Preface
1.Integers (Topic: Numbers)
1.2 Is Not Rational
2.The Irrationality of Other Square Roots
3.Decomposition into Prime Factors
2.Simplest Properties of Polynomials
( Topic: Polynomials)
4.Roots and the Divisibility of Polynomials
5.Multiple Roots and the Derivative
6.Birmmial Formula
Supplement: Polynomials and Bernoulli Numbers
3.Finite Sets (Topic: Sets)
7.Sets and Subsets
8.Combinatorics
9.Set Algebra
10.The Language of Probability
Supplement: The Chebyshev Inequality
4.Prime Numbers (Topic: 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 forr(n)
5.Real Numbers and Polynomials
(Topic: 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 (Topic: Sets)
18.Equipotence
19.Continuum
20.Thin Sets
Supplement: Normal Numbers
7.Power Series (Topic: Polynomials)
21.Polynomials as Generating Functions
22.Power Series
23.Partitio Numerorum
Supplement 1: The Euler Pentagon Theorem.
Supplement 2: Generating Function for
Bernoulli Numbers
Dates of Lives of Mathematicians Mentioned in the Text
Index
