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Inquiry-Based Enumerative Combinatorics : One, Two, Skip a Few... Ninety-Nine, One Hundred / by T. Kyle Petersen
(Undergraduate Texts in Mathematics. ISSN:21975604)
版 | 1st ed. 2019. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2019 |
本文言語 | 英語 |
大きさ | XI, 238 p. 104 illus., 9 illus. in color : online resource |
著者標目 | *Petersen, T. Kyle author SpringerLink (Online service) |
件 名 | LCSH:Discrete mathematics FREE:Discrete Mathematics |
一般注記 | 0. Introduction to this book -- 1. First Principles -- 2. Permutations -- 3. Combinations -- 4. The Binomial Theorem -- 5. Recurrences -- 6. Generating Functions -- 7. Exponential Generating Functions and Bell Numbers -- 8. Eulerian Numbers -- 9. Catalan and Narayana Numbers -- 10. Refined Enumeration -- 11. Applications to Probability -- 12. Some Partition Theory -- 13. A Bit of Number Theory -- A. Supplementary Exercises This textbook offers the opportunity to create a uniquely engaging combinatorics classroom by embracing Inquiry-Based Learning (IBL) techniques. Readers are provided with a carefully chosen progression of theorems to prove and problems to actively solve. Students will feel a sense of accomplishment as their collective inquiry traces a path from the basics to important generating function techniques. Beginning with an exploration of permutations and combinations that culminates in the Binomial Theorem, the text goes on to guide the study of ordinary and exponential generating functions. These tools underpin the in-depth study of Eulerian, Catalan, and Narayana numbers that follows, and a selection of advanced topics that includes applications to probability and number theory. Throughout, the theory unfolds via over 150 carefully selected problems for students to solve, many of which connect to state-of-the-art research. Inquiry-Based Enumerative Combinatoricsis ideal for lower-division undergraduate students majoring in math or computer science, as there are no formal mathematics prerequisites. Because it includes many connections to recent research, students of any level who are interested in combinatorics will also find this a valuable resource HTTP:URL=https://doi.org/10.1007/978-3-030-18308-0 |
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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 | 9783030183080 |
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EB00226857 |
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