An Excursion through Elementary Mathematics, Volume I : Real Numbers and Functions / by Antonio Caminha Muniz Neto.

Format:

Book

Author/Creator:

Caminha Muniz Neto, Antonio., Author.

Series:

Problem Books in Mathematics, 0941-3502

Language:

English

Subjects (All):

Functions of real variables.

Algebra.

Matrix theory.

Real Functions.

General Algebraic Systems.

Linear and Multilinear Algebras, Matrix Theory.

Local Subjects:

Real Functions.

General Algebraic Systems.

Linear and Multilinear Algebras, Matrix Theory.

Physical Description:

1 online resource (XIII, 652 p. 73 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Contents:

Chapter 1 The Set of Real Numbers

Chapter 2 Algebraic Identities, Equations and Systems

Chapter 3 Elementary Sequences

Chapter 4 Induction and the Binomial Formula

Chapter 5 Elementary Inequalities

Chapter 6 The Concept of Function

Chapter 7 More on Real Numbers

Chapter 8 Continuous Functions

Chapter 9 Limits and Derivatives

Chapter 10 Riemann’s Integral

Chapter 11 Series of Functions

Bibliography

Appendix A Glossary

Appendix B Hints and Solutions.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-53871-3

OCLC:

1066183561