Hands-On Combinatorics : Building Colorful Trains to Manifest Pascal's Triangle, Fibonacci Numbers, and Much More / Brian Hopkins.

Format:

Book

Author/Creator:

Hopkins, Brian, author.

Series:

Classroom resource materials ; Volume 74.

Classroom resource materials Volume 74

Language:

English

Subjects (All):

Combinatorial analysis.

Combinatorial designs and configurations.

Physical Description:

1 online resource (xv, 191 pages)

Other Title:

Building Colorful Trains to ManifestPascal’s Triangle, Fibonacci Numbers,and Much More

Place of Publication:

Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society, [2025]

Summary:

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!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.

Contents:

Circular regions and colorful trains

Counting cars

Restricted trains.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9781470479602

1470479605