Mathematical Discovery by Bruckner, Thomson & Bruckner
Mathematical Discovery - Table of Contents
1. Tilings
2. Pick’s Rule
3. Nim
4. Links
A. Induction
B. Nim, A Game with a Complete Mathematical Theory
What You Will Learn in Mathematical Discovery
"Mathematical Discovery" by Andrew M. Bruckner, Brian S. Thomson and Judith B. Bruckner explores how students and mathematicians learn and understand "mathematics" through active exploration and inquiry. The book emphasizes that mathematical concepts are best grasped through discovery rather than rote memorization. By encouraging curiosity and experimentation, it shows how learners can develop a deep understanding of patterns, relationships, and structures in mathematics. The authors focus on fostering "problem-solving" skills and logical reasoning, helping readers see the underlying principles behind formulas and procedures.
The book highlights the importance of "logic" and creative thinking in the learning process. Through examples, exercises, and guided explorations, Bruckner & Thomson demonstrate how learners can construct knowledge independently. The text covers topics from algebra to calculus, emphasizing how discovery leads to better retention, understanding, and appreciation of mathematical ideas. It shows that mathematics is not just about answers but about thinking critically and developing methods to approach new problems.
Designed for educators, students, and enthusiasts, "Mathematical Discovery" provides practical strategies for encouraging exploration in classrooms and self-study. It demonstrates how "pattern recognition", experimentation, and reflective thinking contribute to "mathematical thinking". The book is a valuable resource for anyone seeking to enhance their understanding of mathematics and cultivate a love for its "concepts" and creative processes.
Book Details & Specifications
Title:
Mathematical Discovery by Bruckner, Thomson & Bruckner
Publisher:
CreateSpace
Year:
2011
Pages:
267
Type:
PDF
Language:
English
ISBN-10 #:
1453892923
ISBN-13 #:
978-1453892923
License:
Educational External Links
Amazon:
Amazon
About the Author: Andrew M. Bruckner and Brian S. Thomson and Judith B. Bruckner
The author
Andrew M. Bruckner and Brian S. Thomson and Judith B. Bruckner
are mathematicians and educators specializing in "mathematical thinking", "problem-solving", and the "process of discovery" in mathematics. They study how creativity, intuition, and reasoning shape the development of new mathematical ideas. In "Mathematical Discovery", they explore how mathematicians approach "mathematical reasoning", solve challenging problems, and generate novel concepts. The book emphasizes the role of "exploration", experimentation, and strategy in uncovering mathematical truths.
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