MAT 175 - Abstract Mathematics

Course Objectives

To introduce proof techniques. To teach notions such as logic,sets, functions and cardinality., equivalence, and order.

Course Description

Symbolic Logic: propositions, quantifiers, negation, proof techniques.Set Theory: sets, operations on sets, lattices, boolean algebra, relations, equivalence andorder relations, functions, composite functions, and inverse functions.
Countablity: finite and infinite sets, countable sets, Cantor’s theorems.Ordered Sets: partial orders, well orders, posets, Zorn’s lemma.Natural Numbers: Peano axioms, the principle of mathematical induction.
Integers: construction of integers, ordering and divisibility, congruances.