|
Movies Books Music Food Tv Shows Technology Politics Video Games Parenting Fashion Green Living more >

Lunch » Tags » Books » Reviews » How to Think Like a Mathematician: A Companion to Undergraduate Mathematics » User review

A systematic and gentle approach to explaining the main ideas of mathematics

  • Jul 18, 2010
Rating:
+5
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

What did you think of this review?

Helpful
3
Thought-Provoking
3
Fun to Read
3
Well-Organized
0
Post a Comment
About the reviewer
Charles Ashbacher ()
Ranked #78
Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more
Consider the Source

Use Trust Points to see how much you can rely on this review.

You
CharlesAshbacher
Your ratings:
rate more to improve this
About this book

Wiki

"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
view wiki

Details

ISBN-10: 052171978X
ISBN-13: 978-0521719780
Author: Kevin Houston
Genre: Mathematics
Publisher: Cambridge University Press
© 2014 Lunch.com, LLC All Rights Reserved
Lunch.com - Relevant reviews by real people.
()
This is you!
Ranked #
Last login
Member since
reviews
comments
ratings
questions
compliments
lists