Elementary Lectures in Undergraduate Algebra, Volume I

This book contains the first twenty (20) lectures of the author on elementary topics that form the foundation of the study of all types of traditional and modern mathematics. These lectures contain every elementary concept and result on basic set theory that are taught to honours students right from the first year of their study and which will always be needed throughout their mathematical career. All the concepts and results considered in these lectures are motivated from examples while the proofs of these results are detailed enough to allow independent study by students. The first thirteen (13) lectures of this book on set theory (treating relations and operations in and on sets) may be used by 100 Level students offering elements of mathematics (especially Lectures 1 to 4), by those 200 Level students who are just starting their courses in Real Analysis,Linear and Abstract Algebra, as well as 300 Level students (offering Metric-space Topology, Groups and Rings) and 400 Level students (offering General Topology, Algebraic Topology and Commutative Algebra) who need to be reminded where their subject started from.