From Calculus to computers : using 200 years of mathematics history in the teaching of mathematics

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 Among the topics included are: projects with significant historical content successfully used in a numerical analysis course, a discussion of the role of probability in undergraduate statistics courses, integration of the history of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 Content: Arthur Cayley and the first paper on group theory / David J. Pengelley -- Putting the differential back into differential calculus / Robert Rogers -- Using Galois' ideas in the teaching of abstract algebra / Matt D. Lunsford -- Teaching elliptic curves using original sources / Lawrence D'Antonio -- Using the historical development of predator-prey models to teach mathematical modeling / Holly P. Hirst -- How to use history to clarify common confusions in geometry / Daina Taimina and David W. Henderson -- Euler on Cevians / Eisso J. Atzema and Homer White -- Modern geometry after the end of mathematics / Jeff Johannes -- Using 20th century history in a conbinatories and graph theory class / Linda E. McGuire -- Public key cryptography / Shai Simonson -- Introducing logic via Turing machines / Jerry M. Lodder -- From Hilbert's program to computer programming / William Calhoun -- From the tree method in modern logic to the beginning of automated theorem proofing / Francine F. Abeles -- Numerical methods history projects / Dick Jardine -- Foundations of statistics in American textbooks: probability and pedagogy in historical context / Patti Wilger Hunter -- Incorporating the mathematical achievements of women and minority mathematicians into classrooms / Sarah J. Greenwald -- Mathematical topics in an undergraduate history of science course / David Lindsay Roberts -- Building a history of mathematics course from a local perspective / Amy Shell-Gellasch -- Protractors in the classroom: an historical perspective / Amy Ackerberg-Hastings -- The metric system enters the American classroom: 1790-1890 / Peggy Aldrich Kidwell -- Some wrinkles for a history of mathematics course / Peter Ross -- Teaching history of mathematics through problems / John R. Prather. 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
*  ideas on how to implement history into any class and how to develop history of mathematics courses. 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. Arthur Cayley's 1854 paper On the theory of groups, as depending on the symbolic equation n = 1 inaugurated the abstract idea of a group [2].