Maths Hacks 100 Clever Ways to Help You Understand and Remember the Most Important Theories

Maths Hacks 100 Clever Ways to Understand and Remember Theories

Maths Hacks 100 Clever Ways to Help You Understand and Remember the Most Important Theories by Rich Cochrane

Contents of Maths Hacks Book

  • Introduction
  • Tricks of the Trade
  • Numerous Numbers
  • The Science of Structure
  • Continuity
  • Maths in Space
  • Maths Meets Reality

How to Use This Ebook

Select one of the chapters from the main contents list and you will be taken straight to that chapter.

Look out for linked text (which is in blue) throughout the ebook that you can select to help you navigate between related sections.

You can double tap images and tables to increase their size. To return to the original view, just tap the cross in the top left-hand corner of the screen.

Parts of the Book

We start with “Tricks of the Trade”: ideas and techniques that pervade almost all of mathematics.

Part 2 is on “Numerous Numbers”, the things most lay folk think mathematics is all about.

The idea of number itself has been radically re-imagined over the last two centuries.

Mathematics is actually about much more than numbers. One plausible claim is that it is “The Science of Structure”, which is the focus of Part 3.

Parts 4 and 5 pick up on a different but closely related strand: broadly, mathematics as the study of space and time.

In “Continuity” we look at the calculus, a family of techniques for studying processes of change and other continuous phenomena that have undergone a vast generalization since their invention by Newton and Leibniz.

In “Maths in Space” we see how geometry has also evolved into a rich field populated by strange and exotic objects.

I have restrained myself from describing things like the Möbius strip, which are discussed in almost every popular mathematics book; here we go quite a bit deeper, visiting topology and Riemannian and algebraic geometries.

Finally, in “Maths Meets Reality”, I try to do some justice to the areas of mathematics that have mostly evolved in relation to practical applications, especially around statistics, algorithms, decision-making and modelling.

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