Happenings – 2011 Jun 18

Well, this past week’s color post certainly wasn’t advanced mathematics – but it was fun.

I’ve made a little progress on a few things.

I’ve looked through Kippenhahn & Weigert’s “Stellar Structure and Evolution” – from where I sit, it looks pretty comprehensive for modeling the interiors of stars. That’s why I ordered a while ago.

And that book I ordered specifically about stresses in thin shells… it doesn’t look hard, but there’s an awful lot of it. Of course, that’s what I was hoping for.

I think I’ve worked just about all the examples of dimensional analysis that I think I need… so I should write it up sometime.

There’s a lot of things I should write up sometime…

  • finding the final tableau of linear programming problem, given the initial tableau and the optimal solution (as Mathematica would provide it);
  • what I call the magic omega formula, relating the instantaneous axis of rotation to the rates of change of the Euler angles;
  • at least three posts about group theory;
    1. introduction and examples;
    2. the structure of finite abelian groups;
    3. homomorphisms and fibers;

  • matrix norms;
  • the Frenet-Serret equations of a curve;
  • the fundamental forms of surface;
  • mechanics of solids:
    1. distributed and point loads on beams;
    2. trusses;
  • time on parabolic and hyperbolic orbits;
  • regression;
    1. multicollinearity in all subsets of the standardized Hald data; ditto for all subsets of the centered Hald data;
    2. and far less detail, multicollinearity in a couple of other data sets;
    3. at least two more posts about the theory behind ordinary least squares;
    4. two more posts: a summary and a bibliography.

And I’m sure that list is incomplete. Unfortunately, I’m already writing two posts every weekend… and by the time I do that, I want to do math not more writing.

And yet, I have found another forum for writing. Just what I need.

Not.

Actually, I’ve talked about this before, namely stack exchange for non-research mathematics.

There was a question I just had to answer. Although its heading suggests that it’s about the study of mathematics, further detail shows that it’s about getting good enough grades to stay in school – in a school that effectively requires significant memorization.

One of the responses to that question included the following quotation by Gian-Carlo Rota:

The facts of mathematics are verified and presented by the axiomatic method. One must guard, however, against confusing the presentation of mathematics with the content of mathematics. An axiomatic presentation of a mathematical fact differs from the fact that is being presented as medicine differs from food. It is true that this particular medicine is necessary to keep mathematicians at a safe distance from the self-delusions of the mind. Nonetheless, understanding mathematics means being able to forget the medicine and enjoy the food.

I like that… and more math majors should know about it.

While I was there, I answered another question about evaluating an integral. I may have opened a can of worms by including a link to my post about organizing techniques of integration. We’ll see if I get flooded by a host of new readers… or if I get blasted by pure mathematicians for my lack of rigor and understanding.

Anyway, I am now a registered user out on the math stack exchange.

Closer to home, I’m ready to write up multi-collinearity in the standardized Hald data. I think I have decided that it is worth posting.

And, finally, my useless earthquake predictions for June are still perfect: there was at least one earthquake of magnitude 5 or greater somewhere on earth every day this past week (hence, every day so far in June). There was only one last Saturday, followed by 8 last Sunday… 4 already today… and three of the quakes since last Saturday have been at least magnitude 6 (6.0, 6.2, and 6.6).

OK, let me turn my alter ego the kid loose and see what math he wants to do. Oh, let me first tackle an outstanding comment/question.

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