Mathematics

A review of algebra and the study of functions, including the polynomial, rational, exponential, and logarithmic functions and their graphs.

Exponential growth and decay, simple interest, compound interest, inflation, loans, combinations, permutations, probability, odds, expectation, frequency distributions, descriptive statistics, and the normal distribution.

Exponential, logarithmic, and trigonometric functions and elementary matrix theory including determinants and systems of equations in preparation for calculus.

Sets and set operations, combinatorics, and elements of graph theory.

Limits, differentiation, and integration of algebraic, trigonometric, logarithmic, and exponential functions with their applications.

Applications and techniques of integration, sequences, infinite series, and transcendental functions.

Vectors and polar coordinates, functions of several variables, partial differentiation, multiple integration, and line integrals, as well as Green’s Theorem, Stokes’ Theorem, and Gauss’ Theorem.

An introduction to the method of formal proof. Topics include logic, set theory, relations, functions and cardinality.

Ordinary differential equations and Laplace transforms.

Algebra of finite dimensional linear spaces, linear transformations and matrices, eigenvalues, and eigenvectors.

Elementary probability, distribution functions, sampling, and testing statistical hypothesis.

Euclidean and non-Euclidean geometries.

Preparation of mathematics students for their roles as secondary mathematics teachers.

Error analysis, interpolation, approximate differentiation, approximate integration, solutions to differential equations, matrix manipulation, and solutions to systems of linear equations. (Same as CSC 415)

An introduction to the algebraic structure of the integers and groups, including equivalence relations, subgroups, normal subgroups, homomorphisms, Lagrange’s theorem, and Sylow’s theorem.

A continuation of MTH 420, including rings, fields, Galois theory, and solvability by radicals.

The real numbers; series; continuous, uniformly continuous, differentiable, and integrable functions; sequences; compact sets; the Heine-Borel theorem; the Bolzano-Weierstrass theorem; limits; and the fundamental theorem of calculus.

A continuation of MTH 440 to multivariate calculus, including sequences and series of functions, uniform convergence and power series, partial derivatives, the Inverse and Implicit Function Theorems, and multiple integrals.

An exploration of one or more advanced undergraduate topics in mathematics not included in the list of courses in the catalog. The course name and appropriate prerequisites will be announced well in advance.

Taken in the senior year, resulting in a paper to be presented to the faculty.

Individual work on special topics in mathematics.