The Little Book of Mathematical Principles, Theories & Things. Robert Solomon

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The Little Book of Mathematical Principles, Theories & Things - Robert Solomon

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as Part of Logic

       The Snowflake Curve

       Axiom of Choice

       The Jordan Curve Theorem

       Special Relativity

       Intuitionism

       Zermelo–Fraenkel Set Theory

       The Hairy-Ball Theorem

       General Relativity

       The Hilbert Program

       Gödel’s Theorem

       The Travelling Salesman

       Turing Machines

       Binary Numbers

       The Ham Sandwich Theorem

       The Enigma Machine

       Colossus

       Game Theory

       ENIAC

       The Prisoner’s Dilemma

       Electronic Calculators

       Polya’s Principles

       Erdös Number

       Chaos Theory

       The Secretary Problem

       Catastrophe Theory

       Life

       Matiyasevich’s Theorem

       P = NP?

       Public Key Codes

       Fractals

       The Four-Color Theorem

       The Logistic Model

       Stacking Oranges

       Fermat’s Last Theorem

       The Seven Millennium Prize Problems

       Appendix

       Glossary

       Acknowledgements

       Index

      HOW TO USE THIS BOOK

      The Little Book of Mathematical Principles, Theories, & Things is an easy-to-use comprehensive guide to mathematics. It features over 130 entries on key principles or theories essential to understanding the subject. Written in an easily accessible manner, the Little Book explains sometimes very difficult concepts and theories, putting them in their historical context, giving background information on the experts who proposed them in the first place, analysing influences and proposing, where relevant, links to other related entries. The book also features tables, equations and illustrations, and ends with a glossary, and a comprehensive index.

      The Little Book of Mathematical Principles, Theories, & Things is arranged chronologically and the country of origin is listed, where appropriate. Each entry includes a clear main heading, the person or people responsible for the discovery, birth and death dates, where relevant, followed by a short introductory paragraph explaining the concept concisely. In some cases, the main essay is also cross referenced to linked subjects. The key on the opposite page explains the order of information in each entry.

illustration

      3000 BC Global

      Writing Numbers

      The place value system uses only a finite number of symbols to write any number.

      _______________

      In some number systems, there are different symbols for each power of 10. In a place value system, only a small number of symbols are used.

      In the Ancient Egyptian number system, dating from about 3000 BC, there were symbols for units, symbols for 10s, and so on. The number 365 was written:

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