How to Think Like a Mathematician: A Companion to Undergraduate Mathematics 1st Edition by Kevin Houston (PDF)

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.

User’s Reviews

Editorial Reviews: 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 Book Description This arsenal of tips and techniques eases new students into undergraduate mathematics, unlocking the world of definitions, theorems, and proofs. About the Author Kevin Houston is Senior Lecturer in Mathematics at the University of Leeds. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a wonderful text for college students learning to write proofs for the first time. The chapters are clear and concise, and they cover a wide range of topics.You’ll need a good professor running the class, as the book has a few mistakes. To be fair, the author’s website highlights in great detail where these occur, and many of the corrections are minor. I can easily overlook these.My main problem with the text is that there are inadequate solutions available. I know that providing them in advance may tempt some students to forego “getting their own hands dirty with the material,” but I feel like most of the people who are at this point in their mathematics studies are the ones who will give good effort before consulting a solutions manual. Even just providing hints is better than going almost 20 chapters without guidance. And I don’t even need them in the book; having them available with the others on the website would be good enough.But, Dr. Houston’s writing style is clear, concise, and entertaining enough to merit 4 stars. This is a fundamental area of mathematics that needs good textbooks, and Dr. Houston’s is among the best!

⭐The book itself is a good textbook, but do not get the kindle edition. Many of the math formulas have typos that make it impossible to figure out what was actually meant. This was especially difficult when working through homework problems from the book.This is not like misspelled words in other books where you still know the meaning. If math typesetting is wrong, you can not figure out what the question meant. There have been many times I have to borrow a friend’s hardcover book to figure out what the correct formula or question is. Do not buy the kindle, get hardcover or paperback.

⭐This book is fantastic and I wish I had it years ago. Like the author says, things I wish someone had told me before. I started reading it and I can’t put it down. My primary reason for buying it is to learn how to do proofs well as requited in a college course.Basically, this should be a standard text for everyone that ever takes a math class. This book can be easily taught in high school or lower.

⭐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!

⭐I have read quite a few books trying to prepare myself to tackle college mathematics. It has been difficult since I decided to improve myself in it much later in life. This book has presented the ideas in the clearest manner for me thus far. Will probably re-read with an emphasis on more of the assignments.

⭐This book is great, the author is amazing I love reading it however, when I received the book the binding was pathetic. The book fell apart as soon as I opened the first page. It is now held together by duct tape so I can use it for my college courses. To those who purchase this book, ITS AWESOME but make sure the book your getting is held together properly so you don’t have the same issues I had.

⭐This is a wonderful and enlightening book that went perfectly as a prerequisite for my set theory class, but after I received it it began to fall apart so I went searching online. I found a free copy within the first three links I clicked. DO NOT BUY THE HARD COPY IF YOU CAN DEAL WITH AN ELECTRONIC ONE! It’s FREE.

⭐This book is a great companion for anyone taking discrete mathematics (even if it is not a required book). It is very detailed and has plenty of examples. It’s only downfall is as far as I can tell, it has no provided solutions making it hard to check your work.

⭐A good book for undergrad pure mathematicians – not so useful for engineering or applied mathematicians.

⭐A very interesting read. This is a must have book for any undergraduate studying maths as it forms the bridge between A-Levels and university maths. This definitely gets you thinking and engages you from the first page. This book saved my degree!

⭐Brilliant book but disappointed the exercise answers are not included!

⭐As a math undergrad this book is very useful

⭐Name on the tin tells you exactly what it’ll provide you with. Recommended if you need another perspective of thinking

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