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Diophantus and Diophantine Equations

Diophantus and Diophantine Equations

Out of Print

Part of Dolciani Mathematical Expositions

  • Date Published: August 1998
  • availability: Unavailable - out of print
  • format: Paperback
  • isbn: 9780883855263

Out of Print
Paperback

Unavailable - out of print
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  • This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus - a person whose very existence has long been doubted by most historians of mathematics - will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman who notes the most recent developments including the proof of Fermat's Last Theorem.

    • Afterword by Professor Joseph Silverman, expert on Fermat's Last Theorem
    • Lots of historical details
    • Ever-popular subject
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    Product details

    • Date Published: August 1998
    • format: Paperback
    • isbn: 9780883855263
    • length: 103 pages
    • dimensions: 217 x 147 x 7 mm
    • weight: 0.14kg
    • availability: Unavailable - out of print
  • Table of Contents

    Introduction
    1. Diophantus
    2. Numbers and symbols
    3. Diophantine equations
    4. Evaluation of Diophantus' methods by historians of science
    5. Indeterminate quadratic equations
    6. Indeterminate cubic equations
    7. Diophantus and number theory
    8. Diophantus and the mathematicians of the 15th and 16th centuries
    9. Diophantus' methods in the works of Viete and Fermat
    10. Diophantine equations in the works of Euler and Jacobi: addition of points on an elliptic curve
    11. The geometric meaning of the operation of addition of points
    12. The arithmetic of algebraic curves
    13. Conclusion
    14. Supplement: the role of concrete numbers in Diophantus' 'Arithmetic'.

  • Author

    Isabella G. Bashmakova, Moscow State University

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