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| author | bnewbold <bnewbold@eta.mit.edu> | 2009-02-17 12:51:05 -0500 |
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| committer | bnewbold <bnewbold@eta.mit.edu> | 2009-02-17 12:51:05 -0500 |
| commit | d1ea607d5596d784c734d1432c23a0051e049a2e (patch) | |
| tree | 5552e931d69d643dca878152d620447dc5cd641c /journal/16feb2009.html | |
| parent | 1538a3b5ba8f97b84fa466e1e8d9a3913e03658e (diff) | |
| download | 8thesis-d1ea607d5596d784c734d1432c23a0051e049a2e.tar.gz 8thesis-d1ea607d5596d784c734d1432c23a0051e049a2e.zip | |
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diff --git a/journal/16feb2009.html b/journal/16feb2009.html new file mode 100644 index 0000000..49b8130 --- /dev/null +++ b/journal/16feb2009.html @@ -0,0 +1,97 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head><title>bnewbold thesis</title></head> +<body style="margin: 25px; font-family: helvetica;"> +<h1 style="border-bottom: 2px solid;"> +Journal: Feb 16, 2009</h1> +<i>Bryan Newbold, <a href="mailto:bnewbold@mit.edu">bnewbold@mit.edu</a></i><br /> +<i><a href="http://web.mit.edu/bnewbold/thesis/"> +http://web.mit.edu/bnewbold/thesis/</a></i> +<br /><p /> +<!-- ================================================================ --> +<!-- ================================================================ --> + +This past week we've been covering generic operators in 6.945, which is great +because it's a set of questions I'm just getting around to. What are the +important data-types/-structures/objects in general relativity, what are the +important operators and procedures, and what are their arities and +applicabilities? + +Here are some potential object types (I'm using "object" in a general sense, +not with the usual CS implications): +<ul> + <li />manifold (arbitrary dimension) + <li />vector + <li />tensor + <li />vector and tensor fields + <li />metric (a rank-2 tensor) + <li />1-form (with implied metric) + <li />chart, atlas + <li />coordinate system + <li />parameterized curve + <li />coordinate basis + <li />intervals + <li />Hamiltonian, Lagrangian + <li />geodesic +</ul> + +Some basic operators: +<ul> + <li />norm/inner-product + <li />contraction + <li />tensor raising/lowering (w.r.t. a metric) + <li />differential form + <li />symmetrize/anti-symmetrize +</ul> + +Some tests: +<ul> + <li />Lorentzian? (of transformations) + <li />Poincare? (Lorentzian plus translation) + <li />timelike?, spacelike?, lightlike? (of intervals and curves) + <li />zero-curvature? (of manifolds) + <li />rank? (of tensors) + <li />dimension? (of manifolds) +</ul> + +Some more specific operators: +<ul> + <li />Riemann curvature +</ul> + +And some tools: +<ul> + <li />evolve + <li />find-geodesic + <li />find-interval +</ul> + +<hr /> + +Turns out I wasn't using the latest version of scmutils and that's why a bunch +of calculus functionality was missing... whoops! + +<hr /> + +Time is tick ticking away but I feel that things are starting to fall together, +doing problem sets for my GR class is super valuable, I wish i'd done more +practice exercises before to test myself. But overall I feel pretty +mathematically prepared. +<br /> +Over the weekend I went back and tried to review some topics from topology like +Baire dimension theory, embedding, and the fundamental group. I never really +covered these topics when I studies topology before, so I wasn't able to gleam +any insight. + +<pre style="margin:20px; border-left: solid grey 3px; background-color:lightgrey +;padding:5px;width:750px;"> +</pre> + +<br /><br /> +<a href="05feb2009.html"><i>(previous entry)</i></a> + +<!-- ================================================================ --> +<!-- ================================================================ --> +</body> +</html> |