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How to Think Like a Mathematician

4.17  ·  Rating details ·  200 ratings  ·  13 reviews
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, ...more
Paperback, 265 pages
Published February 1st 2009 by Cambridge University Press
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Tareq Elderawi
Jun 11, 2016 rated it really liked it
*Don't believe everything you read .
*simplicity is the ultimate sophistication .
* If it isn't hurting , then it isn't working .
*Be scaptical of everything and try to prove that the text is wrong , search for hidden assumptions and try to use extreme cases and examples .
*Learn as much by writing as by reading .
*It isn't that they can't see the solution , It is that they can't see the problem .
*Everything is simpler that you think and at the same time more complex that you imagine .
*The highes
...more
Ali
Nov 15, 2016 rated it really liked it
This book contains very useful techniques for anyone who wants to gain a deeper understanding of mathematics, especially chapters on how to read definitions, theorems and proofs. Maybe it requires more acquaintance with mathematics to highly appreciate other advice given, but I found those mentioned the most useful ones. There is also a good treatment of main techniques of proof. Some exercises are a bit challenging for an undergraduate but overall it does not require any especial prerequisite k ...more
Sambasivan
May 22, 2016 rated it it was amazing
Written with incredible clarity. This book streamlines your thought process and helps you discipline yourself to think logically as well. Surprisingly good.
Philip
Dec 13, 2018 rated it it was amazing  ·  review of another edition
Shelves: studies
Was hat mich dieses Buch gelehrt?
Besser noch: Was hat dieses Buch getan?

Also zunächst einmal hat es mit einigen grundlegenden Begriffen und Symbolen aufgeräumt. Langsam aber stetig wird man näher an die komplizierten Kernstücke der Mathematik heran geführt. Und dabei bekommt man wieder und wieder Methoden vorgestellt, wie man mit diesen Teilen arbeiten kann, wie man damit denken kann, und wie man denken sollte, um die Mathematik zu ergründen und für sich zu erobern.

Ich finde, es ist in der Tat e
...more
Aleksandra Taranov
Sep 11, 2017 rated it really liked it
Shelves: math
I found the book too basic, but it does give good study tools to people beginning to learn mathematics. However, I was often annoyed by the pompous tone and snide digs at other disciplines like history/sociology that showed ignorance about how they work. There was a lot of 'this matters in math' but you could just look up a date in history to know an event happened. That's a strawman and not how high level history works at all. That said, the math ideas are very clearly written and accurate and ...more
Anand
Oct 25, 2019 rated it it was amazing
Shelves: freshman-year
Should be required reading for everyone, not just people studying for a maths degree. While it's intended for an aspiring mathematician, the thought processes outlined in this book give practical advice to just about anyone. Knowing the ways that a mathematician deducts their arguments and their thought processes is a valuable life skill, and this book shows the way.

It provides good study advice too if you're just trying to do well in math, if that convinces you further.
Akashdeep Singh
May 05, 2019 rated it really liked it  ·  review of another edition
Good book for the confused

The book is good enough for college students to get hang of how to think in mathematics, especially proofs & statements. Ample examples & no assumption by the author that only experienced math students will read it.
...more
Samuel
Aug 21, 2018 rated it really liked it
For gradeschoolers entering university
Robert Murphy
Apr 14, 2019 rated it it was amazing
Shelves: kindle
Perfect for undergrad, not bad at all for high school
Ben G
Aug 01, 2017 is currently reading it
Shelves: learning
I bought this so I could understand the language of mathematics (e.g. theorems, proofs, etc.). I'm not a mathematician by trade, but use mathematical techniques (i.e. constructing ODE models of biological systems) in my everyday work. Thus, an absolute necessity to understand more of maths beyond the crash course I did in biomathematics at university.

Beyond chapter 1 which gives a thorough overview of sets theory and brief introductions to maps and functions. Chapter's 2 and 3 are concerned with
...more
Perro
Aug 06, 2016 rated it it was amazing
Definitely worth reading even for people who don't study maths, but I find it hard to comprehend, not the mathematical bit but it's a bit dull for me and sometimes it feels like the author spent pages and pages to say about one thing, which should be a lie to explain or clarify in one chapter. Also there are many excises without solution, if you are reading it on your own, how can you know your answer is right?
Bashnev
Aug 16, 2013 rated it liked it
Shelves: maths
A lot of good material explained well. Wish I had something like this when I was an undergraduate.
Irene
Nov 14, 2016 rated it it was amazing
Excellent book for anyone taking classes heavy in mathematics.
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