Discrete Mathematics

This course introduces the student to logic and to the idea that one can use logical techniques to "prove" mathematical statements. To some extent most students have already "proved" mathematical statements by mechanically manipulating algebraic equations in order to arrive at an answer; however, they are probably unaware that logic is at work underneath these manipulations. Logic and its descriptive power are explored, and then used to construct more complicated proofs about abstract objects like sets, relations and functions. Students learn how to structure and execute a logically correct mathematical proof and to analyze proofs written by others. The course covers elementary logic, deductive reasoning, basics of set theory, variables, operations on sets, proof strategies, relations, functions, mathematical induction, recursion, and infinite sets.

REFERENCES:

• How to Prove It: A Structured Approach; Daniel J. Velleman; 2nd Ed.