Author | Herman, Jiลรญ. author |
---|---|
Title | Equations and Inequalities [electronic resource] : Elementary Problems and Theorems in Algebra and Number Theory / by Jiลรญ Herman, Jaromรญr ล imลกa, Radan Kuฤera |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1270-6 |
Descript | XI, 344 p. online resource |
1 Algebraic Identities and Equations -- 1 Formulas for Powers -- 2 Finite Sums -- 3 Polynomials -- 4 Symmetric Polynomials -- 5 Systems of Equations -- 6 Irrational Equations -- 7 Some Applications of Complex Numbers -- 2 Algebraic Inequalities -- 1 Definitions and Properties -- 2 Basic Methods -- 3 The Use of Algebraic Formulas -- 4 The Method of Squares -- 5 The Discriminant and Cauchyโs Inequality -- 6 The Induction Principle -- 7 Chebyshevโs Inequality -- 8 Inequalities Between Means -- 9 Appendix on Irrational Numbers -- 3 Number Theory -- 1 Basic Concepts -- 2 Prime Numbers -- 3 Congruences -- 4 Congruences in One Variable -- 5 Diophantine Equations -- 6 Solvability of Diopha,ntine Equations -- 7 Integer Part and Fractional Part -- 8 Base Representations -- 9 Dirichletโs Principle -- 10 Polynomials -- 4 Hints and Answers -- 1 Hints and Answers to Chapter 1 -- 2 Hints and Answers to Chapter 2 -- 3 Hints and Answers to Chapter 3