Product Description

Looking for a head start in your undergraduate degree in mathematics? Maybe you’ve already started your degree and feel bewildered by the subject you previously loved? Don’t panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you’ll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you’ll soon learn how to think like a mathematician.

Product Details

• Amazon Sales Rank: #18859 in Books
• Published on: 2009-02-12
• Original language: English
• Number of items: 1
• Binding: Paperback
• 278 pages

Review
"In this book, Houston has created a primer on the fundamental abstract ideas of mathematics; the primary emphasis is on demonstrating the many principles and tactics used in proofs. The material is explained in ways that are comprehensible, which will be a great help for people who seem to hit the wall regarding what to do when confronted with the creation of a proof... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof."
Charles Ashbacher, Journal of Recreational Mathematics

"The author provides concise, crisp explanations, including definitions, examples, tips, remarks, warnings, and idea-reinforcing questions. Houston expresses thoughts clearly and concisely, and includes succinct remarks to make points, clarify arguments, and reveal subleties."
W.R. Lee, Choice Magazine

About the Author
Kevin Houston is Senior Lecturer in Mathematics at the University of Leeds.

Customer Reviews

Excellent introduction to undergraduate mathematics
As a teacher of A level Maths and Further Maths, I found this book very helpful. I think every prospective maths student should read it, and do all the exercises, before starting their undergraduate mathematics course. It introduces in a rigorous but very readable style the vast majority of the topics that will be covered in the first year at university, and links them all together in a way that cultivates the more formal approach that university level mathematics requires. The author Dr Kevin Houston has been a maths lecturer at Leeds University for more than 15 years, and the book is based on his personal experience of helping to develop students' capacity for mathematical thinking and expression. There are over 300 exercises. Although the answers are not included, Dr Houston is planning to make them available on the internet over the next few months.

Conclusion--thoroughly recommended!