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

* PhysicalThe book has a good font size printing in B&W text.* Target AudienceThis volume is clearly designed using feedback from students to help in the areas where perceived difficulties are common and repeatedly encountered. I feel this book's syllabus covers such a wide area it is capable of addressing new or refreshing forgotten knowledge gaps of many student's, beyond its initial design. Its so beautifully and carefully composed that I would be surprised if you were unable to find nothing totally new or refreshed by this book, almost independent of the level you may be at the moment.* Personal areasThe parts that I particularly enjoyed were sections iii, iv, v, or to those without the book 'Definitions, Theorems and Proofs', 'Techniques of Proof', and 'Mathematics that all good mathematicians need'. As this is the stuff that I had understood, but things had become bit rusty. Its has a clear ability to remind the reader that scores with me. Its such a well - designed, helpful and monumentally clear exposition of these vital skills that I read it in 3 days and read for hours totally delighted by the way is written and the pitch its put to help its target audience.*SummaryUnfortunately, a number of pages from my copy became out of its binding, which is a pity. However, I stapled them together, and with regards of the authors skills I still consider the book as a recommended read and very enjoyable to go over topics in a fresh and entertaining manner.

This book won't teach you how to do any specific maths techniques, but it will help you to learn how to "do maths". Some of the advice is quite simple, but it really does take it to be written down before you think about it. Other techniques are less obvious, but equally helpful. I found the book helped me move form A-level thinking, where you are in effect given all the information you need, to University level where you need to explore and work with concepts and techniques more. The section on proofs was particularly helpful and useful.

Really good book, does exactly what it says on the tin. Filled with lots of info and exercises that get you thinking about mathematics in a different way. I found the sections on how to write and solve problems like a mathematician particularly useful. Well worth buying if you want to enhance your understanding of the world of mathematics. I started the book having done half a physics degree; you could probably just about get away with reading it if you have a good GCSE understanding but it's probably best if you learn some A-level maths first.

An amazing read. Not only has it really helped with my studies (First year at Uni) doing Maths but it's also really interesting. The author is great. He really connects with his reader in a beautiful manner. Thank you so much Dr Kevin Houston.

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!

This is a well structured book that has some excellent guidance on how to approach and solve mathematical problems. However, throughout the book exercises are set for the reader. Unfortunately, the book doesn’t contain any of the solutions to those exercises, and the downloadable PDF only gives a fraction of the solutions. Entire chapters of the book are without solutions to any of the exercises set. This makes self study much harder. It’s a real shame, as I think providing solutions to most (if not all) the exercises would make this an incredibly valuable resource.

Great Maths books for anyone studying Mathematics at undergraduate level, the only reason the book lost a star was because the answers to the exercises are not provided.Here is a link for anyone who can't find them [...]

As a math undergrad this book is very useful