An Introduction to Mathematical Reasoning

By Peter J. Eccles

Book Overview

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.

• Format: Paperback
• Language: English
• ISBN: 0521597188
• ISBN13: 9780521597180
• Release Date: January 1998
• Publisher: Cambridge University Press
• Length: 361 Pages
• Weight: 1.28 lbs.
• Dimensions: 0.7" x 5.9" x 8.9"

Customer Reviews

Short and to the point

This book is excellent! It chapters are broken down into short sections and the content in each section is to the point! I also bought the book Proofs and Fundamentals by Ethan D. Bloch but found it to be long and drawn out. If you liked The Nuts and Bolts of Proofs by Antonella Cupillari then this book is for you!

Very well written book

I have a mathematics degree. Like most math majors, I struggled with proofs all through college. This book really has help me understand the art of writing proofs. The book is very well written and easy to read. This is just an awesome book!!!

Just buy this

I needed a book that covered fundamental background information behind mathematical proof techniques for an undergraduate univeristy level linear algebra class.With this book, I was able to truly learn and understand the major concepts behind mathematical logic and proof. This text brings a whole new meaning to teaching the reader about being precise; and I mean the author does an extremely terrific job of doing just that. Wow!Seriously, the focus here is on content so you won't find any sexy graphs or anything. The content is so good that I often felt that just by reading it I was propelled into a quasi- pseudo-lecture meeting.After following this text, I can say that I now appreciate the act of being precise to the point that is required for mathematical proof. If you want to extend the knowledge of your 'white board' then just buy this thing. I am so glad I did.BTW, I only needed the content from the first five chapters, I can't say much about the rest of the text. However, taking an inductive approach, I must assume that the other chapters are also very excellent. Yess, see it worked!

Fabulous So Far.

I'm at the end of my first discrete mathematics course and have struggled to find clear explainations of how to write a proof, meaning how to choose what method and how to choose what the next statement should be to lead to the desired conclusion. I'm only on chapter five and it is a breath of fresh air to read this. Rather than just showing the completed proof Eccles shows the "scratch" work that goes into making the proof, discusses the reasoning and alternative paths, and then has the final proof that is easily understood. An excellent supplement for a typical college text.

User-Friendly! Almost makes learning analysis fun!

If you are struggling with a first analysis course or any course that uses proofs, this is the book for you! It introduces basic analysis topics like logic, sets, and the real numbers. And it is written in almost plain english! Moreover, the author focuses on teaching proof writing.