From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom从计算到计算机

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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 provide 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 Among the topics included are: projects with significant historical content successfully used in a numerical analysis course, a discussion of the role of probability in undergraduate statistics courses, integration of the history of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, and ideas on how to implement history into any class and how to develop history of mathematics courses.

目录

Preface

Introduction

Part 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' idea 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 teach mathematical modeling Holly P. Hirst

Part 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

Part III. Discrete Mathematics, Computer Science, Numerical Methods, Logic, and Statistics

9. Using 20th century history in a combinatorics and graph theory class Linda E. MacGuire

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

Part IV. History of Mathematics and Pedagogy

16. Incorporating the mathematical achievements of women and minority mathematicians into classrooms 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

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