Softcover ISBN:  9781470450489 
Product Code:  DOL/54 
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eBook ISBN:  9781470450496 
Product Code:  DOL/54.E 
List Price:  $30.00 
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AMS Member Price:  $22.50 
Softcover ISBN:  9781470450489 
eBook: ISBN:  9781470450496 
Product Code:  DOL/54.B 
List Price:  $65.00 $50.00 
MAA Member Price:  $48.75 $37.50 
AMS Member Price:  $48.75 $37.50 
Softcover ISBN:  9781470450489 
Product Code:  DOL/54 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 
eBook ISBN:  9781470450496 
Product Code:  DOL/54.E 
List Price:  $30.00 
MAA Member Price:  $22.50 
AMS Member Price:  $22.50 
Softcover ISBN:  9781470450489 
eBook ISBN:  9781470450496 
Product Code:  DOL/54.B 
List Price:  $65.00 $50.00 
MAA Member Price:  $48.75 $37.50 
AMS Member Price:  $48.75 $37.50 

Book DetailsDolciani Mathematical ExpositionsVolume: 54; 1997; 90 ppMSC: Primary 11; Secondary 01
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.

Table of Contents

Chapters

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 Viéte 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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This book deserves the highest praise. For general readers: undergraduates through professionals.
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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.

Chapters

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 Viéte 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.”

This book deserves the highest praise. For general readers: undergraduates through professionals.
Choice