boot camp day 9

well, class-wise bootcamp today was not necessarily great. we started doing series in analysis, which is good material, but i didn't feel like we necessarily covered much ground. although we did sketch out the proof of a pretty cool result, which is that if a series is conditionally convergent but not absolutely convergent, you can rearrange its terms to get it to sum to anything you want, or you can even get it to diverge. the idea is that if your series converges but not absolutely, then you can take its positive terms and negative terms separately, form two new sums from them, and both of these sums will diverge. so you can pick some 'target' L, and then sum from the positive terms until you get past L; then sum from the negative terms til you get below L. you'll always overshoot/undershoot L eventually because of the divergence of the two new separate series. but since the whole series converges, the terms of the series are approaching 0, so the terms of the two new series you have formed are approaching 0, so although you can continue to overshoot then undershoot L, you will be overshooting and undershooting by less and less. there's a slightly different argument to get it to diverge, but basically you sum positive until you're >1, then you sum negative until you're <-1, then sum positive til >2, etc. etc. and linear algebra was interesting but i think pretty off-topic as far as preparing us for the basic exam goes; we talked about expressing change of basis in terms of conjugation by a non-singular matrix, as well as the difference between diagonalizing a typical generic (diagonalizable) matrix and diagonalizing orthogonal matrices... this led to a discussion of basically classifying general orthogonal matrices... which led to a discussion of the orthogonal matrices as a topological group... for example, he proved that the subgroup of orthogonal matrices with determinant one is a connected group. anyway, then he went on to discuss exponentiation of matrices. it was interesting material, but i'll have to look over it to really get anything out of it, i think.

i also learned my TA assignments for the fall; i am TA for 2 sections of differential calculus (the typical 1st semester calculus stuff). so i do TA sessions tuesday and thursday at 10 in the morning, and it also says i'm responsible for 1 office hour, 1 hour of tutoring, and helping out with grading quizzes, tests, finals, etc. so, hopefully that will all work out; i was hoping for something standard like calculus, so i am happy with my assignment. anyway, no cardinals game today... but i am feeling like maybe i didn't get quite enough sleep last night, so maybe i'll replace the game with a nap before i get to work for the evening... anyway, thanks for reading!