Authors:
- Equips readers with the fundamentals of enumerative combinatorics with an emphasis on generating function techniques
- Promotes an engaging learning experience by utilizing Inquiry-Based Learning (IBL)
- Offers an accessible entry-point to enumerative combinatorics that builds from minimal prerequisites to a selection of advanced topics
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- Inquiry-based combinatorics
- Undergraduate combinatorics textbook
- Inquiry-Based Learning
- Discrete Mathematics
- Generating Functions
- Bijective Combinatorics
- Eulerian Numbers
- Introductory combinatorics
- Enumerative combinatorics
- Ordinary generating functions
- Exponential generating functions
- Catalan numbers
- Narayana numbers
- combinatorics
Reviews
Authors and Affiliations
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Department of Mathematical Sciences, DePaul University, Chicago, USA
T. Kyle Petersen
About the author
Bibliographic Information
Book Title: Inquiry-Based Enumerative Combinatorics
Book Subtitle: One, Two, Skip a Few... Ninety-Nine, One Hundred
Authors: T. Kyle Petersen
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-18308-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-18307-3Published: 24 August 2019
Softcover ISBN: 978-3-030-18310-3Published: 25 August 2020
eBook ISBN: 978-3-030-18308-0Published: 28 June 2019
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XI, 238
Number of Illustrations: 95 b/w illustrations, 9 illustrations in colour
Topics: Combinatorics