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Diophantus and Diophantine Equations

Diophantus and Diophantine Equations

By I.G. Bashmakova

Print ISBN: 978-0-88385-526-3
104 pp., Paperbound, 1997
List Price: $27.00
MAA Member: $20.25
Series: Dolciani Mathematical Expositions

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Most readers associate the mathematics of antiquity with Euclid’s Elements and the works of Archimedes and Apollonius. This wonderful little book will introduce the reader to a new aspect of the mathematics of antiquity in the works of Diophantus. The object of this book is to present the work of Diophantus, focusing on Diophantus’ methods of obtaining rational solutions of indeterminate equations of the second and third order.

The book is intended for a broad audience. It can be enjoyed by teachers as well as students.

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 15rh and 16th Centuries
9. Diophantus’ Methods in the Works of Viete and Fermat
10. Diophantine Equations in the Works of Euler and Jacobi
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”
Table of Notation
Bibliography
Name Index

About the Author

Isabella Grigoryevna Bashmakova was born in 1921 in Rostov-on Don. Her family moved to Moscow when she was in high school. She obtained her training in mathematics at Moscow University, and has spent her professional career teaching in the Faculty of Mechanics and Mathematics at Moscow University. She obtained her Ph.D. in Physics and Mathematics in 1948, and the Degree of Doctor of Science in 1961 both from Moscow State University. She has written numerous books (in the Russian language) notably, From the History of the Theory of Divisiblity, History of Diophantine Analysis from Diophantus to Fermat (written in collaboration with E.I. Slavutin), and Lectures on the History of Mathematics in Ancient Greece.

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