Sets, Logic and Algebra I

At the end of the course, students should be able to: 1. solve various problems using the concepts of set theory; 2. understand Algebraic structures; and 3. understand the meaning of logic in mathematics.

Introduction to the language and concepts of modern Mathematics. Topics include; Basic set theory: mappings, relations, equivalence and other relations, Cartesian products. Binary logic, methods of proof. Binary operations. Algebraic structures, semi-groups, rings, integral domains, fields. Homeomorphics. Number systems; properties of integers, rationals, real and complex numbers.