Cover image for Math through the ages : a gentle history for teachers and others / William P. Berlinghoff, Fernando Q. Gouvêa.
Math through the ages : a gentle history for teachers and others / William P. Berlinghoff, Fernando Q. Gouvêa.
Expanded 2nd edition.
Farmington, ME ; Washington, DC : A Joint Publication of Oxton House Publishers and the Mathematical Association of America, [2015]
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Includes bibliographical references (pages 301-318) and index.
Preface to the second edition -- Preface to the first edition -- History in the mathematics classroom -- The history of mathematics in a large nutshell. Beginnings ; Greek mathematics ; Meanwhile, in India ; Arabic mathematics ; Medieval Europe ; The 15th and 16th centuries ; Algebra comes of age ; Calculus and applied mathematics ; Rigor and professionalism ; Abstraction, computers, and new applications ; Mathematics today -- Sketches. 1. Keeping count : writing whole numbers ; 2. Reading and writing arithmetic : the basic symbols ; 3. Nothing becomes a number : the story of zero ; 4. Broken numbers : writing fractions ; 5. Less than nothing? : negative numbers ; 6. By tens and tenths : metric measurement ; 7. Measuring the circle : the story of pi ; 8. The Cossic art : writing algebra with symbols ; 9. Linear thinking : solving first degree equations ; 10. A square and things : quadratic equations ; 11. Intrigue in Renaissance Italy : solving cubic equations ; 12. A cheerful fact : the Pythagorean theorem ; 13. A marvelous proof : Fermat's last theorem ; 14. On beauty bare : Euclid's plane geometry ; 15. In perfect shape : the Platonic solids ; 16. Shapes by the numbers : coordinate geometry ; 17. Impossible, imaginary, useful : complex numbers ; 18. Half is better : sine and cosine ; 19. Strange new worlds : the non-Euclidean geometries ; 20. In the eye of the beholder : projective geometry ; 21. What's in a game? : the start of probability theory ; 22. Making sense of data : statistics becomes a science ; 23. Machines that think? : electronic computers ; 24. The arithmetic of reasoning : Boolean algebra ; 25. Beyond counting : infinity and the theory of sets ; 26. Out of the shadows : the tangent function ; 27. Counting ratios : logarithms ; 28. Any way you slice it : conic sections ; 29. Beyond the pale : irrational numbers ; 30. Barely touching : from tangents to deriatives -- What to read next. The reference shelf ; Twelve historical books you ought to read ; History online -- When they lived.
"What's new in this edition? We have added new content and also tried to make improvements to the existing material. There are five new historical sketches, on: The tangent function and how it made its way into trigonometry. Logarithms, both decimal and natural. Conic sections: ellipses, parabolas, and hyperbolas. Irrational numbers. The derivative. As always, each of these come with Questions and Projects that try to address both the mathematics and the history, challenging students to go deeper into the topic. We also worked through the whole book to improve, correct, and update. Research on the history of mathematics continues, and we have learned new things over the last ten years. Historians make mistakes, especially when they are quoting other historians, and we have tried to correct all the ones that we knew about. Many new books have been published over the last dozen years, so the bibliography has been completely updated and the notes on "what to read next" reflect the latest resources. The questions and projects have been examined and, when it seemed appropriate, revised. The Instructor's Guide was thoroughly revised as well"--
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