Proofs and Ideas
eBook - PDF

Proofs and Ideas

A Prelude to Advanced Mathematics

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Proofs and Ideas

A Prelude to Advanced Mathematics

About this book

Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts.The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine.This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India.

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Yes, you can access Proofs and Ideas by B. Sethuraman in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Title page
  2. Copyright
  3. Contents
  4. Preface
  5. Chapter 1. Introduction
  6. Chapter 2. The Pigeonhole Principle
  7. Chapter 3. Statements
  8. Chapter 4. Counting, Combinations
  9. Chapter 5. Sets and Functions
  10. Chapter 6. Interlude: So, How to Prove It? An Essay
  11. Chapter 7. Induction
  12. Chapter 8. Cardinality of Sets
  13. Chapter 9. Equivalence Relations
  14. Chapter 10. Unique Prime Factorization in the Integers
  15. Chapter 11. Sequences, Series, Continuity, Limits
  16. Chapter 12. The Completeness of R
  17. Chapter 13. Groups and Symmetry
  18. Chapter 14. Graphs: An Introduction
  19. Index