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+<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>
+
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+</html>