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Inquiry-Based Enumerative Combinatorics

One, Two, Skip a Few... Ninety-Nine, One Hundred

  • T. Kyle┬áPetersen
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. T. Kyle Petersen
    Pages 1-14
  3. T. Kyle Petersen
    Pages 15-31
  4. T. Kyle Petersen
    Pages 33-41
  5. T. Kyle Petersen
    Pages 43-53
  6. T. Kyle Petersen
    Pages 55-64
  7. T. Kyle Petersen
    Pages 65-76
  8. T. Kyle Petersen
    Pages 77-88
  9. T. Kyle Petersen
    Pages 101-111
  10. T. Kyle Petersen
    Pages 113-128
  11. T. Kyle Petersen
    Pages 129-146
  12. T. Kyle Petersen
    Pages 147-163
  13. T. Kyle Petersen
    Pages 165-177
  14. T. Kyle Petersen
    Pages 179-196
  15. Back Matter
    Pages 197-238

About this book

Introduction

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 Combinatorics is 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

Authors and affiliations

  • T. Kyle┬áPetersen
    • 1
  1. 1.Department of Mathematical SciencesDePaul UniversityChicagoUSA

Bibliographic information