Get Free Ebook How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, by Dr Kevin Houston
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How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, by Dr Kevin Houston
Get Free Ebook How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, by Dr Kevin Houston
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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.
- Sales Rank: #477192 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2009-02-23
- Original language: English
- Number of items: 1
- Dimensions: 9.69" h x .75" w x 7.44" l, 1.15 pounds
- Binding: Paperback
- 274 pages
- Used Book in Good Condition
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.
Most helpful customer reviews
54 of 54 people found the following review helpful.
Great Introduction to Mathematical Method
By Edmon Begoli
I am reading a great book that is in author's words intended for undergraduate students of mathematics, but that in my opinion offers much more to a motivated reader.
"How to Think Like Mathematician" by Dr. Kevin Houston is a very engaging, readable and pragmatic text on mathematical "technique". It is a non-pompous, well written, valuable, easy to follow and understand valuable set of lessons and tips on understanding and adopting mathematical method, language, theorems, proofs and techniques.
It is an introductory text, so for more in depth treatment of the subjects such as proofs and number theory you may need to look further into books such as Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition) orThe Princeton Companion to Mathematics but if you are looking to understand the mathematical method and how to be able to read and write "serious" math this is an ideal book.
I specially have to point out Dr. Houston's writing style - it is engaging, humorous, but substantial, pedagogical and never trivial.
46 of 47 people found the following review helpful.
Exercises with no solutions
By Marcia H Cupery
I have just started reading this book, in which the author strongly encourages the reader to do all of the exercises. Upon finishing the first exercise, I went to check my answers, and found that there were no solutions provided in the book to any of the exercises that appear in any of the chapters. After doing some research online, I found that the author has his own website and has since provided a PDF with the solutions to many of the exercises. I'm not sure if all of them are covered, but the list of solutions does appear to be quite extensive. So, in case you were like me and were wondering if your solutions were correct, you can check your answers by downloading the PDF at [...]
So far, I am really enjoying the read!
18 of 18 people found the following review helpful.
Good book. Really helped me out.
By Joshua S. Infiesto
This book and the paper "Lockhart's Lament" really helped me understand what real Math is about, at least at a very basic level. I was ineptly fumbling through my math classes before I read both. Lockhart's Lament is freely available from the AMA and I highly recommend it to anyone starting in math.
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