Mathematical Bridges

ISBN-13: 9781493979189 / Angielski / Miękka / 2018 / 309 str.

Titu Andreescu; Cristinel Mortici; Marian Tetiva

Opis

Bridging classical results and contemporary nonstandard problems, this book covers important topics in analysis and algebra from a problem-solving perspective. The text offers numerous mathematical "gems" that help illustrate the inherent beauty of the topic.

Recenzje

"The book under review is an excellent collection of gems of undergraduate mathematics. ... The book is very well written, and very pleasant to read." (Mowaffaq Hajja, zbMATH 1421.00001, 2019)

Spis treści

Mathematical (and Other) Bridges.- Cardinality.- Polynomial Functions Involving Determinants.- Some Applications of the Hamilton-Cayley Theorem.- A Decomposition Theorem Related to the Rank of a Matrix.- Equivalence Relations on Groups and Factor Groups.- Density.- The Nested Intervals Theorem.- The Splitting Method and Double Sequences.- The Number e.- The Intermediate Value Theorem.- The Extreme Value Theorem.- Uniform Continuity.- Derivatives and Functions' Variation.- Riemann and Darboux Sums.- Antiderivatives.

O autorze

Titu Andreescu is an internationally acclaimed problem solving expert who has published more than 30 books in this area. 

Cristinel Mortici is a Romanian mathematics professor who efficiently uses a problem base approach in his teaching. 

Marian Tetiva is a Romanian high school teacher who strongly believes in the importance of meaningful problem solving in teaching and learning mathematics. 

Blurb

Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics.

Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics.

Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bridges a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students desiring to hone and develop their mathematical skills or with an interest in mathematics competitions must have this book in their personal libraries.