Number Theory Revealed: A Masterclass
eBook - PDF

Number Theory Revealed: A Masterclass

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Number Theory Revealed: A Masterclass

About this book

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the "Queen of Mathematics". The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves.This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials.About the Author:Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.

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Yes, you can access Number Theory Revealed: A Masterclass by Andrew Granville in PDF and/or ePUB format, as well as other popular books in Mathematics & Number Theory. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title page
  3. Preface
  4. Gauss’s Disquisitiones Arithmeticae
  5. Notation
  6. Prerequisites
  7. Preliminary Chapter on Induction
  8. Chapter 1. The Euclidean algorithm
  9. Chapter 2. Congruences
  10. Chapter 3. The basic algebra of number theory
  11. Chapter 4. Multiplicative functions
  12. Chapter 5. The distribution of prime numbers
  13. Chapter 6. Diophantine problems
  14. Chapter 7. Power residues
  15. Chapter 8. Quadratic residues
  16. Chapter 9. Quadratic equations
  17. Chapter 10. Square roots and factoring
  18. Chapter 11. Rational approximations to real numbers
  19. Chapter 12. Binary quadratic forms
  20. Chapter 13. The anatomy of integers
  21. Chapter 14. Counting integral and rational points on curves, modulo 𝑝
  22. Chapter 15. Combinatorial number theory
  23. Chapter 16. The 𝑝-adic numbers
  24. Chapter 17. Rational points on elliptic curves
  25. Hints for exercises
  26. Recommended further reading
  27. Index
  28. Back Cover