Customer Reviews

How to Think Like a Mathematician: A Companion to Undergraduate Mathematics

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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.

To be successful in mathematics, your mind must perform operations that are unlike the operations needed to do most other things. You must be able to hold abstract ideas, sometimes several at a time, as well as see the relationships between multiple concepts. Furthermore, those abstract ideas are built on other abstract ideas; for example, most of mathematics is built on the fundamental abstract idea of the use of a variable.
However, being different and at times being hard does not mean that the ideas of mathematics are incomprehensible. Humans excel at understanding abstract ideas, a strong argument can be made that such a skill is the very definition of human intelligence. 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.
Many students are capable of leaping the comprehension hurdle; yet hit a wall when it comes time to apply the concepts in order to generate 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.

Published in Journal of Recreational Mathematics, reprinted with permission

Loved the book, It's definately going to be a go-to book for my other advanced classes. It is wrote in an extraordinarily user-friendly way and is actually somewhat fun to read.

This book will help you with proofs. You still have to do them. No one has written the magic book that gets you out of the rolled up shirt sleeves effort, but this book certainly helps make the learning easier.

An excellent book that will introduce a complete novice to mathematical thinking.
There is a chapter also on Set theory which is a nice touch (and it is used illustratively so it doesn't feel like you are studying sets specifically). The book gives an excellent outline on how to approach a proof and how to study mathematics which often perplexes even the most talented of mathematicians (problems or theory etc.?)

That said it is extremely basic. Anyone who has competed in math olympiads for a year or two will know the proof techniques and be familiar to some extent on how to set them out. Also the problem solving component is so-so. I suppose the study tips could be useful but I feel that they are self-explanatory to some extent if one has a certain degree of mathematical experience.

A good book for neophytes. But if you are in your second year at University/College then this book will NOT help you. For first-year it will be of limited value, as one learns best by DOING.