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

doi:10.5948/UPO9781614443032

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 Among the topics included are: projects with significant historical content successfully used in a numerical analysis course; a discussion of the role of probability in undergraduate statistics courses; integration of the history of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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Contents

1 - Arthur Cayley and the First Paper on Group Theory
pp 3-8
- By David J. Pengelley, New Mexico State University
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2 - Putting the Differential Back Into Differential Calculus
pp 9-20
- By Robert Rogers, SUNY Fredonia
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3 - Using Galois' Ideas in the Teaching of Abstract Algebra
pp 21-24
- By Matt D. Lunsford, Union University
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4 - Teaching Elliptic Curves Using Original Sources
pp 25-44
- By Lawrence D'Antonio, Ramapo College of New Jersey
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5 - Using the Historical Development of Predator-Prey Models to Teach Mathematical Modeling
pp 45-54
- By Holly P. Hirst, Appalachian State University
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6 - How to Use History to Clarify Common Confusions in Geometry
pp 57-74
- By Daina Taimina, Cornell University, David W. Henderson, Cornell University
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7 - Euler on Cevians
pp 75-92
- By Eisso J. Atzema, University of Maine, Homer White, Georgetown College
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8 - Modern Geometry after the End of Mathematics
pp 93-98
- By Jeff Johannes, State University of New York College at Geneseo
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9 - Using 20th Century History in a Combinatorics and Graph Theory Class
pp 101-108
- By Linda E. McGuire, Muhlenberg College
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11 - Introducing Logic via Turing Machines
pp 125-134
- By Jerry M. Lodder, New Mexico State University
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12 - From Hilbert's Program to Computer Programming
pp 135-148
- By William Calhoun, Bloomsburg University
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13 - From the Tree Method in Modern Logic to the Beginning of Automated Theorem Proving
pp 149-160
- By Francine F. Abeles, Kean University
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14 - Numerical Methods History Projects
pp 161-164
- By Dick Jardine, Keene State College
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15 - Foundations of Statistics in American Textbooks: Probability and Pedagogy in Historical Context
pp 165-180
- By Patti Wilger Hunter, Westmont College in Santa Barbara, California
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16 - Incorporating the Mathematical Achievements of Women and Minority Mathematicians into Classrooms
pp 183-200
- By Sarah J. Greenwald, Appalachian State University
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17 - Mathematical Topics in an Undergraduate History of Science Course
pp 201-206
- By David Lindsay Roberts, Laurel, Maryland
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18 - Building a History of Mathematics Course from a Local Perspective
pp 207-216
- By Amy Shell-Gellasch, Grafenwoehr, Germany. Formerly of the United States Military Academy, West Point, New York
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19 - Protractors in the Classroom: An Historical Perspective
pp 217-228
- By Amy Ackerberg-Hastings, Anne Arundel Community College
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20 - The Metric System Enters the American Classroom: 1790–1890
pp 229-236
- By Peggy Aldrich Kidwell, National Museum of American History, Smithsonian Institution
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21 - Some Wrinkles for a History of Mathematics Course
pp 237-242
- By Peter Ross, Santa Clara University
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22 - Teaching History of Mathematics Through Problems
pp 243-250
- By John R. Prather, Ohio University–Eastern
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From Calculus to Computers

Using the Last 200 Years of Mathematics History in the Classroom

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