Inquiry-Based Enumerative Combinatorics
Springer International Publishing (Verlag)
978-3-030-18307-3 (ISBN)
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.
T. Kyle Petersen is Professor of Mathematics at DePaul University in Chicago. His research interests lie in algebraic, enumerative, and topological combinatorics, and he has been an active member of the Inquiry-Based Learning (IBL) community for over a decade. His graduate textbook, Eulerian Numbers, appears in Birkhauser Advanced Texts Basler Lehrbucher.
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.
"The book is particularly suitable for IBL enthusiasts majoring in math or computer science." (Andreas N. Philippou, zbMATH 1428.05001, 2020)
“The book is particularly suitable for IBL enthusiasts majoring in math or computer science.” (Andreas N. Philippou, zbMATH 1428.05001, 2020)
| Erscheinungsdatum | 23.08.2019 |
|---|---|
| Reihe/Serie | Undergraduate Texts in Mathematics |
| Zusatzinfo | XI, 238 p. 104 illus., 9 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 534 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| Schlagworte | Bijective Combinatorics • Catalan numbers • combinatorics • Discrete Mathematics • Enumerative Combinatorics • Eulerian numbers • Exponential generating functions • Generating functions • Inquiry-based combinatorics • inquiry-based learning • Introductory combinatorics • Narayana numbers • Ordinary generating functions • Undergraduate combinatorics textbook |
| ISBN-10 | 3-030-18307-6 / 3030183076 |
| ISBN-13 | 978-3-030-18307-3 / 9783030183073 |
| Zustand | Neuware |
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