Hands-on Combinatorics : Building Colorful Trains to Manifest Pascal's Triangle, Fibonacci Numbers, and Much More (Classroom Resource Materials)

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Hands-on Combinatorics : Building Colorful Trains to Manifest Pascal's Triangle, Fibonacci Numbers, and Much More (Classroom Resource Materials)

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 196 p.
  • 言語 ENG
  • 商品コード 9781470477578
  • DDC分類 511.6

Full Description

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!

Contents

Circular regions and colorful trains
Counting cars
Restricted trains
Circular regions redux
A fleet of restricted trains
Barrycades
Other triangles of trains
A culminating connection
Additional train topics
Generating functions
Bibliography
Index