The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. An introduction to linear programming, duality theory, simplex algorithm, the transportation problem, network analysis, dynamic programming and game theory. An introductory survey of probability theory, queuing theory, inventory theory, Markovian decision theory and applications. An introduction to numerical methods for solving algebraic and differential equations. Topics include numerical solution of systems of linear equations, approximating functions with polynomials and splines, solutions of nonlinear equations, numerical integration, numerical solution of ordinary differential equations and eigenvalue problems.
Some computer programming is required.
Credit is not given for both MATH 318 and MATH 423 or PHYS 333. An introduction to the theory of probability, with applications to the physical sciences and engineering. Topics include discrete and continuous random variables, conditional probability and independent events, generating functions, special discrete and continuous random variables, laws of large numbers and the central limit theorem. The course emphasizes computations with the standard distributions of probability theory and classical applications of them. An introduction to mathematical statistics.