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Friendly Introduction to Number Theory, 4th(P) 요약정보 및 구매

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지은이 Silverman. Joseph H.
발행년도 2012-01-18
판수 4판
페이지 431
ISBN 9780321782366
도서상태 구매가능
판매가격 45,000원
포인트 0점
배송비결제 주문시 결제

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  • A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet Number theory. Starting with nothing more than basic high school algebra, readers are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results. 
  • Preface Flowchart of Chapter Dependencies Introduction 1. What Is Number Theory? 2. Pythagorean Triples 3. Pythagorean Triples and the Unit Circle 4. Sums of Higher Powers and Fermat's Last Theorem 5. Divisibility and the Greatest Common Divisor 6. Linear Equations and the Greatest Common Divisor 7. Factorization and the Fundamental Theorem of Arithmetic 8. Congruences 9. Congruences, Powers, and Fermat's Little Theorem 10. Congruences, Powers, and Euler's Formula 11. Euler's Phi Function and the Chinese Remainder Theorem 12. Prime Numbers 13. Counting Primes 14. Mersenne Primes 15. Mersenne Primes and Perfect Numbers 16. Powers Modulo m and Successive Squaring 17. Computing kth Roots Modulo m 18. Powers, Roots, and "nbreakable" Codes 19. Primality Testing and Carmichael Numbers 20. Squares Modulo p 21. Is -1 a Square Modulo p? Is 2? 22. Quadratic Reciprocity 23. Proof of Quadratic Reciprocity 24. Which Primes Are Sums of Two Squares? 25. Which Numbers Are Sums of Two Squares? 26. As Easy as One, Two, Three 27. Euler's Phi Function and Sums of Divisors 28. Powers Modulo p and Primitive Roots 29. Primitive Roots and Indices 30. The Equation X4 + Y4 = Z4 31. Square-Triangular Numbers Revisited 32. Pell's Equation 33. Diophantine Approximation 34. Diophantine Approximation and Pell's Equation 35. Number Theory and Imaginary Numbers 36. The Gaussian Integers and Unique Factorization 37. Irrational Numbers and Transcendental Numbers 38. Binomial Coefficients and Pascal's Triangle 39. Fibonacci's Rabbits and Linear Recurrence Sequences 40. Oh, What a Beautiful Function 41. Cubic Curves and Elliptic Curves 42. Elliptic Curves with Few Rational Points 43. Points on Elliptic Curves Modulo p 44. Torsion Collections Modulo p and Bad Primes 45. Defect Bounds and Modularity Patterns 46. Elliptic Curves and Fermat's Last Theorem 47. The Topsy-Turvey World of Continued Fractions [online] 48. Continued Fractions, Square Roots, and Pell's Equation [online] 49. Generating Functions [online] 50. Sums of Powers [online] A. Factorization of Small Composite Integers [online] B. A List of Primes [online]
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