• 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
• Share This:  

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.

• Amazon

• Popular, Recreational, and Miscellaneous Mathematics
• Elementry Mathematics
• Mathematical Logic - Set Theory, Model Theory, Computability, etc

• The Essence of Mathematics Through Elementary Problems (Alexandre Borovik, et al)
• The Mirror Site (1) - PDF

• Model and Mathematics: From the 19th to the 21st Century

  The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models.

• Men of Mathematics: Great Mathematicians from Zeno to Poincaré

  This book provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension.

• Making up Numbers: A History of Invention in Mathematics

  This book offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.

• Mathematical Omnibus: Thirty Lectures on Classic Mathematics

  This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics.

• Street-Fighting Math: Guessing & Opportunistic Problem Solving

  This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.

• What is Mathematics: Godel's Theorem and Around (K. Podnieks)

  This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities.

• Mathematics in the Age of the Turing Machine (Thomas C. Hales)

  Computers have rapidly become so pervasive in mathematics that future generations may look back to this day as a golden dawn. The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

• An Infinite Descent into Pure Mathematics (Clive Newstead)

  The goal of this book is to help the reader make the transition from being a consumer of mathematics to a producer of it. Throughout, strategies are provided that help readers to see how mathematical concepts and results can be used in a proof.

• Men of Mathematics: Great Mathematicians from Zeno to Poincaré

  This book provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension.

• Blast Into Math! (Julie Rowlett)

  It is a fun and rigorous introduction to pure mathematics, is suitable for both students and a general audience interested in learning what pure mathematics is all about. Pure mathematics is presented in a friendly, accessible, and nonetheless rigorous style.

• The Millennium Prize Problems (James Carlson, et al)

  Guided by the premise that solving some of the world's most important mathematical problems will advance the field, this book offers a fascinating look at the seven unsolved Millennium Prize problems.

• Mathematical Discovery (A.M. Bruckner, et al)

  A course introducing the idea of mathematical discovery, especially to students who may not be particularly enthused about mathematics as yet, in which the students could actually participate in the discovery of mathematics.