M 242 - Methods of Proof

Credit(s): 3

Prerequisite(s): M 171 or Math Department consent.
Methods of Proof is an introduction to the axiomatic nature of modern mathematics. Emphasis is placed on the different methods of proof that can be used to prove a theorem. Mathematical topics discussed include symbolic logic, methods of proof, specialized types of theorems and proofs. (Fall Semester, Even Years)

Course Learning Outcomes: Upon completion of the course, students will be able to

Define the various terms used in mathematical logic including: logical equivalence, quantifiers, conjecture, generalization, existence statement, open sentence, contrapositive, converse, mathematical induction, counter example.
Identify and classify mathematical statements as conditional statements, existence statements, or generalizations.
Manipulate various mathematical statements to produce forms more easily examined for meaning and truth using logical tools such as negation and logical equivalences.
Evaluate the truth of a mathematical generalization and construct a counterexample if it is false and prove it if it is true.
Take mathematical statements in casual conversational language and write the statement in its equivalent, mathematically correct logical form so that its meaning and truth can be examined.
Explain the difference between beliefs, intuition, informal justifications (heuristics), and formal mathematical proof.
Construct mathematical proofs using any of the basic different types of proofs, including direct and indirect proofs and proofs by mathematical induction.
Evaluate the validity of mathematical arguments based on their logical correctness.
Read mathematical definitions and theorems they have not seen before well enough to use them properly.
Develop an understanding of what mathematicians do as professionals and how mathematicians determine truth.