Discrete Mathematics

This course is open to students who have successfully achieved a minimum of 3 on the AP exam or a B+ in AP Calculus BC. Whenever possible, examples will be selected from AP Calculus curriculum to illustrate the theoretical concepts. All the topics will be complemented with computer laboratory projects.

Fall Term: Logic - The study of reasoning will include truth tables, proofs using binary logic, and tautologies. Set Theory: Algebra of Sets, Relations: Partial Orders, Linear Orders, Equivalence Relations and Classes, The construction of Rational Numbers. Functions: Injection, Surjection, Bijection, Inverses

Winter Term: Elementary Number Theory - Divisibility, Euclidian Algorithm, Greatest Common Divisors, Perfect Numbers, Congruences, Fermat's Little Theorem, Euler's Theorem, The Chinese Remainder Theorem, the Law of Quadratic Reciprocities, The Moebius Function, The Euler Function, Fibonacci Numbers

Spring Term: Linear Algebra - Systems of Linear Equations, Vector Spaces, Linear Transformations, Eigenvector and Eigenvalues
Prerequisite: B+ in BC Calculus, departmental permission. Offered: Full Year

Quizzes (.pdf format)
Quiz I: Truth Tables- Fall 2008

Practice Problems

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