Assignments
Weekly assignments are due Fridays at 11am. Occasionally, as on the first day of class, you will be given one problem due at the start of the next class.
Diagostic exercises are indicated by DX; these should not be submitted. All other exercises require written solutions. Exercises marked * are worth gold stars.
Assignment 1, due F., 1/22
Assignment 2, due F., 2/5
- Required: 1.24, 1.28, 1.38 (all from Adams)
- Submit at least 2 of these problems: 1.23, 1.25, 1.34, 1.35*, 1.36, 1.37 (all from Adams)
Assignment 3, due F., 2/12
- Required: Cromwell 1.2
- Required: Show torus knots T(p,q) and T(q,p); you may want to follow Adams' argument in section 5.1.
- Required: Show that Σ(Hopf link) has 8 elements. To accomplish this, you need to find three explicit isotopies (e.g., mirror-invert1, pure exchange, and pure invertibility) and use linking number to rule out a symmetry (e.g., individually invertible or mirror).
- Submit at least 1 of these problems: Adams 5.6, 5.7; Cromwell 1.3c, 1.3d*, 1.6
Assignment 4. Submit all of your work on paper, and include your results on our Pet Knots document.
Assignment 5, due F., 3/4. What is the product of surgery along a longitude of a torus? Draw pictures, and discuss its genus.
Assignment 6, due F., 3/18.
Assignment 7, due Th., 3/24
- Find the unknotting number of your pet knot. For all but one of you, your pet's unknotting number is either 1 or 2. Though you can look up the answer on KnotInfo KnotInfo. Please spend some time trying to unknot your knot first (at least ten minutes, or until you're fairly confident in your answer).
- Adams 3.4
Assignment 8, due F., 4/1
- Think about, don't submit: Adams 4.1, 4.2, 4.5, 4.7, 4.13, 4.15
- Required: Adams 4.6, 4.10, 4.14
- Required: There are five Platonic solids. Each is an compact, orientable surface with no boundary. Find the number of vertices, edges, and faces for each. Compute the Euler characteristic. Conclude each is homeomorphic to a sphere. Indeed, each can be inscribed in a sphere, and thus produce a cell decomposition of the sphere -- you need not draw this.
- Submit at least 1 of these problems: Adams 4.3, 4.4, 4.9; Cromwell 5.6
- Bonus: Adams 4.12
Assignment 9, due F., 4/8
- Think about, don't submit: Adams 4.17, 4.19, 4.22
- Required: Adams 4.16, 4.20, 4.27
- Required: Apply Seifert's algorithm to two different diagrams of your pet knot. What genus do you get for each surface? Add this information (and unknotting number results, if you haven't already) to our Pet Knots page.
- Submit at least 1 of these problems: Adams 4.23, 4.25, 4.28, 4.29
Assignment 10, due F., 4/22
- Think about, don't submit: Adams 9.4, 9.5
- Required: Adams 9.2, 9.3
- Required: In lieu of class last week, you watched three videos. Write a 1-3 paragraph reaction to one of the videos; what did you learn? what connections did you make?
- Required: Attend both Gentry Lectures. If you miss one, complete an extra problem from Assignment 8, 9, or 10. If you miss both, complete two extra problems. (If you cannot make one for an important academic reason, you may state your case to me in person.)
- Submit at least 1 of these problems: Adams 9.1, 9.6, 9.7, 9.8
Announcements
- [4/27/2016] Please submit all colloquium reactions by the last day of classes, so I can award gold stars.
- [4/25/2016, 4/27/2016] Presentations in class these days
- [4/27/2016] Bring your laptop to complete course evalutions.
- [5/5/2016] Presentations begin at 2pm.