Publisher: Firefly Books

Author Statement: by Dr. Richard Elwes

Audience: Trade

Specs: 200 black-and-white illustrations, index

Pages: 416

Trim Size: 7 1/2" X 10" X 1 1/8"

Language code 1: eng

Publication Date: 20140911

Copyright Year: 2014

Author Statement: by Dr. Richard Elwes

Audience: Trade

Specs: 200 black-and-white illustrations, index

Pages: 416

Trim Size: 7 1/2" X 10" X 1 1/8"

Language code 1: eng

Publication Date: 20140911

Copyright Year: 2014

Price: Select Below

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A comprehensive study of math principles in one volume for the general reader.

A comprehensive study of math principles in one volume for the general reader.

This practical reference provides clear and concise explanations of the most fascinating fundamental mathematical concepts. Distilled into 1001 mini-essays arranged thematically, this unique book moves steadily from the basics through to the most advanced areas of math, making it the ideal guide for both the beginner and the math wiz.

The book covers all of the fundamental mathematical disciplines:

- Geometry

- Numbers

- Analysis

- Logic

- Algebra

- Probability and statistics

- Applied mathematics

- Discrete mathematics

- Games and recreational mathematics

- Philosophy and metamathematics

Expert mathematician Richard Elwes explains difficult concepts in the simplest language with a minimum of jargon. Along the way he reveals such mathematical magic as how to count to 1023 using just 10 fingers and how to make an unbreakable code.

Enlightening and entertaining, ** Mathematics 1001** makes the language of math come alive.

Bio: | Dr. Richard Elwes is a writer, lecturer and researcher in mathematics. He contributes to |

First Chapter: | INTRODUCTION THE FIRST MATHEMATICIAN KNOWN BY NAME is Ahmes, an Egyptian scribe who around 1650 BC copied out and studied a list of complex mathematical problems he called the 'ancient writings'. Today, Ahmes' text is known as the The study of mathematics, then, is as ancient as civilization; but it also represents the modernity of today's world. In the millennia since Ahmes' work, we have seen scientific and technological progress of which he could not have dreamt. Central to this advance has been the march of mathematics, which has contributed the basic language used in all scientific contexts. Probably mathematics' most fundamental contribution has been in the sphere of physics. Galileo's revolutionary insight in the early 17th century that the universe might yield to a purely mathematical description set the direction towards the world-changing theories of quantum mechanics and relativity. This reliance on mathematics is not confined to the physical sciences. The social sciences depend on techniques of probability and statistics to validate their theories, as indeed do the worlds of business and government. More recently, with the emergence of information technology, mathematics became entangled in another love-affair, with computer science. This too has had a profound impact on our world. As its influence has broadened, the subject of mathematics itself has grown at a startling rate. One of history's greatest mathematicians, Henri Poincare, was described by Eric Temple Bell as 'the last universalist', the final person to have complete mastery of every mathematical discipline that existed during his lifetime. He died in 1912. Today, no-one can claim to have mastered the whole of topology, let alone geometry or logic, and these are just a fraction of the whole of mathematics. Poincare lived through a turbulent period in the history of mathematics. Old ideas had been blown away, and new seeds planted which flourished during the 20th century. The result is that the mathematical world we know today is rich and complex in ways that even the greatest visionaries of the past could not have imagined. My aim in this book is to give an overview of this world and how it came to be. I might have tried to sketch a low-resolution map of the entire mathematical landscape, but this would be neither useful nor entertaining. Instead, I have presented 1001 short 'postcards' from interesting landmarks around the mathematical world that nonetheless give a feel for the bigger picture of mathematics. In the scheme of things, 1001 is a very small number (see the frivolous theorem of arithmetic). My challenge has been to select the real highlights: the truly great theorems, the outstanding open problems and the central ideas. I have also sought to represent the surprises and quirks that make the subject truly fascinating. This book is organized thematically, on three levels. It is divided into ten chapters, each covering a broad subject, beginning with 'Numbers'. Each chapter is subdivided into sections, which are more narrowly focused on a single topic, such as 'Prime numbers'. Each section comprises a series of individual entries, such as the one on the Riemann hypothesis. How you should read Who is this book aimed at? The answer is anyone with a curiosity about mathematics, from the novice to the informed student or enthusiast. Whatever the reader's current knowledge I'm sure that there will be material here to enlighten and engage. Some parts of the book undoubtedly cover highly complex subjects. That is the nature of the subject; shying away from it would defeat the purpose. However, the book is structured so that the relevant basic concepts precede the complex ones, giving a foundation for understanding. My job in writing has been to discuss all ideas, from the basic to the most abstract, in as direct and focused a way as possible. I have done my best, and have certainly relished the challenge. Now I can only hope that you will enjoy it too. Richard Okura Elwes |

TOC: | Contents - Introduction
Numbers - The Basics
Arithmetic Number Systems Rational Numbers Factors and Multiples Induction Representation of Numbers Transcendental Numbers Ruler and Compass Constructions Diophantine Equations Prime Numbers Geometry - Euclidean Geometry
Triangles Circles Polygons and Polyhedra Transformations Tessellations Curves and Surfaces Polar Coordinates Discrete Geometry Differential Geometry Topology Knot Theory Non-Euclidean Geometry Algebraic Topology Algebraic Geometry Diophantine Geometry Algebra - Letters and Numbers
Equations Vectors and Matrices Group Theory Abstract Algebra Discrete Mathematics - Combinatorics
Graph Theory Ramsey Theory Analysis - Sequences
Series Continuity Differential Calculus Integral Calculus Complex Analysis Power Series Exponentiation Fractals Dynamics Systems Differential Equations Fourier Analysis Logic - Basic logic
The Science of Deduction Set Theory Hilbert's program Complexity theory Computability theory Model Theory Uncertainty and Paradoxes Metamathematics - What Mathematicians Do
Mathematics and Technology Philosophies and Mathematics Probability & Statistics - Statistics
Probability Probability Distributions Stochastic Processes Cryptography Mathematical Physics - Newtonian Mechanics
Waves Fields and Flows Special Relativity Gravity Quantum Mechanics Quantum Field Theory Games and Recreation - Game Theory
Fibonacci Puzzles and Perplexities Index |