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Mathematical bridges

Andreescu, Titu.

Mathematical bridges

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mathematical bridgesby Titu Andreescu, Cristinel Mortici, Marian Tetiva.
作者:	Andreescu, Titu.
其他作者:	Mortici, Cristinel.
出版者:	New York, NY :Springer New York :2017.
面頁冊數:	viii, 309 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mathematics.
電子資源:	http://dx.doi.org/10.1007/978-0-8176-4629-5
ISBN:	9780817646295$q(electronic bk.)

Mathematical bridges
Andreescu, Titu.

Mathematical bridges[electronic resource] /by Titu Andreescu, Cristinel Mortici, Marian Tetiva. - New York, NY :Springer New York :2017. - viii, 309 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9780817646295$q(electronic bk.)

Standard No.: 10.1007/978-0-8176-4629-5doiSubjects--Topical Terms:

184409
Mathematics.

LC Class. No.: QA39.3

Dewey Class. No.: 510

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520 $a 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.
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