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The Essence of Mathematics Through Elementary Problems

Author: Alexandre Borovik, Tony Gardiner
Subject: Mathematics
Source: Open Textbook Library
Publisher: Open Book Publishers
ISBN: 9781783747016
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It is increasingly clear that the shapes of reality – whether of the natural world/ or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’/ and to appreciate why its shapes/ patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience/ but the authors of this book concentrate on the first part/ and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics 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. The book consists of 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.

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