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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.11.2013

Verlag

Pearson

Seitenzahl

468

Maße (L/B/H)

27,6/21,6/2,6 cm

Gewicht

848 g

Auflage

4

Sprache

Englisch

ISBN

978-1-292-02709-8

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.11.2013

Verlag

Pearson

Seitenzahl

468

Maße (L/B/H)

27,6/21,6/2,6 cm

Gewicht

848 g

Auflage

4

Sprache

Englisch

ISBN

978-1-292-02709-8

Herstelleradresse

Pearson
St.-Martin-Straße 82
81541 München
DE

Email: salesde@pearson.com

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  • Produktbild: Friendly Introduction to Number Theory, A

  • 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 “Unbreakable” Codes

    19. Primality Testing and Carmichael Numbers

    20. Squares Modulo p

    21. Quadratic Reciprocity

    22. Proof of Quadratic Reciprocity

    23. Which Primes Are Sums of Two Squares?

    24.Which Numbers Are Sums of Two Squares?

    25. Euler’s Phi Function and Sums of Divisors

    26. Powers Modulo p and Primitive Roots

    27. Primitive Roots and Indices

    28. The Equation X4 + Y4 = Z4

    29. Square–Triangular Numbers Revisited

    30. Pell’s Equation

    31. Diophantine Approximation

    32. Diophantine Approximation and Pell’s Equation

    33. Number Theory and Imaginary Numbers

    34. The Gaussian Integers and Unique Factorization

    35. Irrational Numbers and Transcendental Numbers

    36. Binomial Coefficients and Pascal’s Triangle

    37. Fibonacci’s Rabbits and Linear Recurrence Sequences

    38. Cubic Curves and Elliptic Curves

    39. Elliptic Curves with Few Rational Points

    40. Points on Elliptic Curves Modulo p

    41. Torsion Collections Modulo p and Bad Primes

    42. Defect Bounds and Modularity Patterns

    43. Elliptic Curves and Fermat’s Last Theorem

     

    Index

     

    *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]

     

    *These chapters are available online