Minor in Mathematics

Limit processes, including the concepts of limits, continuity, differentiation, the natural logarithm and exponential functions, and integration of functions. Applications to physical problems will be discussed.

Applications of integration, inverse functions, and hyperbolic functions. Techniques of integration, sequences, series of numbers and functions, and Taylor series.

Vectors, partial derivatives, multiple integrals, line integrals, Green's Theorem, the Divergence Theorem, and Stokes Theorem. Applications to physical problems will be given.

A study of functional principles and proof techniques. Topics will include statements, consequence, proof, sufficient and necessary conditions, contraposition, induction, sets, relations, functions, cardinality, divisibility, prime numbers, congruence, Fermat's Theorem, counting principles, permutations, variations, combinations, binomial coefficients, graphs, planar and directed graphs, and graph coloring.

This course covers the fundamental concepts of vector spaces, linear transformations, systems of linear equations, and matrix algebra from a theoretical and a practical point of view. Results will be illustrated by mathematical and physical examples. Important algebraic (e.g., determinants and eigenvalues), geometric (e.g., orthogonality and the Spectral Theorem), and computational (e.g., Gauss elimination and matrix factorization) aspects will be studied.

This course is the first part of a two-semester sequence with MAT 314, with a focus on basic probability. It covers descriptive statistics, sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distribution of discrete and continuous random variables, joint distributions, and the central limit theorem.

This course is the second part of a two-semester course sequence with MAT 313, with a focus on applied statistics. It covers basic statistical concepts, graphical displays of data, sampling distribution models, hypothesis testing, and confidence intervals. A statistical software package is used.

A survey of the history of mathematics from antiquity through modern times.

Ordinary differential equations of first-order and first-degree, high order linear ordinary differential equations with constant coefficients, and properties of solutions.

A study of properties of integer numbers. Divisibility of integers, primes and greatest common divisors, congruencies, Euclidean algorithm, Euler Phi-function, quadratic reciprocity and integer solutions to basic equations, Diophantine equations, and applications to cryptography and primality testing.

This is an introductory course in cryptography. It covers classical cryptosystems, Shannon's perfect secrecy, block ciphers and the advanced encryption standard, RSA cryptosystem and factoring integers, public-key cryptography and discrete logarithms, and linear and differential cryptanalysis.

This course covers linear programming, the simplex algorithm, duality theory and sensitive analysis, network analysis, transportation, assignment, game theory, inventory theory, and queuing theory.

Numerical differentiation, integration, interpolation, approximation of data, approximation of functions, iterative methods of solving nonlinear equations, and numerical solutions of ordinary and partial differential equations.

A survey of Euclidean, non-Euclidean, and other geometries. The emphasis will be on formal axiomatic systems.

This course covers statistical techniques with applications to the type of problems encountered in real-world situations. These topics include categorical data analysis, simple linear regression, multiple regression, and analysis of variance. A statistical software package is used.

An axiomatic treatment of groups, rings, and fields that bridges the gap between concrete examples and abstraction of concepts to general cases.

This is an introductory course in complex analysis. The algebra of complex numbers, analytic functions, contour integration, Cauchy integral formula, theory of residues and poles, and Taylor and Laurent series.

This course is the first part of a two-semester course sequence with MAT 456. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.

This course is the second part of a two-semester course sequence with MAT 455. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.

Special topics in the discipline, designed primarily for seniors who are majors or minors. Students may enroll in 495 Special Topics multiple times, as long as the topics differ.