Creative Mathematics, according to Wall, “is not a compendium of mathematical facts and inventions to be read over as a connoisseur of art looks over paintings.” It is, instead, a sketchbook in which readers try their hands at mathematical discovery. The book is self-contained, and assumes little formal mathematical background on the part of the reader. Wall is earnest about developing mathematical creativity and independence in students. Wall developed Creative Mathematics over a period of many years of working with students at the University of Texas at Austin. In less than 200 pages, he takes the reader on a stimulating tour starting with numbers, and then moving on to simple graphs, the integral, simple surfaces, successive approximations, linear spaces of simple graphs, and concluding with mechanical systems. The student who has worked through Creative Mathematics will come away with heightened mathematical maturity.
Table of Contents
Short Biography of H. S. Wall
2. Ordered Number Pairs
4. Combinations of Simple Graphs
5. Theorems about Simple Graphs
6. The Simple Graphs of Trigonometry
7. The Integral
8. Computation Formulas Obtained by Means of the Integral
9. Simple Graphs Made to Order
10. More about Integrals
11. Simple Surfaces
12. Successive Approximations
13. Linear Spaces of Simple Graphs
14. More about Linear Spaces
15. Mechanical Systems
Index of Simple Graphs
Glossary of Definitions
About the Author
Wall received his PhD from the University of Wisconsin-Madison in 1927. He was a professor of pure mathematics at the University of Texas at Austin (1946-1971) where he directed the doctoral work of over 60 students. Wall utilized the discovery-based method of teaching in his classroom. His research interests included continued fractions, Hellinger integrals, group theory and infinite processes.
I first discovered and was intrigued by the R. L. Moore approach to teaching mathematics when reading the article “The Moore Method: What Discovery Learning Is and How It works” in FOCUS (August/September 1999). Moore’s approach to “discovery learning” was developed from 1920 to 1969 at the University of Texas, Austin, and has since been known as “Texas school” or the “Moore Method.” This approach of axioms, questions, and proofs is designed to challenge students while leading them to points of discovery. The idea is to teach mathematical thinking, not manipulation. H. S. Wall worked along with Moore and other colleagues in transmitting this style to 139 Ph.D. students, many of whom became prolific researchers and teachers.
Professor H. S. Wall (1902–1971) developed this book over those years of working with students at the University of Texas. Applying the Moore Method, his aim was to lead students to develop their mathematical abilities and intuition. Wall himself called this book “a sketchbook in which readers try their hands at mathematical discovery.” That is a fair and accurate assessment. What it lacks in depth it makes up for in breadth. Over less than two hundred pages the reader travels from elementary number theory to simple graphs, from integrals and surfaces to linear spaces of simple graphs. Continued...