| 书目名称 | Elements of Mathematics | | 副标题 | A Problem-Centered A | | 编辑 | Gabor Toth | | 视频video | | | 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 | | 丛书名称 | Undergraduate Texts in Mathematics | | 图书封面 |  | | 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 | | 关键词 | Axiomatic mathematics before calculus; Axiomatic precalculus; Rigorous precalculus textbook; Mathematic | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-75051-0 | | isbn_softcover | 978-3-030-75053-4 | | isbn_ebook | 978-3-030-75051-0Series ISSN 0172-6056 Series E-ISSN 2197-5604 | | issn_series | 0172-6056 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 17:47:43
