From d1ea607d5596d784c734d1432c23a0051e049a2e Mon Sep 17 00:00:00 2001 From: bnewbold Date: Tue, 17 Feb 2009 12:51:05 -0500 Subject: new entry --- journal/05feb2009.html | 3 +- journal/16feb2009.html | 97 ++++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 99 insertions(+), 1 deletion(-) create mode 100644 journal/16feb2009.html (limited to 'journal') diff --git a/journal/05feb2009.html b/journal/05feb2009.html index 64be27f..14bab1c 100644 --- a/journal/05feb2009.html +++ b/journal/05feb2009.html @@ -39,7 +39,8 @@ skimming through it. Looks like there's plenty of work still to be done! Of course i'm sure a lot of it is in will's calculus additions, i'll have to look through that next.

-(previous entry) +(previous entry) - +(next entry) 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 @@ + + +bnewbold thesis + +

+Journal: Feb 16, 2009

+Bryan Newbold, bnewbold@mit.edu
+ +http://web.mit.edu/bnewbold/thesis/ +

+ + + +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): +

manifold (arbitrary dimension) +
vector +
tensor +
vector and tensor fields +
metric (a rank-2 tensor) +
1-form (with implied metric) +
chart, atlas +
coordinate system +
parameterized curve +
coordinate basis +
intervals +
Hamiltonian, Lagrangian +
geodesic +

+ +Some basic operators: +

norm/inner-product +
contraction +
tensor raising/lowering (w.r.t. a metric) +
differential form +
symmetrize/anti-symmetrize +

+ +Some tests: +

Lorentzian? (of transformations) +
Poincare? (Lorentzian plus translation) +
timelike?, spacelike?, lightlike? (of intervals and curves) +
zero-curvature? (of manifolds) +
rank? (of tensors) +
dimension? (of manifolds) +

+ +Some more specific operators: +

Riemann curvature +

+ +And some tools: +

evolve +
find-geodesic +
find-interval +

+ +

+ +Turns out I wasn't using the latest version of scmutils and that's why a bunch +of calculus functionality was missing... whoops! + +

+ +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. +
+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. + +

+ +

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