A Friendly Introduction to Number Theory, 4e

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A Friendly Introduction to Number Theory, 4e

A friendly introduction to number theory, 4th edition is designed to introduce students to the overall themes and methodology of Mathematics through the detailed study of one particular facet–number theory.

NPR 771.00 771.0 NPR NPR 856.00

NPR 856.00

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A Friendly Introduction to Number Theory, 4e

A friendly introduction to number theory, 4th edition is designed to introduce students 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, students 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 analysed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results. 

Table of Contents: 

  1. Chapter 1: What is number theory? 
  2. Chapter 2: Pythagorean triples 
  3. Chapter 3: Pythagorean triples and the Unit circle 
  4. Chapter 4: sums of higher powers and fermat’s last theorem 
  5. Chapter 5: Divisibility and the greatest common divisor 
  6. Chapter 6: Linear Equations and the greatest common divisor 
  7. Chapter 7: factorization and the fundamental theorem of Arithmetic 
  8. Chapter 8: congruences 
  9. Chapter 9: congruences, powers, and fermat’s little theorem 
  10. Chapter 10: congruences, powers, and euler’s formula 
  11. Chapter 11: euler’s Phi function and the Chinese Remainder theorem 
  12. Chapter 12: prime numbers 
  13. Chapter 13: counting primes 
  14. Chapter 14: Mersenne primes 
  15. Chapter 15: Mersenne primes and perfect numbers 
  16. Chapter 16: powers modulo M and successive Squaring 
  17. Chapter 17: computing kth roots modulo M 
  18. Chapter 18: powers, roots, and “unbreakable” codes 
  19. Chapter 19: primality testing and Carmichael numbers 
  20. Chapter 20: squares modulo 
  21. Chapter 21: is -1 a Square modulo ? 
  22. Chapter 22: Quadratic Reciprocity 
  23. Chapter 23: proof of Quadratic Reciprocity 
  24. Chapter 24: which primes are sums of two squares? 
  25. Chapter 25: which numbers are sums of two squares? 
  26. Chapter 26: as easy as one, two, three 
  27. Chapter 27: euler’s Phi function and sums of divisors 
  28. Chapter 28: powers modulo br And primitive roots 
  29. Chapter 29: primitive roots and Indices 
  30. Chapter 30: The equation X4 + Y4 = Z4 
  31. Chapter 31: square–triangular numbers Revisited 
  32. Chapter 32: pell’s equation 
  33. Chapter 33: diophantine approximation 
  34. Chapter 34: diophantine approximation and pell’s equation 
  35. Chapter 35: Number theory and imaginary numbers 
  36. Chapter 36: The Gaussian Integers and unique factorization 
  37. Chapter 37: irrational numbers and transcendental numbers 
  38. Chapter 38: Binomial coefficients and pascal’s triangle 
  39. Chapter 39: fibonacci’s rabbits and linear recurrence sequences 
  40. Chapter 40: Oh, what a beautiful function 
  41. Chapter 41: cubic curves and Elliptic curves 
  42. Chapter 42: Elliptic curves with few rational points 
  43. Chapter 43: points on Elliptic curves modulo 
  44. Chapter 44: torsion collections modulo br And bad primes 
  45. Chapter 45: defect bounds and modularity patterns 
  46. Chapter 46: Elliptic curves and fermat’s last theorem 
  47. Chapter 47: The topsy-turvey world of continued Fractions [online] 
  48. Chapter 48: continued Fractions, Square Roots, and pell’s equation [online] 
  49. Chapter 49: generating functions [online] 
  50. Chapter 50: sums of powers [online].
Book
Author Silverman
Pages 424
Year 2019
ISBN 9789353433079
Publisher Pearson
Language English
Uncategorized
Edition 4/e
Weight 1 kg
Dimensions 20.3 x 25.4 x 4.7 cm
Binding Paperback