Weekly Calendar with Assigned Readings:
January 19:
- The Edge of Modernity in Mathematics
- Kepler and Galileo; Analytic Geometry
- Boyer and Merzbach, 307 - 348
- Calinger, Classics, 326 - 343 and 354 - 374
- Calinger, Contextual History, 496 - 523
- Discussion: Descartes’ Rule of Signs (329 - 333) and Galileo on the
Continuum (363 - 374)
- Recommended Readings: Mario Biagoli, Galileo Courtier , Stephen
Gaukroger, Descartes: An Intellectual Biography, and Merriman, I: 276 - 354.
January 26:
- Immediate Origins of Differential Calculus
- Boyer and Merzbach, 348 - 390
- Calinger, Classics, 374 - 382
- Calinger, Contextual History, 523 - 555
- Discussion: Fermat on Maxima and Minima (377 - 380) and Pascal on Sines (380 -
383)
- Recommended Readings: Michael Mahoney, The Mathematical Career of Pierre de
Fermat, 1601 - 1665 and Hugh Davidson, Pascal and the Arts of Mind.
February 2:
- Independent Inventions of Two Similar Versions of Differential Calculus (Newton and
Leibniz)
- Boyer and Merzbach, 391 - 414
- Calinger, Classics, 383 - 417
- Calinger, Contextual History, 598 - 627
- Dunham, 155 - 190
- Discussion: Newton’s Binomial Series (400 - 405) and Leibniz’s
"Remarkable Type of Calculus" (387 - 395)
- Recommended Readings: Richard Westfall, The Life of Isaac Newton and S.
Chandrasekhar, Newton’s Principia for the Common Reader.
February 9:
- The Work of the Bernoullis and Initial Controversies over Calculus at the Paris Academy
and Royal Society
- Boyer and Merzbach, 415 - 427
- Calinger, Classics, 418 - 428
- Calinger, Contextual History, 627 - 654
- Dunham, 191 - 202
- Discussion: The Brachistochrone Problem (426 - 428)
- Recommended Readings: A. Rupert Hall, Philosophers at War (1980) and G.
Macdonald Ross, Leibniz (1984)
February 16:
- Fluxions and Criticisms in Britain;
- Paris Academy Debates over Newtonian Science
- Boyer and Merzbach, 427 - 438
- Calinger, Classics, 428 - 479
- Mary Terrall, "Representing the Earth’s Shape," Isis 83 (1992):
218 - 237.
-
Discussion: Taylor’s Series (466 - 468) and Berkeley’s Analyst
(471 - 475)
- Recommended Readings: Judith Grabiner,
"Some Disputes of Consequence: Maclaurin among the Molasses Barrels," Social
Studies of Science, 28 (1998): 139 – 168, Robert Ilife, "Aplatisseur du
monde et de Cassini: Maupertuis, Precision Measurement, and the Shape of the Earth in the
1730s," History of Science 31 (1993): 335 - 375, and Kenneth Winkler, Berkeley:
an Interpretation (1989).
February 23:
-
The European Enlightenment: the Age of d’Alembert and Euler (1):
-
Calculus and its New Branches; Metaphysics of Mathematics
- Boyer and Merzbach, 439 – 466
- Calinger, Classics, pp. 479 – 497
- Calinger, "Leonhard Euler: The First St. Petersburg Years (1727 – 1741)",
Isis 23 (1996): 121 – 166.
-
Discussion: Foundations of Analysis (482 – 485) and an Evolving Definition
of Functions (490 – 496)
- Recommended Readings: Thomas Hankins, Science and Enlightenment , 1
– 46, Thomas Hankins, Jean d’Alembert: Science and the Enlightenment,
Merriman, 354 – 442, and A. P. Youschkevitch, "The Concept of Function Up to the
Middle of the 19th Century," Archive for History of Exact Sciences 16
(1976): 7 - 85.
March 1:
-
The Age of d’Alembert and Euler (2):
-
Number Theory, Algebra, and Euclid Vindicated
- Dunham, 207 – 235
- Fraser, Calculus and Analytical Mechanics in the Age of Enlightenment,
selections tba
- Clifford Truesdell, An Idiot’s Fugitive Essays on Science, 293 – 380
- Discussion: A Comparison of the Historical Methods and Analysis of Fraser and
Truesdell
March 8:
-
Algebraic Analysis and Analytical and Celestial Mechanics: Lagrange and Laplace
- Calinger, Classics, 487 – 503 and 510 - 520
- Fraser, tba
- C. C. Gillispie, Pierre-Simon Laplace, 1749 – 1827: A Life in Exact Science,
tba.
-
Discussion: Lagrange and the Foundations of Calculus as well as the life of
Laplace: the Newton of France
- Recommended Reading: Helmut Pulte, "Jacobi’s Criticism of Lagrange: The
Changing Role of Mathematics in the Foundations of Classical Mechanics," Historia
Mathematica 25 (1998): 154 – 184.
First Test Put Online
March 22:
-
The French Revolution and the Metric System;
-
the Rise of Research-Intensive Universities, notably the Ecole polytechnique and the
University of Berlin
- Boyer and Merzbach, 466 – 496
- Merriman, Modern Europe, 495 – 548
-
Discussion: Science and the State during the French Revolution
- Recommended Readings: Keith Baker, Condorcet: From Natural Philosophy to Social
Mathematics (1975) and C. C. Gillispie on the Ecole polytechnique.
Turn in Book Review on March 24
March 29:
-
Gauss: Number Theory Becomes a Science
- Boyer and Merzbach, 466 - 510
- Calinger, Classics, 521 - 536 and 613 - 617
- Merriman, 548 - 597
-
Discussion: Gauss’s Disquistiones arithmeticae (613 - 617).
- Recommended Reading: Tord Hall, Carl Friedrich Gauss.
April 5:
-
The Inventions and Acceptance of Non-Euclidean Geometries
- Abbot, Flatland, entire book
- Boyer and Merzbach, 510 - 522 and 5333 - 553
- Calinger, Classics, 566 - 585
- Eves, 51 - 78
-
Discussion: Emergence of Non-Euclidean Geometries in Eves, Flatland, and
Riemann in Calinger, 577 - 585.
- Recommended Reading: Jeremy Gray, Ideas of Space: Euclidean, Non-Euclidean,
and Relativistic (1989)
April 12:
-
The Evolution of Satisfactory Foundations for Mathematical Analysis: Abel - Weierstrass,
Didactics, and Crelle’s Journal
- Boyer and Merzbach, 522 - 532 and 553 - 574
- Calinger, 586 - 613
- Merriman, 587 - 637 and 715 - 753
-
Discussion: Cauchy’s Criterion for Convergence (599 - 601)
- Recommended Readings: Bruno Belhoste, Augustin-Louis Cauchy: A Biography
(1991) and Judith Grabiner, The Origins of Cauchy’s Rigorous Calculus (1981)
Submit a Draft of the Term Paper for Comments.
April 19:
-
Set Theory and the Transfinite: Cantor: A New Paradise
- Boyer and Merzbach, 560 - 574
- Calinger, 613 - 646
- Dunham, 245 - 285
- Eves, 173 - 242
-
Discussion: Dedekind Cuts (627 - 634) and the Real Number System in Eves and
Dunham
- Recommended Reading: Joseph Dauben, Georg Cantor: His Mathematics and
Philosophy of the Infinite (1979)
April 26:
-
From Classical to Abstract Algebra
- Boyer and Merzbach, 575 - 598
- Calinger, 521 - 565
- Eves, 113 - 146
-
Discussion: Galois’s Group Theory and Boolean Logic in Eves (118 - 128) and
Calinger (542 - 548)
- Recommended Reading: Desmond McHale, George Boole: His Life and Work
(1984)
May 3:
-
Peano’s Axioms and the Supposed Foundational Crisis at the Turn of the 20th
Century:
-
(the Logicists, Formalists, and Constructivists)
- Boyer and Merzbach, 599 - 615
- Calinger, 646 - 695
- Eves, 147 - 211 and 243 - 275
- Discussion: The Work of Russell, Hilbert, and Brouwer (668 - 677, 696 -698, and
732 - 740)
The Final Test Will Be Put Online.
Submit Revised Term Paper on May 5.