Hands-on Combinatorics by Brian Hopkins
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!-
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Proofs Without Words
Hands-on Combinatorics is a wonderful book, cleverly designed for readers of all mathematical levelsWith 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
Brian Hopkins, Saint Peter's University, Jersey City, NJ.
| SKU | Unavailable |
| ISBN 13 | 9781470477578 |
| ISBN 10 | 1470477572 |
| Title | Hands-on Combinatorics |
| Author | Brian Hopkins |
| Series | Classroom Resource Materials |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2025-03-31 |
| Number of pages | 196 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |