Advanced Mathematics
Advanced Mathematics is a course for those students who have shown an aptitude for math beyond topics covered in AP Calculus BC. In the course, students explore three major areas of the discipline: abstract mathematical thought in the fall, elementary number theory in the winter, and linear algebra in the spring. The abstract mathematical thought component consists of binary logic, truth tables, direct and indirect proof techniques, the principle of mathematical induction, set theory, equivalence relations, functions, and a basic introduction to higher structures such as groups, rings, and fields. We extend our discussion of equivalence relations and functions to elementary number theory in the winter term by investigating some of the major accomplishments in the field. Students will be introduced to RSA cryptography and use it to encode and decode messages through computer algebra systems. An introductory approach to linear algebra will give students a hands-on experience in the computer lab. Some of the topics include solving systems of linear equations, understanding linear and vector spaces, eigenvalues and eigenvectors, and QR factorization.

Introduction to Abstract Mathematics: Second Edition (John F. Lucas)

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Quizzes (.pdf format)
Quiz I - Fall 2006
Quiz III - Fall 2006
Quiz IV - Fall 2006 Equivalence Relations
Final Exam- Fall 2006
Quiz I - Winter 2007
Quiz II - Winter 2007

Practice Problems
Order Relations - Practice handout
Types of Mappings - Problems

Links and Downloads
Truth Table Constructor
Logic Gate Simulator
Linear Algebra Toolkit