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Titlebook: Mathematical Olympiad Challenges; Titu Andreescu,R?zvan Gelca Textbook 20001st edition Birkh?user Boston 2000 algebra.geometry.number theo

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發(fā)表于 2025-3-21 20:02:55 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Mathematical Olympiad Challenges
編輯Titu Andreescu,R?zvan Gelca
視頻videohttp://file.papertrans.cn/627/626480/626480.mp4
圖書封面Titlebook: Mathematical Olympiad Challenges;  Titu Andreescu,R?zvan Gelca Textbook 20001st edition Birkh?user Boston 2000 algebra.geometry.number theo
描述.Mathematical Olympiad Challenges. is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. ..The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems. ..Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for s
出版日期Textbook 20001st edition
關(guān)鍵詞algebra; geometry; number theory; binomial; calculus; combinatorics; Invariant; Mathematica; matrices; Prime;
版次1
doihttps://doi.org/10.1007/978-1-4612-2138-8
isbn_ebook978-1-4612-2138-8
copyrightBirkh?user Boston 2000
The information of publication is updating

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Geometry and Trigonometrye following property of the equilateral triangles, which was noticed by the Romanian mathematician D. Pompeiu in 1936. Pompeiu’s theorem is a simple fact, part of classical plane geometry. Surprisingly, it was discovered neither by Euler in the eighteenth century nor by Steinitz in the nineteenth.
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Algebra and AnalysisIn this section we will consider some applications of the simplest inequality in algebra:.,where equality holds if and only if . = 0.
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Geometry and Trigonometry1. The idea is to look at what happen in a neighborhood of a vertex. Let . be a triangle that is not equilateral and suppose that . < .. Let .. Choose . inside . such that . and .. This is possible because of the continuity of the distance function.
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Algebra and Analysis1. If the inequalities.hold simultaneously, then by adding them we obtain .(.+.+.+) > 1.
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