Math Courses I've Taken
PreCalculus
A careful study of elementary functions with emphasis on their graphical properties. Particular functions treated include polynomi- als and rational functions, exponential and logarithmic functions, trigonometric and inverse trigonometric functions.
Calculus 1
constitute the first two-thirds of the standard 12-credit calculus sequence, 173-174-276. Topics include functions and their graphs, limits, differentiation, integration, derivatives and integrals of the elementary functions, polar coordinates, parametric equations, infinite series
Calculus 2
constitute the first two-thirds of the standard 12-credit calculus sequence, 173-174-276. Topics include functions and their graphs, limits, differentiation, integration, derivatives and integrals of the elementary functions, polar coordinates, parametric equations, infinite series
Calculus 3
constitutes the last third of the standard 12-credit calculus sequence, 173-174-276. Topics include functions of two or more variables, partial derivatives, multiple integrals.
Statistics
Axioms of probability and elementary laws. Random variables. Discrete and continuous probability distributions and applications. Expectation and variance of random variables. Jointly distributed random variables, conditional probability. Descriptive statistics. Estimation and hypothesis testing. Use of a statistical software package.
Modern Geometry
A postulational approach to some Euclidean and non-Euclidean geometries. Topics include incidence and separation properties of planes and space, constructions with compass and straightedge, geometric inequalities, the parallel postulate, similarity theorems, circles, properties of triangles, and metric relationships.
Abstract Algebra
Introductory concepts of modern algebra and their applications to the solution of polynomial equations over various fields. Elementary properties of groups, rings, integral domains, fields, and vector spaces; introductory Galois theory and applications including Abel’s theorem and compass-straightedge constructions.
Discrete Mathematics
An introduction to topics in discrete structures. Topics include set theory, combinatorics, logic, proof techniques, functions, relations, pigeonhole principle, equivalence relations, recurrence and recursion, graph and trees, number theory. Optional topics may include applications of combinatorics and graph theory.
Linear Algebra
Finite dimensional vector spaces; linear transformations and their matrix representations; eigenvalues; rational and Jordan canonical forms; inner product spaces; quadratic and bilinear forms; applications.
Real Analysis
The real number system, sets, functions, sequences, Cauchy sequences, point set topology, continuity, uniform continuity, differentiability, the Riemann and Riemann-Stieltjes integral, series, convergence tests, sequences and series of functions, pointwise and uniform convergence.