i'm back

hi. it's been a while, but i thought it was time to start posting again. i'm reading Steven Pinker's new book The Stuff of Thought, and he mentions the classic short film by Charles and Ray Eames, Powers of Ten. here it is for your viewing pleasure

class summaries, June 4 and 5

welcome to number theory! so far we've covered the integers, induction, fibonacci numbers, the division algorithm, and representations of integers in various bases.

hiatus

no posts for a while. i'm enjoying May, catching up on some yard work, and trying to finish off that paper on multi-dimensional persistence. summer school starts June 5; see you then.

requiem, part 2

as a proud alumnus of Virginia Tech, i've spent the last two days in a state of utter dismay. my heart hurts. i'm horrified beyond belief. please say a little prayer for the victims and their families.

requiem

R.I.P. K.V.

so it goes.

class summaries: April 4

calc III: vector-valued functions and space curves.

topology: cellular homology.

class summaries: April 2

calc III: quadric surfaces, cylindrical and spherical coordinates.

topology: adjunction spaces and cell complexes.

class summaries: March 30

calc III: lines and planes.

topology: homotopy invariance of homology.

class summaries: March 28

calc III: cross products. long live torque!

topology: the homology of a point, the 0-th homology group. algebra rules!

class summaries: March 26

calc III: vectors and dot products.

topology: introduced singular homology.

class summaries: March 23

calc III: 3-d coordinate systems; handed back tests.

topology: finished the proof of the Poincare-Hopf Theorem. next up: singular homology!

class summaries: March 21

calc III: test.

topology: more of the proof of the Poincare-Hopf theorem. will finish this next time.

class summaries: March 19

well, spring break is over and it's back to the grind.

Calc III: review for test #2. remember, it's on Wednesday, March 21.

Topology: trying to prove the Poincare-Hopf Theorem. lots of technicalities. nondegenerate zeros are better, so we'll try to reduce to that.

class summaries: March 7

calculus III: areas and lengths of polar curves. the cardioid has length 8(!).

topology: the index of a vector field on a manifold.

class summaries: March 5

calculus III: polar graphs, etc. almost done with chapter 11!

topology: tangent vector fields on manifolds; there's a nowhere-vanishing vector field on the n-sphere if and only if n is odd.