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.
Rezensionen / Stimmen
"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)
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Lower undergraduate
Illustrationen
3
3 s/w Abbildungen
VIII, 309 p. 3 illus.
Maße
Höhe: 241 mm
Breite: 160 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-8176-4394-2 (9780817643942)
DOI
10.1007/978-0-8176-4629-5
Schweitzer Klassifikation
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.
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.
