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Titlebook: Elements of Mathematics; A Problem-Centered A Gabor Toth Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive lic

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發(fā)表于 2025-3-21 17:47:43 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Elements of Mathematics
副標(biāo)題A Problem-Centered A
編輯Gabor Toth
視頻videohttp://file.papertrans.cn/308/307604/307604.mp4
概述Develops fundamental concepts in algebra, geometry, and number theory from the foundations of set theory.Engages readers through challenging examples and problems inspired by mathematical contests.Ill
叢書(shū)名稱Undergraduate Texts in Mathematics
圖書(shū)封面Titlebook: Elements of Mathematics; A Problem-Centered A Gabor Toth Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive lic
描述.This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed...Beginning with a thorough treatment of the natural numbers via Peano’s axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff’s axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections betw
出版日期Textbook 2021
關(guān)鍵詞Axiomatic mathematics before calculus; Axiomatic precalculus; Rigorous precalculus textbook; Mathematic
版次1
doihttps://doi.org/10.1007/978-3-030-75051-0
isbn_softcover978-3-030-75053-4
isbn_ebook978-3-030-75051-0Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 22:17:15 | 只看該作者
板凳
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Rational and Real Exponentiation,s due to Besicovitch, the Young inequality, some sharp estimates on the .-series, equiconvergence through the Cauchy condensation test, power sums, and the lesser known method of (arithmetic) means. A short section on logarithms along with a few contest level problems is followed by a final section
地板
發(fā)表于 2025-3-22 04:37:59 | 只看該作者
Real Analytic Plane Geometry, existence and properties of the circular arc length are shown using purely metric tools, and paving the way to trigonometry (Chapter .). This also gives a precise answer to the question: “What is .?” Once again, this relies on the Least Upper Bound Property of the real number system, the main commo
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Rational and Algebraic Expressions and Functions,contest problems involving these means, we chose a representative sample to demonstrate the principal methods. The lesser known permutation (arrangement) inequality is also introduced here pointing out that it implies all the other classical inequalities such as the AM–GM, Cauchy–Schwarz (Sections .
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Eugenia Larjow,Christian Reuschenbachorresponding Bernoulli inequality. This opens the first opportunity to present a whole cadre of contest problems some of which are on Olympiad level. Working with the Dedekind model of the real number system is cumbersome, and not well suited to do analysis, however. We therefore build another model
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發(fā)表于 2025-3-23 07:19:23 | 只看該作者
Laura Maa?,Xiange Zhang,Julian Gansen existence and properties of the circular arc length are shown using purely metric tools, and paving the way to trigonometry (Chapter .). This also gives a precise answer to the question: “What is .?” Once again, this relies on the Least Upper Bound Property of the real number system, the main commo
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