Author | Shafarevich, Igor R. author |
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Title | Discourses on Algebra [electronic resource] / by Igor R. Shafarevich |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-642-56325-6 |
Descript | X, 279 p. 2 illus. online resource |
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. Binomial Formula -- 3. Finite Sets (Topic: Sets) -- 7. Sets and Subsets -- 8. Combinatorics -- 9. Set Algebra -- 10. The Language of Probability -- 4. Prime Numbers (Topic: Numbers) -- 11. The Number of Prime Numbers is Infinite -- 12. Eulerโs Proof That the Number of Prime Numbers is Infinite -- 13. Distribution of Prime Numbers -- 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 -- 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 -- Dates of Lives of Mathematicians Mentioned in the Text