Homework Assignments

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, 12gon, Pentagon, 15gon.

Due Wednesday, February 3
PDF version
 Reading
 Euclid's Elements Book I Proposition 47, 48. Book X, Proposition 29.
 Stillwell, Chapter 1
 Joseph, Pages 112 (but feel free to finish Chapter 1)
 Joseph, Chapter 4 (Mesopotamia).
 Exercises

Due Wednesday, February 10 (or whenever)
PDF version
 Reading
 Stillwell, Chapter 3, 5.1, 5.35.5, 5.7
 Joseph, Pages 380392
 Exercises
 Problems on Formulas for primes, GCD and Linear Diophantine Equations

Due Monday, February 22
PDF version
 Reading
 Stillwell, Chapter 3.4, 5.4, 5.5, 5.7
 Joseph, Pages 372392
 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

Due Friday, March 4
PDF version
 Reading
 Exercises
 Problems on computation and polynomial equations

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 Borwein^{2}

Due Wednesday, March 6
PDF version
 Reading
 Exercises
 Stillwell 9.5.3, 9.5.4 (binomial series)
 Exercise 4 from Borwein^{2}
 Logarithms: Computing log(2), log(3) and log(2.5)
 A few historical factoids

Due Monday, April 18
PDF version
 Reading
 Exercises
 Davis, page 8283, problems 4,5,6,7,8,9
 Projective geometry axiom problems
 Parallel postulate problems 1,2 only.

Due Monday, April 25
PDF version
 Reading
 Stillwell, Chapter 18.2, 18.3, 18.7
 Logicomix, sections 3 and 4.
 Exercises
 Spherical geometry problems

Due Friday, April 29
PDF version
 Reading
 Exercises
 Hyperbolic Geometry problems
 A look at one of Hilbert's 23 problems.
 Russell's paradox.
