This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures. Abstract algebra gives to student a good mathematical maturity and enable learners to build mathematical thinking and skill. The topics to be covered are injective, subjective and objective mappings. Product of mappings, inverse of a mapping. Binary operations on a set. Properties of binary operations (commutative, associative and distributive properties). Identity element of a set and inverse of an element with respect to a binary operation. Relations on a set. Equivalence relations, equivalence classes. Partition of set induced by an equivalence relation on the set. Partial and total order relations on a set. Well-ordered sets. Natural numbers; mathematical induction. Sum of the powers of natural numbers and allied series. Integers; divisors, primes, greatest common divisor, relatively prime integers, the division algorithm, congruencies, the algebra of residue classes. Rational and irrational numbers. Least upper bound and greatest lower bound of a bounded set of real numbers. Algebraic structures with one or two binary operations. Definition, examples and simple properties of groups, rings, integral domains and fields.
Course Code:
MAT 201
No. of Credits:
3
Level:
Level 200
Course Semester:
First Semester
Pre-requisite:
MAT 102
Select Programme(s):
Mathematics
Mathematics-with-Business