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Diophantus & Diophantine Equationsby Isabella Bashmakova
Synopses & ReviewsPublisher Comments: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. Synopsis:This is the story of Diophantine analysis, a subject that, owing to its proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. 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. Synopsis:Semi-popular maths on an area of number theory related to Fermat. Table of ContentsIntroduction; 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'.
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