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The European Mathematical Awakening


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Preface Perspective: The European Mathematical Awakening Historical Exhibit 1: The Growth of Mathematical Knowledge 1. Counters: Computing if You Can Count to Five Historical Exhibit 2: Bede's Finger Mathematics 2. Gerbert's Letter to Adelbold Historical Exhibit 3: The Geometry of Gothic Church Windows 3. The Arithmetic of Medieval Universities 4. The Craft of Nimbryng Historical Exhibit 4: Algorist versus the Abacist 5. Leonardo Fibonacci 6. Leonardo of Pisa and his Liber quadratorum 7. Some Uses of Graphing before Decartes 8. Adam Riese 9. Tangible Arithmetic: Finger Reckoning and Other Devices 10. The Cardano-Tartaglia Dispute Historical Exhibit 5: Cardano's Technique for the Solution of a Reduced Cube Equation 11. Complex Numbers: An Example of Recurring Themes in the Development of Mathematiocs. 12. Robert Recorde's Whetstone of Witte, 1557 13. The Teaching of Arithmetic in England from 1550 until1880 as Influenced by Social Change 14. Tangible Arithmetic: Napier's and Genaille's Rods 15. The Life and Times of Johann Kepler Historical Exhibit 6: Multiplication Algorithm of the Fifteenth and Sixteenth Centuries 16. Simon Steven and Decimal Fractions Historical Exhibit 7: Mathematical Considerations on the Trajectory of a Cannon Ball 17. Viete's Use of Decimal Fractions 18. John Napier and His Logarithims Historical Exhibit 8: The Evolution of Algebraic Symbolism 19. Projective Geometry 20. Pisa, Galileo, Rome Historical Exhibit 9: Torricelli's Wine Glass 21. Analytic Geometry: The Discovery of Fermat and Descartes 22. The Young Pascal Historical Exhibit 10: Roberval's Quadrature of the Cycloid 23. Isaac Newton: Man, Myth, Mathematics Historical Exhibit 11: Newton's Method of Fluxions 24. The Newton-Leibniz Controversy Concerning the Discovery of Calculus Historical Exhibit 12: Mengoli's Proof for the Divergence of the Harmonic Series 25. The Bernoulli Family 26. The Bernoullis and the Harmonic Series 27. The First Calculus Textbooks 28. The Origin of L'Hopital's Rule 29. Euler, the Master Calculator 30. Gaspard Monge and the Descriptive Geometry 31. Mathematicians of the French Revolution 32. The Ladies Diary...Circa 1700 Historical Exhibit 13: Women in Mathematics Epilogue: The Process Continues Suggested Readings Index

About the Author

Professor Emeritus at Penn State University, Frank J. Swetz is co-founding editor of Convergence, an e-journal devoted to the history of mathematics. He is also the author of 20 books and more than 300 articles.

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