From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom

Using the history of mathematics enhances the teaching and learning of mathematics. To date, much of the literature prepared on the topic of integrating mathematics history in undergraduate teaching contains predominantly ideas from the 18th century and earlier. This volume focuses on 19th and 20th century mathematics, building on the earlier efforts, but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines.

From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Among the topics included are:

• Projects with significant historical content successfully used in a numerical analysis course
• A discussion of the role of probability in undergraduate statistics courses
• Integration of the history of mathematics in undergraduate geometry instruction, to include non-Euclidean geometries
• The evolution of mathematics education and teacher preparation over the past two centuries
• The use of a seminal paper by Cayley to motivate student learning in an abstract algebra course
• The integration of the history of logic and programming into computer science courses
• Ideas on how to implement history into any class and how to develop history of mathematics courses

Table of Contents

Preface
Introduction
I. Algebra, Number Theory, Calculus, and Dynamical Systems
1. Arthur Cayley and the First paper on Group Theory, David J. Pengelley
2. Putting the Differential Back Into Differential Calculus, Robert Rogers
3. Using Galois’ Ideas in the Teaching of Abstract Algebra, Matt D. Lunsford
4. Teaching Elliptic Curves Using Original Sources, Lawrence D’Antonio
5. Using the Historical Development of Predator-Prey Models to Teaching Mathematical Modeling, Holly P. Hirst
II. Geometry
6. How to Use History to Clarify Common Confusions in Geometry, Daina Taimina and David W. Henderson
7. Euler on Cevians, Eisso J. Atzema and Homer White
8. Modern Geometry after the End of Mathematics, Jeff Johannes
III. Discrete Mathematics, Computer Science, Numerical Methods, Logic, and Statistics
9. Using 20th Century History in a Combinatorics and Graph Theory Class, Linda E. McGuire
10. Public Key Cryptography, Shai Simonson
11. Introducing Logic via Turing Machines, Jerry M. Lodder
12. From Hilbert’s Program to Computer Programming, William Calhoun
13. From the Tree Method in Modern Logic to the Beginning of Automated Theorem Proving, Francine F. Abeles
14. Numerical Methods History Projects, Dick Jardine
15. Foundations of Statistics in American Textbooks: Probability and pedagogy in Historical Context, Patti Wilger Hunter
IV. History of Mathematics and Pedagogy
16. Incorporating the Mathematical Achievements of Women and Minority Mathematicians in the Classroom, Sarah J. Greenwald
17. Mathematical Topics in an Undergraduate History of Science Course, David Lindsay Roberts
18. Building a History of Mathematics Course from a Local Perspective, Amy Shell-Gellasch
19. Protractors in the Classroom: An Historical Perspective, Amy Ackerberg-Hastings
20. The Metric System Enters the American Classroom: 1790-1890, Peggy Aldrich Kidwell
21. Some Wrinkles for a History of Mathematics Course, Peter Ross
22. Teaching History of Mathematics through Problems, John R. Prather
About the Authors