Honors 228J, Spring 1999

Selected Mathematical Classics

Schedule

• 1/28: Hilbert, "A continuous mapping of a line onto a piece of a planar surface" (handout)
• 2/2: Euclid, Elements, beginning of Book I, infinitude of primes (Book IX, Prop. 20) (handout)
• 2/4: Euclid, Elements, the Pythagorean Theorem and its converse (Book I, Props. 47-48) (handout)
• 2/9: Archimedes, On the Sphere and Cylinder (handout)
• 2/11: Diophantus, Arithmetica, beginning of Book I (handout)
• 2/16: Al-Khwarizmi, The quadratic formula (Struik, pp. 55-60)
• 2/18: Leonardo Pisano, The Book of Squares (handout)
• 2/23: Cardano on cubic equations (Smith, pp. 203-206; Struik, pp. 62-69)
• 2/25: Regiomontanus on trigonometry (Smith, pp. 427-433; Struik, pp. 138-142)
• 3/2: Descartes on geometry (Smith, pp. 397-402; Struik, pp. 87-89, 150-157)
  Note: the full text of Descartes' La Géométrie is available in the original French here.

  3/4: Pascal, The arithmetical triangle (Smith, pp. 67-79; Struik, pp. 21-26). Note change of room to 1310 in Math Bldg.

  3/9: Fermat, Contributions to number theory (Smith, pp.213-216, p. 561, pp. 563-564; Struik, pp. 26-31). Note change of room to 1310 in Math Bldg.

  3/11: Newton, Roots of equations (Struik, pp. 93-99. See also Struik, p.173). Note return to regular room.

  3/16: Leibniz on calculus (Struik, pp. 271-284)

  3/18: Newton and Gregory, Infinite binomial series (Smith, pp. 219-228; Struik, pp.284-291)

  Spring Break

  3/30: J. Bernoulli on sums of powers (Smith, pp. 85-90; Struik, pp. 316-324)

  4/1: no meeting (first day of Passover)

  4/6: Euler, The bridges of Königsberg (Struik, pp. 183-187, and handout)

  4/8: Euler, General researches on the mortality ... of the human species (handout, also available here)

  4/13: Legendre on Legendre symbols and quadratic reciprocity (Struik, pp. 49-54)

  4/15: Gauss on the fundamental theorem of algebra (Struik, pp. 115-122)

  4/20: Cauchy, On imaginary roots of equations (handout, also available here in postscript format)

  4/22: Galois on polynomial equations (Smith, pp. 278-285)

  4/27: Riemann, On the hypotheses which lie at the foundations of geometry (Smith, pp. 411-425)

  4/29: Cantor, Contributions to the foundation of transfinite set theory (handout)

  5/4: Hamilton on "Hamiltonian circuits" (handout)

  5/6: Dedekind on real numbers (Smith, pp. 35-45)

  5/11: Weyl, Mathematics and logic, a brief survey (handout)

  5/13: von Neumann, The mathematician (handout). Final papers due.