Making up Numbers / Ekkehard Kopp.

Format:

Book

Author/Creator:

Kopp, Ekkehard, author.

Language:

English

Subjects (All):

Mathematical instruments.

Complex organizations.

Physical Description:

1 online resource (ix, 267 pages) : illustrations

Place of Publication:

Cambridge, UK : Open Book Publishers, 2020.

Summary:

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.

Contents:

Intro; Preface; Prologue: Naming Numbers; 1. Naming large numbers; 2. Very large numbers; 3. Archimedes' Sand-Reckoner; 4. A long history; Chapter 1. Arithmetic in Antiquity; Summary; 1. Babylon: sexagesimals, quadratic equations; 2. Pythagoras: all is number; 3. Incommensurables; 4. Diophantus of Alexandria; Chapter 2. Writing and Solving Equations; Summary; 1. The Hindu-Arabic number system; 2. Reception in mediaeval Europe; 3. Solving equations: cubics and beyond; Chapter 3. Construction and Calculation; Summary; 1. Constructions in Greek geometry; 2. `Famous problems' of antiquity; 3. Decimals and logarithms; Chapter 4. Coordinates and Complex Numbers; Summary; 1. Descartes' analytic geometry; 2. Paving the way; 3. Imaginary roots and complex numbers; 4. The fundamental theorem of algebra; Chapter 5. Struggles with the Infinite; Summary; 1. Zeno and Aristotle; 2. Archimedes' `Method'; 3. Infinitesimals in the calculus; 4. Critique of the calculus; Chapter 6. From Calculus to Analysis; Summary; 1. D'Alembert and Lagrange; 2. Cauchy's `Cours d'Analyse'; 3. Continuous functions; 4. Derivative and integral Chapter 7. Number Systems; Summary; 1. Sets of numbers; 2. Natural numbers; 3. Integers and rationals; 4. Dedekind cuts; 5. Cantor's construction of the reals; 6. Decimal expansions; 7. Algebraic and constructible numbers; 8. Transcendental numbers; Chapter 8. Axioms for number systems; Summary; 1. The axiomatic method; 2. The Peano axioms; 3. Axioms for the real number system; 4. Appendix: arithmetic and order in C; Chapter 9. Counting beyond the finite; Summary; 1. Cantor's continuum; 2. Cantor's transfinite numbers; 3. Comparison of cardinals; Chapter 10. Solid Foundations?; Summary; 1. Avoiding paradoxes: the ZF axioms; 2. The axiom of choice; 3. Tribal conflict; 4. Gödel's incompleteness theorems; 5. A logician's revenge?; Epilogue; Bibliography; Name Index; Index.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references and index.

ISBN:

9781800640979

1800640978