• Title: The Essence of Mathematics Through Elementary Problems
• Author(s) Alexandre V. Borovik, Tony Gardiner
• Publisher: Open Book Publishers (June 11, 2019); eBook (Creative Commons Licensed)
• License(s): CC BY 4.0
• Hardcover/Paperback: 398 pages
• eBook: HTML and PDF
• Language: English
• ISBN-10/ASIN: 1783746998
• ISBN-13: 978-1783746996
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Book Description

This book consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

It has six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

• Alexandre V. Borovik is a Professor of Pure Mathematics at the University of Manchester, United Kingdom, where he has been working for the past 20 years.
• Tony Gardiner is a British mathematician who until recently held the position of Reader in Mathematics and Mathematics Education at the University of Birmingham.

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