The Essence of Mathematics

The Essence of Mathematics Alexandre Borovik and Tony Gardiner
Forthcoming in 2019

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. So it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and 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.



The Essence of Mathematics
Alexandre Borovik and Tony Gardiner | Forthcoming 2019
OBP Series in Mathematics, vol. 3 | ISSN: 2397-1126 (Print); 2397-1134 (Online)
ISBN Paperback: 9781783746996
ISBN Hardback: 9781783747009
ISBN Digital (PDF): 9781783747016
ISBN Digital ebook (epub): 9781783747023
ISBN Digital ebook (mobi): 9781783747030
DOI: 10.11647/OBP.0168
BIC subject codes: PB (Mathematics) | YQM (Educational: Mathematics and numeracy) | PBK (Calculus and mathematical analysis) | PBM (Geometry) | PBT (Probability and statistics)