses like Bayesian Statistics, Statistical Theory, and Design & Experiment.
This course is primarily made up of the statistics (not probability) content in M315 coupled with additional content for Actuaries Exams.
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.