MA1025 Introduction to Mathematical Reasoning

An introductory course in logic and elementary discrete mathematics to be taken by students in Operations Research, Mathematics, and Computer Science. Considerable emphasis is placed on propositional and predicate logic, and on techniques of proof in mathematics. Mathematical topics include sets, functions, and relations. Coverage of combinatorics includes an introduction to permutations, combinations, the pigeon-hole principle, and the principle of inclusion/exclusion. No previous experience with this material is assumed. Prerequisite: None.

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

• Define, as well as explain with examples, the basic terminology of functions, relations and sets. Apply the properties of relations, functions, and sequences to complete operations on discrete structures such as sets, functions, relations, and sequences.
• Convert logical statements from informal language to propositional (and quantified) logic expressions and vice-versa; verify the validity of an argument using propositional logic, predicate logic, the rules of inference and truth tables.
• Construct mathematical proofs using counter-examples, direct proofs, proof by contrapositive, proof by contradiction, case analysis, and mathematical induction.
• Apply counting techniques, including sum and product rules, inclusion-exclusion principle, the Pigeonhole Principle, and Combinatorics to determine discrete probability.