Hands-On Combinatorics: Building Colorful Trains to Manifest Pascal's Triangle, Fibonacci Numbers, and...

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Brian Hopkins

Hands-On Combinatorics

Building Colorful Trains to Manifest Pascal's Triangle, Fibonacci Numbers, and Much More

Brian Hopkins

$152

Paperback

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QTY:

English

American Mathematical Society
31 March 2025

Discrete mathematics; Combinatorics & graph theory

Series: Classroom Resource Materials

This book provides an active-learning approach to combinatorial reasoning and proof through a thoughtful sequence of low threshold, high ceiling activities. A novel feature is its narrative format, with much of the text written from the perspective of a student working through the material with peers. Furthermore, each chapter includes detailed notes for the instructor such as additional scaffolding, extensions, and notation for more advanced students. The exposition is complemented by over 300 colorful illustrations. The main focus of the book is the study of integer compositions with forays into graph theory and recreational mathematics. Befitting the constructive nature of the book, compositions are represented by trains made up of cars. By physically constructing these objects, students become proficient in hands-on verifications of numerous identities.

Developed by a recipient of the MAA's Haimo Award for Distinguished Teaching and used in several teacher professional development workshops and college courses, the book has very modest prerequisites. In particular, no prior experience with symbolic formalism is presumed, allowing this material to be used in multiple classroom settings, from enrichment activities for secondary school students through undergraduate classes in discrete mathematics. The structure of the book also makes it conducive to self-study. Get ready to """"build some trains"""" and explore the enlightening world of combinatorial proofs!

By: Brian Hopkins
Imprint: American Mathematical Society
Country of Publication: United States
Volume: 74
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470477578
ISBN 10: 1470477572
Series: Classroom Resource Materials
Pages: 196
Publication Date: 31 March 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Brian Hopkins, Saint Peter's University, Jersey City, NJ.

Reviews for Hands-On Combinatorics: Building Colorful Trains to Manifest Pascal's Triangle, Fibonacci Numbers, and Much More

Hands-on Combinatorics is a wonderful book, cleverly designed for readers of all mathematical levels. With eye-catching illustrations, Brian Hopkins creates beautiful bijections and clever combinatorial arguments with binomial coefficients, Fibonacci numbers, and beyond."""" - Arthur T. Benjamin, Harvey Mudd College, co-author of Proofs That Really Count