دانلود کتاب Discourses on Algebra

فهرست مطالب :

Title
Abstract
Preface
Contents
1. Integers
1. sqrt(2) Is Not Rational
2. The Irrationality of Other Square Roots
3. Decomposition into Prime Factors
2. Simplest Properties of Polynomials
4. Roots and the Divisibility of Polynomials
5. Multiple Roots and the Derivative
6. Binomial Formula
3. Finite Sets
7. Sets and Subsets
8. Combinatorics
9. Set Algebra
10. The Language of Probability
Supplement: The Chebyshev Inequality
4. Prime Numbers
11. The Number of Prime Numbers is Infinite
12. Euler\'s Proof That the Number of Prime Numbers is Infinite
13. Distribution of Prime Numbers
Supplement: The Chebyshev Inequality for pi(n)
5. Real Numbers and Polynomials
14. Axioms of the Real Numbers
15. Limits and Infinite Sums
16. Representation of Real Numbers as Decimal Fractions
17. Real Roots of Polynomials
Supplement: Sturm\'s Theorem
6. Infinite Sets
18. Equipotence
19. Continuum
20. Thin Sets
Supplement: Normal Numbers
7. Power Series
21. Polynomials and Generating Functions
22. Power Series
23. Partitio Numerorum
Supplement 1: The Euler Pentagon Theorem
Supplement 2: Generating Function for Bernoulli Numbers
Dates of Lives
Index