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From Calculus to Computers: Using 200 years of Mathematics History in the Teaching of Mathematics

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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 Among the topics included are: *  projects with significant historical content successfully used in a numerical analysis course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.
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Product Details

  • ISBN-13: 9780883851784
  • Publisher: Mathematical Association of America
  • Publication date: 3/1/2005
  • Series: MAA Notes Series , #68
  • Pages: 260
  • Product dimensions: 8.40 (w) x 10.80 (h) x 0.60 (d)

Table of Contents

Preface vii
Introduction xi
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 {25}
5. Using the Historical Development of Predator-Prey Models to Teach 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 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
About the Authors
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Preface

In the summer of 2001, the editors of this volume organized a contributed papers session at the MAA MathFest in Madison, Wisconsin. The topic was ways to use the history of mathematics in teaching. We received many wonderful abstracts. Due to time limitations, we had to make some cuts. Two or three of the abstracts dealt with more recent topics. The majority of the topics however, were more ``traditional" in that they addressed ways to use the history of Greek mathematics or calculus for example. We decided to use talks which dealt with topics up to the development of the calculus. The abstracts that addressed more recent mathematics were very intriguing, and made us realize that even though using the history of mathematics in the classroom is becoming very popular, the topic of recent history may be overlooked.

We decided to organize a follow-up session the next year in Burlington. This session was entitled The Use of History in the Teaching of Mathematics, with a focus on roughly the last two hundred years. Again, we had many excellent abstracts. The talks covered a range of topics from Galois theory to using the history of women and minorities in teaching.

The interest at MathFest in the topic of recent mathematical history, and a noticeable lack of information for educators on how to incorporate that history into the classroom, was the motivation for this volume. Several of the papers are from that 2002 session, while others are new. The papers cover a range of topics, from logic and computer science to Galois theory to the evolution of statistical thought in education. There are a variety of levels of detail, from general course outlines to ideas for projects and units in specific courses. Some papers focus on the history, while others focus on teaching.

This volume is by no means an exhaustive survey, simply a first step toward building a body of knowledge and ideas for incorporating recent history into the classroom. Whether you teach lower or upper division courses, mathematics, computer science or statistics, there should be something of interest to you.

We thank Andrew Sterrett for his support of this project from the beginning. Additionally, Barbara Reynolds and Donald Albers were instrumental in guiding our effort. Of course we appreciate the determination of all the contributing authors, many of whom were speakers at the contributed papers sessions we chaired at the MathFests. Both of us are very thankful for the mentorship provided by V. Frederick Rickey and Victor Katz. Finally, special thanks goes to our spouses, Chris Gellasch and Deb Jardine, who provided support on the home front, which is immeasurably important.

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