Essentials of Mathematical Thinking  book cover
1st Edition

Essentials of Mathematical Thinking

ISBN 9781138197701
Published November 7, 2017 by Chapman and Hall/CRC
336 Pages 174 B/W Illustrations

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Book Description

Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies.

The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world.

The book explains:

  • What goes behind a Google search algorithm
  • How to calculate the odds in a lottery
  • The value of Big Data
  • How the nefarious Ponzi scheme operates

Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.

Table of Contents

First Thoughts. Diverse Mathematical Thoughts. Strategy. Focus. Science. Counting. Games. Geometry. Practical Matters. Breaking the Code. Discrete Problems. Advanced Ideas. Concluding Remarks

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Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has written more than 65 books and more than 175 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D from Princeton University.


With a title like Essentials of Mathematical Thinking one might expect a philosophical treatise, or possibly a research exposition about cognitive processes and math education. But at the top of the cover, you can see that it is announced as a "Textbook in Mathematics". Since that is what it is: a textbook in mathematics, but a rather unconventional one. Several writers of popular science or recreational mathematics have written books in which they collect mathematical topics that are accessible for a general public and that should illustrate that mathematics can be fun and that there are many practical applications in everyday life involving mathematics. The items discussed in these books can involve integers, prime numbers, geometry, probability, counting problems, logic and paradoxes, games, puzzles, etc. But they are mostly "recreational" or at most they can serve as a source of inspiration for math teachers to embellish their courses and candy-coat the theorems and proofs of the actual textbook.

Here however, Steven Krantz uses all these entertaining subjects to use them as an actual textbook to teach mathematical awareness and some skills to students who have not the slightest ambition of using mathematics in their further career. For example if undergraduate students are required to broaden their curriculum with some math course. There is no point in imposing mathematical abstraction on them or to force them to memorize proofs of theorems they will never need in life. So the idea is to use all these entertaining subjects to develop their ability to use logic arguments, to solve problems, and to convince them that mathematics is indeed everywhere, but that it is nothing to be afraid of. They will not become better mathematicians in the narrow sense of the word, but at the end of the journey they should have acquired some skills one could call mathematical and they should be more open minded towards mathematics and mathematicians.

~Adhemar Bultheel, European Mathematical Society 2017