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Titlebook: Mathematical Bridges; Titu Andreescu,Cristinel Mortici,Marian Tetiva Textbook 2017 Springer Science+Business Media LLC 2017 Real Analysis.

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发表于 2025-3-21 18:28:58 | 显示全部楼层 |阅读模式
书目名称Mathematical Bridges
编辑Titu Andreescu,Cristinel Mortici,Marian Tetiva
视频video
概述Builds bridges between classical results and contemporary nonstandard problems.Embraces important topics in calculus, linear and abstract algebra, and analysis from a problem-solving perspective.Makes
图书封面Titlebook: Mathematical Bridges;  Titu Andreescu,Cristinel Mortici,Marian Tetiva Textbook 2017 Springer Science+Business Media LLC 2017 Real Analysis.
描述.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..
出版日期Textbook 2017
关键词Real Analysis; Linear Algebra; Mathematical Olympiad; Abstract Algebra; Mathematical Problem Solving
版次1
doihttps://doi.org/10.1007/978-0-8176-4629-5
isbn_softcover978-1-4939-7918-9
isbn_ebook978-0-8176-4629-5
copyrightSpringer Science+Business Media LLC 2017
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发表于 2025-3-21 20:57:56 | 显示全部楼层
Textbook 2017 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..
发表于 2025-3-22 02:59:15 | 显示全部楼层
The Nested Intervals Theorem,bound axiom, asserting that any nonempty bounded above set of real numbers has a least upper bound. (Actually this statement is equivalent to the nested intervals theorem that follows, and each of them expresses the completeness of the system of real numbers.)
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,Derivatives and Functions’ Variation,y a local minimum. Then .(.. + .) − .(..) ≥ 0 for all . in an open interval (−., .). By dividing by . and passing to the limit when . approaches 0, we deduce that ..(..) ≥ 0 (for . > 0) and ..(..) ≤ 0 (for . < 0); thus ..(..) = 0.
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Antiderivatives,l the antiderivatives of .. (This is because if . and . are two antiderivatives for the same function . on the interval ., then the derivative of . − . vanishes on .; therefore the difference . − . must be a constant. Note the importance of the fact that . is an interval.) We denote by
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on 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..978-1-4939-7918-9978-0-8176-4629-5
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