MAT 175E - Abstract Mathematics

Course Objectives

1.To introduce proof techniques.
2.To teach notions such as logic,sets, functions and
cardinality., equivalence, and order.
3.To teach partially ordered sets.
4.To give an understanding of axiomatic development from natural numbers to compex numbers.

Course Description

Symbolic Logic: propositions, quantifiers, negation, proof techniques.
Set Theory: sets, operations on sets, lattices, boolean algebra, relations, equivalence and
order 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, diophant equations.
Rational and Reel Numbers: construction of rational numbers, continuous fractions,
construction and and their properties.
Complex numbers: operations with complex numbers, conjugate complex numbers and
modules.