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Making up numbers : a history of invention in mathematics /

Bibliographic Details
Main Author: Kopp, P. E., 1944- (Author)
Corporate Author: ProQuest (Firm)
Format: eBook
Language:English
Published: Cambridge, UK : OpenBook Publishers, [2020]
Subjects:
Mathematics > History.
Inventions > Mathematical models.
Mathematics.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of 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
  • Blank Page
  • Blank Page