Introductory mathematics : algebra and analysis

This text provides a self-contained introduction to Pure Mathematics.

The style is less formal than in most text books and this book can be used either as a first semester course book, or as introductory reading material for a student on his or her own.

An enthusiastic student would find it ideal reading material in the period before going to University, as well as a companion for first-year pure mathematics courses.

The book begins with Sets, Functions and Relations, Proof by induction and contradiction, Complex Numbers, Vectors and Matrices, and provides a brief introduction to Group Theory.

It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with Continuity and Functions.

It provides all that you have to do to make the calculus work.

Geoff Smith's book is based on a course tried and tested on first-year students over several years at Bath University.

Exercises are scattered throughout the book and there are extra exercises on the Internet.