Mathematics Rebooted: A Fresh Approach to Understanding

by Lara Alcock

Would you like to understand more mathematics? Many people would. Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For
more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed about the intrinsic elegance of mathematics, this engaging guide is the place to start.

Genres: Mathematics, Nonfiction, Science

254 pages, Hardcover

Published December 12, 2017

Reviews

[Blair · Rating 3 out of 5]

Perhaps the problem is I have just finished Paul Lockhart’s wonderful "Measurement", and this book does not quite measure up. My favourite chapter about my current obsession, symmetry and tiling, starts with the exact same pattern that Lockhart’s book begins with. Well, it is a wonderful pattern that combines triangles, squares to form hexagons. The discussion would have benefited from using Lockhart’s choice to measure angles using fractions of a rotation rather than degrees. Which makes more intuitive sense, measuring the interior angle of a regular pentagon as 108 degrees (looks like a random number to me) or three tenths of a rotation?

There is some nice work here to visually link normally abstract algebra with geometric shapes. There are also some dead ends. Group theory is introduced and then goes nowhere. She can’t resist trying to teach Cantor’s diagonal proof that the real numbers cannot be counted with rational numbers.

I recommend this as a useful resource if you want to teach high school mathematics, but it was not an amazing book.

[Victória · Rating 4 out of 5]

An amazing book to apreciate the beauty of the mathematics with no need of math background. The book starts off with very simple topics, like the ones learned in fundamental school, and then transitions to more advanced topics in a very understandable way. Lara Alcock will show that everyone is capable of doing math and understanding it, you just need to be curious. Also, the author's passion and explanation of the intuition and insight behind the concepts covered are of great value to any interested in math.

[David Drews · Rating 3 out of 5]

I liked Lara Alcock, her enthusiasm and efforts to make a dent in my mathematical ignorance. I always end with an appreciation for the minds that write these kinds of books. And, as with some other books of this typ (an aspiration/ability mismatch for me), she did make a small impact, not bad at all considering that I may not have held up my end very well. And I will be back, in one way or another, to make at least one more small assault on mathematics.

All of this is to explain that my three star rating is an honest evaluation of what I actually got from the book and at the same time an undeservedly stingy rating of the author.

[Alex · Rating 4 out of 5]

I happened to pick up Lara Alcock's book while passing time in a bookstore, and her style resonated with me: extremely approachable but not dumbed down. Alcock's enthusiasm for mathematics is contagious. Reading this book felt like having a conversation with someone who genuinely wants to share some cool maths with you. I've read a number of popular math books, but besides Singh's books on Fermat and codes they all fell a bit flat. That was until I read this book. Looking forward to reading her books on abstract algebra and analysis.

[James · Rating 4 out of 5]

This was a great primer for beginning my first year in college. The book starts off with very simple topics and then transitions to more advanced topics. Although I did not follow the exercises religiously you can think about the problems mentally and you will see slight improvements in your mathematical intuition. I would recommend this book to first-year college students because it instills curiosity within mathematics. Overall it was a great read and it changed how I thought about math.

[Stefan · Rating 5 out of 5]

This book covers a few elementary topics in a relatable way. It presents the context and a practical approach to numerical and geometric ideas that might be different than most people have been exposed to during their math courses.

[Steven Kim · Rating 5 out of 5]

This book explains math as it should have been presented the first time. There's some math for everyone here. It was a pleasure revisiting mathematical concepts long forgotten. Truly fresh!

[Klaire Hoang · Rating 5 out of 5]

Brings me too much joy