Difference between revisions of "Book:George Eyre Andrews/Number Theory"

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(Created page with "{{Book|Number Theory|1971|W.B. Saunders Company||George Eyre Andrews}} ===Online Copies=== [https://archive.org/details/NumberTheory_862 hosted by archive.org]<br /> ===Cont...")
 
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===Contents===
 
===Contents===
 +
:Part I MULTIPLICATIVITY--DIVISIBILITY
 +
::Chapter 1: BASIS REPRESENTATION
 +
:::1-1 Principle of Mathematical Induction
 +
:::1-2 The Basis Representation Theorem
 +
::Chapter 2: THE FUNDAMENTAL THEOREM OF ARITHMETIC
 +
:::2-1 Euclid's Division Lemma
 +
:::2-2 Divisibility
 +
:::2-3 The Linear Diophantine Equation
 +
:::2-4 The Fundamental Theorem of Arithmetic
 +
::Chapter 3: COMBINATORIAL AND COMPUTATIONAL NUMBER THEORY
 +
:::3-1 Permutations and Combinations
 +
:::3-2 Fermat's Little Theorem
 +
:::3-3 Wilson's Theorem
 +
:::3-4 Generating Functions
 +
:::3-5 The Use of Computers in Number Theory
 +
::Chapter 4: FUNDAMENTALS OF CONGRUENCES
 +
:::4-1 Basic Properties of Congruences
 +
:::4-2 Residue Systems
 +
:::4-3 Riffling
 +
::Chapter 5: SOLVING CONGRUENCES
 +
:::5-1 Linear Congruences
 +
:::5-2 The Theorems of Fermat and Wilson Revisited
 +
:::5-3 The Chinese Remainder Theorem
 +
:::5-4 Polynomial Congruences
 +
::Chapter 6: ARITHMETIC FUNCTIONS
 +
:::6-1 Combinatorial Study of $\phi(n)$
 +
:::6-2 Formulae for $d(n)$ and $\sigma(n)$
 +
:::6-3 Multiplicative Arithmetic Functions
 +
:::6-4 The Möbius Inversion Formula
 +
::Chapter 7: PRIMITIVE ROOTS
 +
:::7-1 Properties of Reduced Residue Systems
 +
:::7-2 Primitive Roots modulo $p$
 +
::Chapter 8: PRIME NUMBERS
 +
:::8-1 Elementary Properties of $\pi(x)$
 +
:::8-2 Tchebychev's Theorem
 +
:::8-3 Some Unsolved Problems About Primes
 +
:Part II QUADRATIC CONGRUENCES
 +
::Chapter 9: QUADRATIC RESIDUES
 +
:::9-1 Euler's Criterion
 +
:::9-2 The Legendre Symbol
 +
:::9-3 The Quadratic Reciprocity Law
 +
:::9-4 Applications of the Quadratic Reciprocity Law
 +
::Chapter 10: DISTRIBUTION OF QUADRATIC RESIDUES
 +
:::10-1 Consecutive Residues and Nonresidues
 +
:::10-2 Consecutive Triples of Quadratic Residues
 +
:Part III ADDITIVITY
 +
::Chapter 11: SUMS OF SQUARES
 +
:::11-1 Sums of Two Squares
 +
:::11-2 Sums of Four Squares
 +
::Chapter 12: ELEMENTARY PARTITION THEORY
 +
:::12-1 Introduciton
 +
:::12-2 Graphical Representation
 +
:::12-3 Euler's Partition Theorem
 +
:::12-4 Searching for Partition Identities
 +
::Chapter 13 GENERATING FUNCTIONS
 +
:::13-1 Infinite Products As Generating Functions
 +
:::13-2 Identities Between Infinite Series and Products
 +
::Chapter 14 PARTITION IDENTITIES
 +
:::14-1 History and Introduction
 +
:::14-2 Euler's Pentagonal Number Theorem
 +
:::14-3 The Rogers-Ramanujan Identities
 +
:::14-4 Series and Product Identities
 +
:::14-5 Schur's Theorem
 +
:Part IV GEOMETRIC NUMBER THEORY
 +
::Chapter 15 LATTICE POINTS
 +
:::15-1 Gauss's Circle Problem
 +
:::15-2 Dirichlet's Divisor Problem
 +
:APPENDICES
 +
::Appendix A
 +
::Appendix B
 +
::Appendix C
 +
::Appendix D
 +
:::THE INTEGRAL TEST
 +
:::NOTES
 +
:::SUGGESTED READING
 +
:::BIBLIOGRAPHY
 +
:::HINTS AND ANSWERS TO SELECTED EXERCISES
 +
:::INDEX OF SYMBOLS
 +
:::INDEX
  
 
[[Category:Books]]
 
[[Category:Books]]

Revision as of 20:31, 9 June 2016

George Eyre Andrews: Number Theory

Published $1971$, W.B. Saunders Company.


Online Copies

hosted by archive.org

Contents

Part I MULTIPLICATIVITY--DIVISIBILITY
Chapter 1: BASIS REPRESENTATION
1-1 Principle of Mathematical Induction
1-2 The Basis Representation Theorem
Chapter 2: THE FUNDAMENTAL THEOREM OF ARITHMETIC
2-1 Euclid's Division Lemma
2-2 Divisibility
2-3 The Linear Diophantine Equation
2-4 The Fundamental Theorem of Arithmetic
Chapter 3: COMBINATORIAL AND COMPUTATIONAL NUMBER THEORY
3-1 Permutations and Combinations
3-2 Fermat's Little Theorem
3-3 Wilson's Theorem
3-4 Generating Functions
3-5 The Use of Computers in Number Theory
Chapter 4: FUNDAMENTALS OF CONGRUENCES
4-1 Basic Properties of Congruences
4-2 Residue Systems
4-3 Riffling
Chapter 5: SOLVING CONGRUENCES
5-1 Linear Congruences
5-2 The Theorems of Fermat and Wilson Revisited
5-3 The Chinese Remainder Theorem
5-4 Polynomial Congruences
Chapter 6: ARITHMETIC FUNCTIONS
6-1 Combinatorial Study of $\phi(n)$
6-2 Formulae for $d(n)$ and $\sigma(n)$
6-3 Multiplicative Arithmetic Functions
6-4 The Möbius Inversion Formula
Chapter 7: PRIMITIVE ROOTS
7-1 Properties of Reduced Residue Systems
7-2 Primitive Roots modulo $p$
Chapter 8: PRIME NUMBERS
8-1 Elementary Properties of $\pi(x)$
8-2 Tchebychev's Theorem
8-3 Some Unsolved Problems About Primes
Part II QUADRATIC CONGRUENCES
Chapter 9: QUADRATIC RESIDUES
9-1 Euler's Criterion
9-2 The Legendre Symbol
9-3 The Quadratic Reciprocity Law
9-4 Applications of the Quadratic Reciprocity Law
Chapter 10: DISTRIBUTION OF QUADRATIC RESIDUES
10-1 Consecutive Residues and Nonresidues
10-2 Consecutive Triples of Quadratic Residues
Part III ADDITIVITY
Chapter 11: SUMS OF SQUARES
11-1 Sums of Two Squares
11-2 Sums of Four Squares
Chapter 12: ELEMENTARY PARTITION THEORY
12-1 Introduciton
12-2 Graphical Representation
12-3 Euler's Partition Theorem
12-4 Searching for Partition Identities
Chapter 13 GENERATING FUNCTIONS
13-1 Infinite Products As Generating Functions
13-2 Identities Between Infinite Series and Products
Chapter 14 PARTITION IDENTITIES
14-1 History and Introduction
14-2 Euler's Pentagonal Number Theorem
14-3 The Rogers-Ramanujan Identities
14-4 Series and Product Identities
14-5 Schur's Theorem
Part IV GEOMETRIC NUMBER THEORY
Chapter 15 LATTICE POINTS
15-1 Gauss's Circle Problem
15-2 Dirichlet's Divisor Problem
APPENDICES
Appendix A
Appendix B
Appendix C
Appendix D
THE INTEGRAL TEST
NOTES
SUGGESTED READING
BIBLIOGRAPHY
HINTS AND ANSWERS TO SELECTED EXERCISES
INDEX OF SYMBOLS
INDEX
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