Exploring, investigating and discovering in mathematics

Vasile Berinde

246 pages, parution le 07/01/2004

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Résumé

This book introduces creative problem solving techniques with particular emphasis on how to develop and train inventive skills to students. It presents an array of 24 carefully selected themes from elementary mathematics: arithmetic, algebra, geometry, analysis as well as applied mathematics. The goal is to offer a systematic illustration of how to organise the natural transition from the problem solving activity towards exploring, investigating, and discovering new facts and results. The target audience are mainly highschool seniors, undergraduate students, instructors and teachers in mathematics.

Features and benefits:

provides solutions to over 100 problems and includes hints or clear ideas of solving for over 150 further problems and exercices
assumes only a basic knowledge of elementary mathematics but opens the way from the problem solving process to the very beginning of a research attitude
teaches natural exploration and investigation skills, starting from the source problem and its solution and leading to the discovery of new interesting and challenging problems
collect many valuable techniques for solving various classes of problems
uses competition-like problem solving as a platform for training typical inventive skills

Sommaire

Preface
Introduction
Chase problems
Sequences of integers simultaneous prime
A geometric construction using ruler and compass
Solving a class of non-linear systems
A class of homogenous inequalities
The first decimal of some irrational numbers
Polynomial approximation of continuous functions
On an interesting divisibility problem
Determinants with alternate entries
Solving some cycling systems
On a property of recurrent affine sequences
Binomial characterizations of arithmetic progressions
Using duality in studying homographic recurrences
Exponential equations having exactly two solutions
A class of functional equations
An extension of the Leibniz-Newton formula
A measurement problem
A class of discontinuous functions admitting primitives
On two classes of inequalities
Another problem of geometric construction
How can we discover new problems by means of the computer
On the convergence of some sequences of real numbers
An application of the integral mean
Difference and differential equations
Addendum

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Vasile Berinde
Parution	07/01/2004
Nb. de pages	246
Format	17 x 24
Couverture	Broché
Poids	530g
Intérieur	Noir et Blanc
EAN13	9783764370190