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This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.
This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.
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Autorenporträt
Jay R. Goldman
Inhaltsangabe
PART 1: FROM FERMAT TO LEGENDRE, Chapter 1. The Founding Fathers, Chapter 2. Fermat, Chapter 3. Euler, Chapter 4. From Euler to Lagrange; The Theory of Continued Fractions, Chapter 5. Lagrange, Chapter 6. Legendre, PART 2: GAUSS AND THE DISQUISfilONES ARITHMETICAE, Chapter 7. Gauss, Chapter 8. Theory of Congruence, Chapter 9. Theory of Congruences, Chapter 10. Primitive Roots and Power Residues, Chapter 11. Congruences of the Second Degree, Chapter 12. Binary Quadratic Forms 1: Arithmetic Theory, Chapter 13. Binary Quadratic Forms 2: Geometric Theory, Chapter 14. Cyclotomy, PART 3: ALGEBRAIC NUMBER THEORY, Chapter 15. Algebraic Number Theory 1: The Gaussian Integers and Biquadratic Reciprocity 1. Gauss and Biquadratic Reciprocity, Chapter 16. Algebraic Number Theory 2: Algebraic Numbers and Quadratic Fields, Chapter 17. Algebraic Number Theory 3: Ideals in Quadratic Fields, PART 4: ARITHMETIC ON CURVES, Chapter 18. Arithmetic on Curves 1: Rational Points and Plane Algebraic Curves, Chapter 19. Arithmetic on Curves 2: Rational Points and Elliptic Curves, Chapter 20. Arithmetic on Curves 3: The Twentieth Century, PART 5: MISCELLANEOUS TOPICS, Chapter 21. Irrational and Transcendental Numbers, Diophantine Approximation, Chapter 22. Geometry of Numbers, Chapter 23. p-adic Numbers and Valuations, Bibliography, Index
PART 1: FROM FERMAT TO LEGENDRE, Chapter 1. The Founding Fathers, Chapter 2. Fermat, Chapter 3. Euler, Chapter 4. From Euler to Lagrange; The Theory of Continued Fractions, Chapter 5. Lagrange, Chapter 6. Legendre, PART 2: GAUSS AND THE DISQUISfilONES ARITHMETICAE, Chapter 7. Gauss, Chapter 8. Theory of Congruence, Chapter 9. Theory of Congruences, Chapter 10. Primitive Roots and Power Residues, Chapter 11. Congruences of the Second Degree, Chapter 12. Binary Quadratic Forms 1: Arithmetic Theory, Chapter 13. Binary Quadratic Forms 2: Geometric Theory, Chapter 14. Cyclotomy, PART 3: ALGEBRAIC NUMBER THEORY, Chapter 15. Algebraic Number Theory 1: The Gaussian Integers and Biquadratic Reciprocity 1. Gauss and Biquadratic Reciprocity, Chapter 16. Algebraic Number Theory 2: Algebraic Numbers and Quadratic Fields, Chapter 17. Algebraic Number Theory 3: Ideals in Quadratic Fields, PART 4: ARITHMETIC ON CURVES, Chapter 18. Arithmetic on Curves 1: Rational Points and Plane Algebraic Curves, Chapter 19. Arithmetic on Curves 2: Rational Points and Elliptic Curves, Chapter 20. Arithmetic on Curves 3: The Twentieth Century, PART 5: MISCELLANEOUS TOPICS, Chapter 21. Irrational and Transcendental Numbers, Diophantine Approximation, Chapter 22. Geometry of Numbers, Chapter 23. p-adic Numbers and Valuations, Bibliography, Index
Rezensionen
A superb combination historical narrative and introductory mathematic text. -- Math Works, May 2003
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