Cover -- copyright page -- title page -- Preface -- Purpose -- How to use Mathematical Time Capsules -- Additional purposes-assessment and teacher certification -- Acknowledgements -- References -- Contents -- 1 The Sources of Algebra, Roger Cooke -- Introduction -- Egyptian problems -- Mesopotamian problems -- ``Algebra'' in Euclid's geometry -- Chinese problems -- An Arabic problem -- A Japanese problem -- Teaching note -- Problems and Questions -- Further reading -- 2 How to Measure the Earth, Lawrence D'Antonio -- Introduction -- Historical Introduction -- In the Classroom -- Taking it Further -- Conclusion -- Bibliography -- 3 Numerical solution of equations, Roger Cooke -- Introduction -- The ancient Chinese method of solving a polynomial equation -- Non-integer solutions -- The cubic equation -- Problems and questions -- Further reading -- 4 Completing the Square through the Millennia, Dick Jardine -- Introduction -- Historical preliminaries -- Student activities -- Summary and conclusion -- Bibliography -- Appendix: Student activities -- 5 Adapting the Medieval ``Rule of Double False Position'' to the Modern Classroom, Randy K. Schwartz -- Introduction -- Historical Background -- In the Classroom -- Taking It Further -- Conclusion -- Bibliography -- 6 Complex Numbers, Cubic Equations, and Sixteenth-Century Italy, Daniel J. Curtin -- Introduction -- Historical Background -- In the Classroom -- Rafael Bombelli -- Conclusion -- Bibliography -- 7 Shearing with Euclid, Davida Fischman and Shawnee McMurran -- Introduction -- Historical Background -- In the Classroom -- Conclusion -- Appendix -- Bibliography -- 8 The Mathematics of Measuring Time, Kim Plofker -- Introduction -- Historical Background -- In the Classroom -- Taking It Further -- Conclusion -- Bibliography -- 9 Clear Sailing with Trigonometry, Glen Van Brummelen.

Introduction -- Historical Background -- Navigating with Trigonometry -- In the Classroom -- Conclusion -- Bibliography -- Appendix: Michael of Rhodes: Did He Know the Law of Sines? -- 10 Copernican Trigonometry, Victor J. Katz -- Introduction -- Historical Background -- In the Classroom -- Conclusion -- Bibliography -- 11 Cusps: Horns and Beaks, Robert E. Bradley -- Introduction -- Historical Background -- In the Classroom -- Conclusion -- Notes on Classroom Use -- Bibliography -- 12 The Latitude of Forms, Area, and Velocity, Daniel J. Curtin -- Introduction -- Historical Background -- In the Classroom -- Taking It Further -- Conclusion -- Comments -- Bibliography -- 13 Descartes' Approach to Tangents, Daniel J. Curtin -- Introduction -- Historical Background -- In the Classroom -- Conclusion -- Bibliography -- 14 Integration à la Fermat, Amy Shell-Gellasch -- Introduction -- Historical Background -- In the Classroom -- Taking it Further -- Conclusion -- Bibliography -- 15 Sharing the Fun: Student Presentations, Amy Shell-Gellasch and Dick Jardine -- Introduction -- Getting Started -- Presentations -- Assessment -- Conclusion -- Bibliography -- 16 Digging up History on the Internet: Discovery Worksheets, Betty Mayfield -- Introduction -- In the Classroom -- Learning about History --- and about the Web -- Conclusion -- Bibliography -- Appendix 1: Who Was Gauss? -- Appendix 2: History of Matrices and Determinants -- Appendix 3: Stephen Smale, a contemporary mathematician -- Appendix 4: Nancy Kopell, a female mathematician -- 17 Newton vs. Leibniz in One Hour!, Betty Mayfield -- Introduction -- Historical Background -- In the Classroom -- Taking it Further -- Conclusion -- Bibliography -- Appendix 1: Instructions to the class -- 18 Connections between Newton, Leibniz, and Calculus I, Andrew B. Perry -- Introduction.

Historical Background -- Newton's Work -- Leibniz's Work -- Berkeley's Critique -- Later Developments -- In The Classroom -- Conclusion -- Bibliography -- 19 A Different Sort of Calculus Debate, Vicky Williams Klima -- Introduction -- Historical Background -- In the Classroom -- Conclusions -- Bibliography -- Appendix A: Fermat's Method Worksheet -- Appendix B: Barrow's Theorem Worksheet -- Appendix C: The Debates: Roles, Structure, Hints -- 20 A `Symbolic' History of the Derivative, Clemency Montelle -- Introduction -- The Derivative -- Isaac Newton (1643--1727): -- Gottfried Wilhelm von Leibniz (1646--1716): -- Joseph-Louis Lagrange (1736--1813) -- Louis François Antoine Arbogast (1759-1803) -- Conclusion -- Reflective Questions -- Bibliography -- 21 Leibniz's Calculus (Real Retro Calc.), Robert Rogers -- Introduction -- Differential Calculus (Rules of Differences) -- Conclusion -- Appendix -- Bibliography -- 22 An ``Impossible" Problem, Courtesy of Leonhard Euler, Homer S. White -- Introduction -- Historical Setting -- In the Classroom -- Conclusion -- Appendix: Remarks on Selected Exercises -- Bibliography -- 23 Multiple Representations of Functions in the History of Mathematics, Robert Rogers -- Introduction (A Funny Thing Happened on the Way to Calculus) -- Area of a Circle -- Ptolemy's Table -- From Geometry to Analysis to Set Theory -- Conclusion -- Bibliography -- 24 The Unity of all Science: Karl Pearson, the Mean and the Standard Deviation, Joe Albree -- Introduction -- Karl Pearson: Historical preliminaries -- A data set -- The Mean and the First Moment -- The Second Moment and the Standard Deviation -- In the Classroom -- Conclusions -- Activities and Questions -- Bibliography -- 25 Finding the Greatest Common Divisor, J.J. Tattersall -- Introduction -- Historical Background -- More Historical Background -- In The classroom.

Conclusion -- Bibliography -- 26 Two-Way Numbers and an Alternate Technique for Multiplying Two Numbers, J.J. Tattersall -- Introduction -- Historical Background -- In The Classroom -- Taking It Further -- Conclusion -- Bibliography -- 27 The Origins of Integrating Factors, Dick Jardine -- Introduction -- Historical preliminaries -- Mathematical preliminaries: Integrating factors -- Bernoulli's and Euler's use of integrating factors -- Student activities -- Summary and conclusion -- Bibliography -- Appendix: Student activities -- 28 Euler's Method in Euler's Words, Dick Jardine -- Introduction -- Historical preliminaries -- Euler's description of the method -- Student Activities -- Summary and conclusion -- Bibliography -- Appendix A: Student Assignments -- Appendix B: Original source translation -- 29 Newton's Differential Equation {\dot y \over \dot x} = 1 - 3x + y + x x + xy, Hüseyin Koçak -- Introduction -- Newton's differential equation -- Newton's solution -- Phaser simulations -- Remarks: Newton, Leibniz, and Euler -- Suggested Explorations -- Bibliography -- 30 Roots, Rocks, and Newton-Raphson Algorithms for Approximating \sqrt{2} 3000 Years Apart, Clemency Montelle -- Introduction -- The Problem -- Solving \sqrt{2} - Second Millennium C.E. Style -- Time Warp: Solving \sqrt{2} - Second Millennium B.C.E. Style -- Taking it Further: Final Reflections -- Conclusion -- Bibliography -- 31 Plimpton 322: The Pythagorean Theorem, More than a Thousand Years before Pythagoras, Daniel E. Otero -- Introduction -- Historical Background -- Reading the Tablet -- Sexagesimal numeration -- So What Does It All Mean? -- Why Tabulate These Numbers? -- Plimpton 322 in the Classroom -- Conclusion -- Bibliography -- 32 Thomas Harriot's Pythagorean Triples: Could He List Them All?, Janet L. Beery -- Introduction -- Mathematical Background.

Historical Background -- In the Classroom -- Conclusion -- Bibliography -- Appendix: Who Was Thomas Harriot? -- 33 Amo, Amas, Amat! What's the sum of that?, Clemency Montelle -- Introduction -- The Harmonic Series -- Bernoulli and the Harmonic Series -- The Mathematical Explanation -- Conclusion -- Bibliography -- 34 The Harmonic Series: A Primer, Adrian Rice -- Introduction -- Historical preliminaries -- Introducing the harmonic series -- A ``prime" piece of mathematics -- Conclusion -- Bibliography -- 35 Learning to Move with Dedekind, Fernando Q. Gouvêa -- Historical Background: What Dedekind Did -- In the Classroom 1: Transition to Proofs -- In the Classroom 2: Abstract Algebra -- Moving with Dedekind -- Bibliography -- About the Editors.