基本説明
Focusing on the developments of the nineteenth and twentieth century the text emphasizes recent history in the teaching of mathematics, computer science, and related disciplines.
Full Description
To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth- and twentieth-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. Examples of topics covered are probability in undergraduate statistics courses, logic and programming for computer science, undergraduate geometry to include non-Euclidean geometries, numerical analysis, and abstract algebra.
Contents
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
