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From Calculus to Computers : Using the Last 200 Years of Mathematics History in the Classroom /
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 w...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Colección: | Notes.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Cover ""; ""copyright page ""; ""title page ""; ""Preface""; ""Contents""; ""Introduction ""; ""Part I: Algebra, Number Theory, Calculus, and Dynamical Systems""; ""1 Arthur Cayley and the First Paper on Group Theory, David J. Pengelley""; ""Introduction""; ""Cayley�s paper""; ""Pedagogy""; ""Conclusion""; ""References""; ""2 Putting the Differential Back Into Differential Calculus, Robert Rogers""; ""Introduction""; ""Brief History of Differentials""; ""Implementation of Differentials in a Calculus Class""; ""Differentiation of sine and cosine""; ""Curvature""
- ""The fundamental theorem of calculus""""The cable on a suspension bridge and the catenary""; ""Brachistochrone""; ""Conclusion""; ""References""; ""3 Using Galois� Ideas in the Teaching of Abstract Algebra, Matt D. Lunsford""; ""Introduction""; ""Historical Background""; ""Applications To Pedagogy""; ""Conclusion""; ""References""; ""4 Teaching Elliptic Curves Using Original Sources, Lawrence D'Antonio""; ""Introduction""; ""Preliminaries""; ""Cubic Curves""; ""Rational Points on Conics""; ""Rational Points on Cubics""; ""The Group Law for Cubics""; ""Mordell�s finite basis theorem""
- ""The Beha Eddn Problem""""Euler�s Conjecture""; ""Further Reading""; ""Conclusion""; ""References""; ""5 Using the Historical Dev. of Predator-Prey Models to Teach Math. Modeling, Holly P. Hirst""; ""Introduction""; ""The Historical Background""; ""Teaching Dynamical Systems in a Liberal Arts Mathematics Course""; ""Teaching Dynamical Systems in a Sophomore Introduction to Modeling Course""; ""Conclusions""; ""References""; ""Appendix: Maple Code""; ""Part II: Geometry""; ""6 How to Use History to Clarify Common Confusions in Geometry, Daina Taimina and David W. Henderson""
- ""Introduction""""The Four Strands of Geometry""; ""Spherical Geometry � the first non-Euclidean geometry""; ""The Parallel Postulate(s)""; ""Hyperbolic Surfaces""; ""Projections, Coordinate Systems, ��Models"" of the Hyperbolic Plane""; ""What is ��Straight""? How Can We Draw a Straight Line?""; ""Conclusion""; ""References""; ""7 Euler on Cevians, Eisso J. Atzema and Homer White""; ""Introduction""; ""Euler�s Theorem""; ""Ceva and Menelaus Revisited""; ""Solving a Triangle to Given Cevians""; ""The Case of Non-Concurrent Cevians""; ""Beyond the Plane""; ""Aftermath""
- ""In Conclusion""""Appendix: Exercises and Projects""; ""References""; ""8 Modern Geometry after the End of Mathematics, Jeff Johannes""; ""Introduction""; ""Non-Euclidean Geometry""; ""Differential Geometry""; ""Projective Geometry""; ""Geometric Topology""; ""Higher Dimensions""; ""References""; ""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. McGuire""; ""Introduction""; ""Motivating Factors""; ""Course Structure""; ""Project Description""; ""Assessment""