Math 4050

History Of Mathematics

General Information

• Math 4050
• Spring 2016 Meets MWF 2:10-3:00 in TBA.
• Dr. Bryan Clair. Office hours: M10-11, W 3:10-4, Th 11-12 in Ritter 109.
• Course syllabus

News

Resources

• How Math Works
• Euclid's Elements online.
• MacTutor History of Mathematics archive
• Babylonian clay tablets: Plimpton 322, YBC 7302.
• More Babylonian clay tablets: A brand new (1/29/16) article by M. Ossendrijver on the calculation of the position of Jupiter, and also the supplement with transliterations and pictures of the tablets. Here's a map of Jupiter's path along the ecliptic.
• Cardan-Tartaglia: Sidelights on the Cardan-Tartaglia Controversy, 1937-8 article by Martin Nordgaard. Letters from the argument: Tartaglia versus Cardan
• The chapter from Borwein-Borwein, On the history of the calculation of π
• George Berkeley, The Analyst , 1734.
• Kevin Brown, "The Fundamental Anagram of Calculus".
• Don Davis, "Non-Euclidean Geometry" from The Nature and Power of Mathematics
• Introduction to Hyperbolic Geometry and Poincaré Disk Model of the Hyperbolic Plane, from D. Royster's Math 6118.
• The NonEuclid applet for the Poincaré disk.

Homework Assignments

1. Due Friday, January 22
   PDF version
   NOTE: On the converse/contradiction problem, proving Prop 19 directly is too hard (here is a proof due to Heron). Just do the second part, and prove I.18 using I.19 as given.
   Reading
   • Euclid's Elements Book I through Proposition 32, and also the Guide at the end of Book I.
   • Stillwell, Chapter 2
   • Betrand Russell, The Teaching of Euclid
   • Totally optional: Clouds by Aristophanes (Ian Johnston, translation). This gives some flavor of Greek intellectual life, around 420BC.
   Exercises
   • Stillwell #2.1.1, 2.1.2, 2.2.1, 2.3.1, 2.3.2, 2.3.3, 2.3.4
   • Four more exercises on the handout:
     Converse/contradction, 12-gon, Pentagon, 15-gon.
2. Due Wednesday, February 3
   PDF version
   Reading
   • Euclid's Elements Book I Proposition 47, 48. Book X, Proposition 29.
   • Stillwell, Chapter 1
   • Joseph, Pages 1-12 (but feel free to finish Chapter 1)
   • Joseph, Chapter 4 (Mesopotamia).
   Exercises
   • Stillwell #1.2.3, 1.2.4, 1.4.2
   • Exercises on the handout
   • An image of the Babylonian clay disk YBC 7302.
3. Due Wednesday, February 10 (or whenever)
   PDF version
   Reading
   • Stillwell, Chapter 3, 5.1, 5.3-5.5, 5.7
   • Joseph, Pages 380-392
   Exercises
   • Problems on Formulas for primes, GCD and Linear Diophantine Equations
4. Due Monday, February 22
   PDF version
   Reading
   • Stillwell, Chapter 3.4, 5.4, 5.5, 5.7
   • Joseph, Pages 372-392
   • Any handouts on this page and sections from Joseph you may need to understand the number systems section of this homework.
   Exercises
   • Number Systems: problems from class presentations on ancient number systems.
   • Pell's Equation problems
5. Due Friday, March 4
   PDF version
   Reading
   • Joseph, Pages 461-487
   • Stillwell, Chapter 6 (except skim over 6.2, 6.6)
   • Tartaglia versus Cardan
   Exercises
   • Problems on computation and polynomial equations
6. Due Wednesday, March 23
   PDF version (Note: 9.5.3, 9.5.4, and Exercise 4 are removed from this assignment)
   Reading
   • Borwein², On the history of the calculation of π
   • Stillwell, Chapter 4 and Chapter 9
   Exercises
   • Stillwell 4.4.1, 4.4.2, 4.4.3, 9.2.1, 9.2.2 (method of exhaustion and area computations)
   • Stillwell 9.3.1, 9.3.2, 9.3.4 (finding tangents)
   • Cancelled: Stillwell 9.5.3, 9.5.4 (binomial series)
   • Cancelled: Exercise 4 from Borwein²
7. Due Wednesday, March 6
   PDF version
   Reading
   • Borwein², On the history of the calculation of π
   • Stillwell, Chapter 9.5-9.7, 10-10.3
   • George Berkeley, The Analyst , Sections I-XX, XLIV-XLVI
   • Kevin Brown, "The Fundamental Anagram of Calculus".
   Exercises
   • Stillwell 9.5.3, 9.5.4 (binomial series)
   • Exercise 4 from Borwein²
   • Logarithms: Computing log(2), log(3) and log(2.5)
   • A few historical factoids
8. Due Monday, April 18
   PDF version
   Reading
   • Don Davis, The Nature and Power of Mathematics, Section 2.1 (pages 69-83).
   • Stillwell, Chapter 18-18.1
   • Logicomix, sections 1 and 2.
   Exercises
   • Davis, page 82-83, problems 4,5,6,7,8,9
   • Projective geometry axiom problems
   • Parallel postulate problems 1,2 only.
9. Due Monday, April 25
   PDF version
   Reading
   • Stillwell, Chapter 18.2, 18.3, 18.7
   • Logicomix, sections 3 and 4.
   Exercises
   • Spherical geometry problems
10. Due Friday, April 29
    PDF version
    Reading
    • Stillwell, Chapter 21.8, 22.9, 24.7*, 24.8*, 24.9
      * these sections are too hard, but have some choice tidbits - do the best you can
    • Finish Logicomix
    • You may find these helpful: Introduction to Hyperbolic Geometry and Poincaré Disk Model of the Hyperbolic Plane, from D. Royster's Math 6118.
    Exercises
    • Hyperbolic Geometry problems
    • A look at one of Hilbert's 23 problems.
    • Russell's paradox.