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 -- Pros and Cons -- Conclusion -- References -- 10 Public Key Cryptography, Shai Simonson -- Introduction -- A Motivating Puzzle -- A Solution to the Puzzle -- Using Programs to Experiment and Understand -- Euclid's Algorithm -- Euclid's Algorithm Extended -- The Complexity of Euclid's Algorithm -- Fermat's Little Theorem -- Cryptography: A Brief History -- Breaking the Vigen ere Cipher: Determining the Length of the Codeword -- Breaking the Vigen ere Cipher Given the Length of the Codeword -- Public Key Cryptography: The RSA Breakthrough of 1978 -- Authentication -- The Mathematics Behind Public Key Cryptography -- The RSA Algorithm -- The Problem of Factoring -- Cryptographic Decoding Challenges for Practice and Review -- Conclusion -- References -- 11 Introducing Logic via Turing Machines, Jerry M. Lodder -- Introduction -- The Decision Problem -- The Projects -- Project I: An Introduction to Turing Machines -- Project II: Turing Machines, Induction and Recursion -- Conclusion.

References -- 12 From Hilbert's Program to Computer Programming, William Calhoun -- Introduction -- Teaching Mathematics and Computer Science Majors -- Why History Works -- Nineteenth Century Logic and Computing -- Logic -- Computing -- The Twentieth Century -- David Hilbert -- Kurt Godel -- Alan Turing -- John von Neumann -- Invention of the Modern Computer -- More Twentieth Century Logic and Computer Science -- Conclusion -- References -- 13 From the Tree Method in Modern Logic to the Beginning of Automated Theorem Proving, Francine F. Abeles -- Introduction -- Natural Deduction and the Roots of the Tree Method -- The Development of the Tree Method in the Second Half of the 20th Century -- The Tree Method -- Connections with the Beginning of Automated Theorem Proving -- Conclusion -- Appendix -- Example 1A -- Example 2A -- References -- 14 Numerical Methods History Projects, Dick Jardine -- Introduction -- The projects -- Conclusion -- References -- Appendix -- 15 Foundations of Statistics in American Textbooks: Probability and Pedagogy in Historical Context, Patti Wilger Hunter -- Introduction -- The Books -- Rietz's Text: Informal Empirical Foundations -- The Textbooks of Samuel Wilks: Foundations in Transition -- Harald Cramér and Measure-Theoretic Probability -- Addressing Today's Questions: Voices from the Past -- References -- Part IV: History of Mathematics and Pedagogy -- 16 Incorporating the Mathematical Achievements of Women and Minority Mathematicians into Classrooms, Sarah J. Greenwald -- Introduction -- Importance of Incorporating Women's and Minorities' Achievements into Classrooms -- Importance of Including Mentoring Issues -- Importance of Including Living Role Models -- Importance of Including Mathematics -- Historical Project Methodology -- Including Women and Minorities in Historical Projects.

Projects in an Introduction to Mathematics Course -- Projects in a Modern Algebra Course -- Projects in a Women and Minorities in Mathematics Course -- Modeling the Worksheet Process in the Introduction to Mathematics Class -- Selections from the Andrew Wiles and Carolyn Gordon Worksheets -- Mathematical Style (from the Andrew Wiles Worksheet) -- Gender Issues (from the Carolyn Gordon Worksheet) -- Mathematical Style (from the Carolyn Gordon Worksheet) -- Mathematics (from the Carolyn Gordon Worksheet) -- Classroom Activities (from the Carolyn Gordon Worksheet) -- Applying the Worksheet Process across a Variety of Courses: Using the Example of David Blackwell -- Sample Student Worksheet for David Blackwell -- Introduction (from the David Blackwell Student Worksheet) -- Influences and Support (from the David Blackwell Student Worksheet) -- Racial Issues (from the David Blackwell Student Worksheet) -- Mathematical Style (from the David Blackwell Student Worksheet) -- The Math (from the David Blackwell Student Worksheet) -- The Prisoner's Dilemma (from the David Blackwell Student Worksheet) -- Class Exercises (from the David Blackwell Student Worksheet) -- David Blackwell Project in a Women and Minorities in Mathematics Course -- Student Responses to David Blackwell Projects -- Conclusion -- References -- Appendix A: References and Comments on How We Used Them for Carolyn Gordon -- Appendix B: References Provided to the Students for David Blackwell -- Appendix C: Reference Section from the Student Worksheet -- 17 Mathematical Topics in an Undergraduate History of Science Course, David Lindsay Roberts -- Introduction -- Celestial Mechanics -- Electromagnetism -- Quaternions -- Statistical Mechanics -- Special Relativity -- General Relativity -- Quantum Theory -- Conclusion -- References.

18 Building a History of Mathematics Course from a Local Perspective, Amy Shell-Gellasch -- Introduction -- General Design of a Course -- The Course at West Point -- Course Topics -- Topics Outline -- Guest Lecturers and Presentations -- Guest Lectures -- In Class -- Class Activities -- Assignments -- List of Research Topics -- The Results -- Conclusion -- 19 Protractors in the Classroom: An Historical Perspective, Amy Ackerberg-Hastings -- Introduction -- The Protractor: A Biographical Sketch -- The Protractor and Practical Geometry -- Marketing the Protractor -- The Protractor and Educational Standards -- Conclusion -- Appendix -- References -- 20 The Metric System Enters the American Classroom: 1790-1890, Peggy Aldrich Kidwell -- Introduction -- The Origins of the Metric System -- Introducing the Metric System in American Textbooks -- Metric Units Made Legal -- Organizations and Objects-The American Metrological Society and the Metric Bureau -- Second Thoughts -- Implications for the Classroom -- References -- 21 Some Wrinkles for a History of Mathematics Course, Peter Ross -- Introduction -- Some Questions to Whet your Appetite -- Beginning Class with an Historical Item for that Date -- Showing Biographical Videos -- Conclusion -- Appendix -- References -- 22 Teaching History of Mathematics Through Problems, John R. Prather -- Introduction -- The Class -- The Problems -- Effects of the Problems -- Improvements -- Conclusion -- References -- Appendix: Sample Student Work -- About the Authors.