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

1 rating: 5.0
A book by Kevin Houston

"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 … see full wiki

Author: Kevin Houston
Genre: Mathematics
Publisher: Cambridge University Press
1 review about How to Think Like a Mathematician: A Companion...

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

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