A Foundation Course in Mathematics

This book has been written in a conversational style to impart critical and analytical thinking which will be beneficial for students of any discipline. It also gives emphasis on problem solving and proof writing skills, key aspects of learning mathematics. The subject matter of the book deals with logic, sets, functions and relations, the essential building blocks for higher mathematics. Numerous problems and exercises are chosen and interspersed inside the sections so that the student participates actively in the discussions. Using this book in their studies will lay the foundations which will enable readers to undertake courses in higher mathematics with confidence and due rigour. Table of Contents Statements and Logic Sets Functions Relation Induction Principles Countability of Sets Order Relations Bibliography Index. A Foundation Course in Mathematics is based on a course on Foundations in one of the most famous and successful mathematics training programme titled Mathematics Training and Talent Search (MTTS) Programme which has been running in India since 1993. Title page 2 Full title page 4 Copyright 5 Preface 8 Acknowledgements 12 Contents 14 Chapter 1 18 Chapter 2 46 Chapter 3 65 Chapter 4 97 Chapter 5 110 Chapter 6 120 Chapter 7 132 Bibliography 145 Index 146