After a long gap we start again with the Little Mathematics Library series. The first one that we see is Algebraic Equations of Arbitrary Degrees by A. G. Kurosh.
This booklet is a revision of the author’s lecture to high
school students taking part in the Mathematics Olympiad at
Moscow State University. It gives a review of the results and
methods of the general theory of algebraic equations with due
regard for the level of knowledge of its readers. No proofs are
included in the text since this would have required copying almost half of a university textbook on higher algebra. Despite such an approach, this booklet does not make for light reading. Even a popular mathematics book calls for the reader’s concentration, thorough consideration of all the definitions and statements; check of calculations in all the examples, application of the methods described to his own examples, etc.
The book was translated from the Russian by Vitaly Kisin and was first published by Mir in 1977.
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1. Complex Numbers 10
2. Evolution. Quadratic Equations 16
3. Cubic Equations 19
4. Solution of Equations in Terms of Radicals and the
of Roots of Equations 22
5. The Number of Real Roots 24
6. Approximate Solution of Equations 27
7. Fields 30
8. Conclusion 35