# Math in Minutes 200 Key Concepts Explained in an Instant

Math in Minutes 200 Key Concepts Explained in an Instant by Paul Glendinning.

## Introduction to Math in Minutes

Mathematics has been evolving for over four thousand years. We still measure angles using the 360-degree system introduced by the Babylonians.

Geometry came of age with the ancient Greeks, who also understood irrational numbers. The Moorish civilization developed algebra and popularized the idea of zero as a number.

Mathematics has a rich history for good reason. It is both stunningly useful in the language of science, technology, architecture, and commerce and profoundly satisfying as an intellectual pursuit.

Not only does mathematics have a rich past, but it continues to evolve, both in the sophistication of approaches to established areas and in the discovery or invention of new areas of investigation.

Recently computers have provided a new way to explore the unknown, and even if traditional mathematical proofs are the end product, numerical simulations can provide a source of new intuition that speeds up the process of framing conjectures.

Only a lunatic would pretend that all mathematics could be presented in 200 bite-sized chunks. What this book does attempt to do is to describe some of the achievements of mathematics, both ancient and modern, and explain why these are so exciting.

In order to develop some of the ideas in more detail, it seemed natural to focus on core mathematics.

The many applications of these ideas are mentioned only in passing. The ideas of mathematics build on each other and the topics in this book are organized so that cognate areas are reasonably close together.

But look out for long-range connections. One of the amazing features of mathematics is that apparently separate areas of study turn out to be deeply connected.

Monstrous moonshine (page 300) provides a modern example of this, and matrix equations (page 272) a more established link.

This book is thus a heady distillation of four thousand years of human endeavor, but it can only be a beginning. I hope it will provide a springboard for further reading and deeper thought.

## Math in Minutes Contents

• Introduction
• Numbers
• Sets
• Sequences and series
• Geometry
• Algebra
• Functions and calculus
• Vectors and matrices
• Abstract algebra
• Complex numbers
• Combinatorics
• Spaces and topology
• Logic and proof
• Number theory
• Glossary
• Index