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| Preface 1.Integers (Topic: Numbers) 1.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.Binomial 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 for π(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 Sats(Topic: Sats) 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 1:Generating Function for Bernoulli Numbers Dates of Lives of Mathematicians Mentioned in the Text Index |
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