Homework Assignments

Homework assignments are due at the start of class. Late work will be accepted, up to twice per student with a penalty. Problems denoted (M) should be worked in Mathematica, and submitted to our Google Drive. Starred problems are optional, challenge problems. Math 334 students may submit any of the 634 problems for bonus credit.

  1. Homework 1, due W., 1/18:
    • Tapp: 1.4, 1.7, 1.8, 1.9, 1.10
    • 634 students only: Tapp 1.6
  2. Homework 2, due W., 1/25:
    • Tapp: 1.21, 1.24,
    • Shifrin: 1.1.1, 1.1.3, 1.1.5, 1.1.6, 1.1.8 [634]
    • Bonus Question: Shifrin 1.1.10, square-wheeled car; a full solution is worth several gold stars; don't consult resources outside our books
  3. Homework 3, due W., 2/1:
    • Tapp: none
    • Shifrin: 1.2.2, 1.2.3acde, 1.2.4, 1.2.6, 1.2.7, 1.2.11
    • Bonus Questions: Shifrin: 1.2.16, 1.2.26 (bicycle tracks)
  4. Homework 4, due W., 2/8:
    • Tapp: 1.52, 1.55
    • Shifrin: 1.2.10, 1.3.3, 1.3.4, 1.3.9 (twist))
    • Bonus Questions: Shifrin: 1.2.15
  5. Homework 5, due W., 2/15:
    • Tapp: 1.52, 2.13
    • Shifrin: 1.3.4
    • (a) Argue that any lune on a sphere is congruent to a lune drawn from north to south poles using longitudes. Use this to conclude the area of a lune of angle θ is 4θ.
      (b) Spherical triangles have areas that depend only upon their angles, which must sum to greater than π radians. Spherical triangles have sides comprised of great circles. Argue that, on a sphere of radius r, the area of a spherical triangle with angles a,b,c is A = (a+b+c - pi) R2. To do this, draw the 3 great circles for the triangle on a sphere. Consider the lunes they make. (There are 6 lunes and 2 triangles created by these 3 great circles.) Then use (a) and count appropriately.
    • Draw a plane curve whose signed curvature κs>0, but the curve is not convex. (Shifrin 1.3.2)
    • For the twisted cubic, γ(t) = (t, t2, t3), find its unit tangent vector T. Then plot its tangent indicatrix on a sphere, for t>0. What is its limit as t approaches infinity?
    • 634 students: Shifrin 1.3.1
    • Bonus Questions: Tapp, 1.66
  6. Homework 6 updated, due F., 3/3:
  7. Homework 7, due W., 3/22:
    • Shifrin: 2.2: 2,3,4,6
  8. Homework 8, due W., 3/29:
    • Tapp: 4.2, 5.1, 5.4
    • Shifrin: 2.2.8, 2.2.9ab
    • 634 problems: 4.5
    • Bonus problems: Tapp 4.26, Shifrin 2.2.9c
  9. Homework 8A, due W., 4/19:
    • note: so, um, I can't count. I assigned two "Homework 8's". We'll call this one Homework 8A.
    • Shifrin: 2.4: 1, 3, 5, 9
    • 634 students: Tapp 5.11/Shifrin 2.4.26a. Shifrin 2.4.26b is a bonus question.
  10. Homework 9, due F., 4/28