Theory of numbers /
| Основен автор: | Stewart, Bonnie Madison. |
|---|---|
| Формат: | Книга |
| Език: | English |
| Публикувано: |
New York :
Macmillan,
1964.
|
| Издание: | 2nd ed. |
| Предмети: |
Съдържание:
- pt. I. An intuitive approach. Preliminary considerations
- Mathematical induction
- The division algorithm
- Number theory in the game of solitaire
- Representation of the integers
- The Euclid algorithm
- More about greatest common divisors
- The fundamental theorem of arithmetic
- Prime and composite integers
- The number-theoretic functions [tau](n) and [sigma](n)
- Multiplicative number-theoretic functions
- The bracket function
- Introduction to the congruence notation
- Linear congruences
- Diophantine equations of the first degree
- Systems of linear congruences
- The Euler-Fermat theorems
- Congruences of higher degree
- Exponents and primitive roots
- The theory of indices
- Quadratic residues and Legendre's symbol
- The quadratic reciprocity law
- Pythagorean triplets
- Homogeneous quadratic Diophantine equations
- Fermat's method of descent
- Sum of four squares
- Sum of two squares
- Egyptian fractions
- pt. II. An axiomatic approach. Mathematical systems and introduction to group theory
- Transformation groups
- Linear transformations and matrices
- Introduction to quadratic forms
- Congruence modulo a subgroup
- Direct products
- Rings, domains, and fields
- The fundamental theorem reconsidered
- Quotient fields
- Ordered rings
- Polynomial rings
- Modular fields
- The real field and decimal representation of rational numbers
- Continued fractions
- Peano's axioms for the natural integers
- Integers-positive, negative, and zero.