History of Mathematics
Class meetings: TuTh 5:00-6:30pm, 70 Evans Hall
Office hours: W 2:00-4:00pm, 821 Evans Hall
Course Control Number: 54233
Math 160 on Piazza
- 01/20: Sections 1.1, 1.2: Beginnings of Arithmetic. Beginnings of Geometry.
- 01/22: Sections 1.3, 1.4: Beginnings of Number Theory. Beginnings of Algebra.
- 01/27: Sections 2.1, 2.2: Improvements in notation and calculation.
- 01/29: Sections 2.3, 2.4: Analytic Geometry. Indivisibles.
- 02/03: Section 3.1: Tangents according to Fermat and Descartes.
- 02/05: Section 3.2: Quadrature: Wallis, Brounker, and others.
- 02/10: Section 3.3, 3.4: Cubature. Rectification.
- 02/12: Sections 4.1, 4.2: The calculus of Newton and Leibniz.
- 02/17: Section 5.1: Newton's Principia.
- 02/19: Sections 6.1, 6.3: Perfect numbers, Fermat's Little and Big Theorem.
- 02/24: Section 7.1: Early combinatorics.
- 02/26: Section 7.2: Early probability.
- 03/03: Section 8.1: Power series.
- 03/05: Section 8.2: Tailor series.
- 03/10: Section 8.3: Convergence.
- 03/12: Section 8.4: Fourier series.
- 03/17: Section 9.1: Early definitions of functions.
- 03/19: Section 9.2: Logarithmic and circular functions.
- 03/24: No class: Spring Break.
- 03/26: No class: Spring Break.
- 03/31: Section 10.1: Uses of calculus.
- 04/02: Section 10.2: Foundations of calculus.
- 04/07: Section 11.1: Limits.
- 04/09: Section 11.2: Continuity.
- 04/14: Section 12.1: Solving cubics and quartics.
- 04/16: Section 12.2: From Cardano to Lagrange.
- 04/21: Section 12.3: Higher-degree equations.
- 04/23: Section 13.1: Beginnings of group theory.
- 04/28: Section 13.1: Group and Galois theory.
- 04/30: Section 13.2: Fields, ideals and rings.
- Homework #1, due 01/27: Rewrite Apollonius' argument about a parabola on pp. 17-19 using modern notation and terminology as clearly and concisely as possible. What is its main point?
- Homework #2, due 02/03: Rewrite Cavalieri's Theorem on pp. 65-67 using modern notation and terminology as clearly and concisely as possible. What does he prove?
- Homework #3, due 02/10: Wallis on pp. 90-95 states four Propositions (two Theorems and two Corollaries). Restate those using modern terminology and prove them in the most efficient way you can.
- Homework #4, due 02/17: Restate Neile's rectification argument on pp. 103-104 using integrals and modern notation but staying as close to his explanations as possible. What result does he prove?
- Homework #5, due 02/24: Restate Newton's inverse square law for a parabola on pp. 151-154 using modern notation but staying as close as you can to Newton's original argument. Does Newton's argument contain any gaps? If so, identify and discuss those.
- Homework #6, due 03/03: State and prove de Moivre's Approximation to the normal distribution II on pp. 177-178. Prepare to discuss all Corollaries he gets out of it on pp. 178-179.
- Homework #7, due 03/10: 'Translate' Newton's arguments on pp.197-198 into modern mathematics. Are there any gaps/unproven facts in his arguments? If so, can you close those gaps?
- Homework #8, due 03/17: Read the excerpt from Lagrange's work on pp.217-222. Restate and reprove his result #49 as clearly as you can; summarize in 1-2 sentences (each) his results ##50-53.
- Homework #9, due 03/31: Read Euler's work on the exponential series on pp.245-249. Restate his results as simply and as completely as you can. If there are any gaps in his arguments, point them out and fill them.
- Homework #10, due 04/07: Restate Jacob Bernoulli's argument about the curve of uniform descent on pp. 260-264 as clearly as possible using modern notation and terminology. Discuss whether his physical assumptions are realistic.
- Homework #11, due 04/14: Write a 1-2 paragraph outline of your final project paper and post it on our Piazza site.
- Homework #12, due 04/21: Write a 1-page summary of the mathematics in your final project paper and post it on our Piazza site.
- Homework #13, due 04/28: Write a 1-page summary of the history in your final project paper and post it on our Piazza site.
- Jacdueline Stedall, Mathematics Emerging, Oxford University Press, 2008.
- S. Chandrasekhar, Newton's Principia for the common reader, Oxford University Press, 1995.
- C. H. Edwards, Jr., The Historical Development of the Calculus, Springer-Verlag, 1979.
- R. Roy, Sources in the development of mathematics, Cambridge University Press, 2011.
Last modified: Apr 29, 2015