Logo - springer
Slogan - springer

Mathematics - Number Theory and Discrete Mathematics | Equations and Inequalities - Elementary Problems and Theorems in Algebra and Number Theory

Equations and Inequalities

Elementary Problems and Theorems in Algebra and Number Theory

Herman, Jiri, Kucera, Radan, Simsa, Jaromir

Translated by Dilcher, K.

Original Czech edition published by Masaryk University, Brno, 1996

2000, XI, 344 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$69.99

(net) price for USA

ISBN 978-1-4612-1270-6

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$89.95

(net) price for USA

ISBN 978-0-387-98942-6

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$89.95

(net) price for USA

ISBN 978-1-4612-7071-3

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

This book is intended as a text for a problem-solving course at the first­ 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 prob­ 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 Level » Lower undergraduate

Keywords » algebra - diophantine equation - number theory - prime number

Related subjects » Algebra - Number Theory and Discrete Mathematics

Table of contents 

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 Cauchy’s Inequality.- 6 The Induction Principle.- 7 Chebyshev’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 Dirichlet’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.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Number Theory.

Additional information