Math 4050

History Of Mathematics

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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
  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
    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
    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
    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
    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
    Exercises
    • Hyperbolic Geometry problems
    • A look at one of Hilbert's 23 problems.
    • Russell's paradox.