<電子ブック>
Problems and Proofs in Numbers and Algebra / by Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn
版 | 1st ed. 2015. |
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出版者 | Cham : Springer International Publishing : Imprint: Springer |
出版年 | 2015 |
大きさ | X, 223 p. 9 illus : online resource |
著者標目 | *Millman, Richard S author Shiue, Peter J author Kahn, Eric Brendan author SpringerLink (Online service) |
件 名 | LCSH:Universal algebra LCSH:Number theory LCSH:Mathematical logic FREE:General Algebraic Systems FREE:Number Theory FREE:Mathematical Logic and Foundations |
一般注記 | Designed to facilitate the transition from undergraduate calculus and differential equations to learning about proofs, this book helps students develop the rigorous mathematical reasoning needed for advanced courses in analysis, abstract algebra, and more. Students will focus on both how to prove theorems and solve problem sets in-depth; that is, where multiple steps are needed to prove or solve. This proof technique is developed by examining two specific content themes and their applications in-depth: number theory and algebra. This choice of content themes enables students to develop an understanding of proof technique in the context of topics with which they are already familiar, as well as reinforcing natural and conceptual understandings of mathematical methods and styles. The key to the text is its interesting and intriguing problems, exercises, theorems, and proofs, showing how students will transition from the usual, more routine calculus to abstraction while also learning how to “prove” or “solve” complex problems. This method of instruction is augmented by examining applications of number theory in systems such as RSA cryptography, Universal Product Code (UPC), and International Standard Book Number (ISBN). The numerous problems and examples included in each section reward curiosity and insightfulness over more simplistic approaches. Each problem set begins with a few easy problems, progressing to problems or proofs with multi-step solutions. Exercises in the text stay close to the examples of the section, allowing students the immediate opportunity to practice developing techniques. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge HTTP:URL=https://doi.org/10.1007/978-3-319-14427-6 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319144276 |
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電子リソース |
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EB00208057 |
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