Author | Herman, Jiล{153}รญ. author |
---|---|

Title | Equations and Inequalities [electronic resource] : Elementary Problems and Theorems in Algebra and Number Theory / by Jiล{153}รญ Herman, Jaromรญr ล imลกa, Radan Kuฤ{141}era |

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 |

SUMMARY

This book is intended as a text for a problem-solving course at the firstยญ or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with algebraic equations or inequalities, or to supplement a standard elementary number theory course. There are already many excellent books on the market that can be used for a problem-solving course. However, some are merely collections of probยญ lems from a variety of fields and lack cohesion. Others present problems according to topic, but provide little or no theoretical background. Most problem books have a limited number of rather challenging problems. While these problems tend to be quite beautiful, they can appear forbidding and discouraging to a beginning student, even with well-motivated and carefully written solutions. As a consequence, students may decide that problem solving is only for the few high performers in their class, and abandon this important part of their mathematical, and indeed overall, education

CONTENT

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 Cauchyโ{128}{153}s Inequality -- 6 The Induction Principle -- 7 Chebyshevโ{128}{153}s 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 Dirichletโ{128}{153}s 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

Mathematics
Algebra
Number theory
Mathematics
Number Theory
Algebra