From ea8890ec434c2bc7539ba6f3687a75202129d495 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Fri, 16 Jan 2009 19:28:22 -0500 Subject: added schedule, reformated --- main.html | 76 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++------ 1 file changed, 69 insertions(+), 7 deletions(-) (limited to 'main.html') diff --git a/main.html b/main.html index 5c08b32..abfe520 100644 --- a/main.html +++ b/main.html @@ -11,23 +11,85 @@ http://web.mit.edu/bnewbold/thesis/

Title: A Compuational Elucidation of Curved Spacetime
Advisor: Prof. Gerald Sussman, EECS
-Year: 2009 +Year: 2009
+
+ +The old version of this page is here, +outlining what kind of projects I was interested in.

Quick Links

+

Schedule

+My course schedule etc can be found at +bryannewbold.com/cal.

+ +
When + What to do +
Jan 16-22 + Self teach some more scheme and differential geometry, documenting + examples. Maybe work through 2 or 3 problems from SICM textbook + or implement some classic physics problems (eg current through + wire cross section, variational principle examples in Feynman + lectures, derivation of magnetism at the 8.022 level). +
Understand and document scmutils package and compiler + interactions (at least conceptually). +
If I'm going to put mit-scheme in sage, this is the time to + do it, after this point I shouldn't be focusing on the software + tools as much. +
Jan 19-26? + Work through "Functional Differential Geometry", rewriting by hand +
Jan 31 + By this date have a proposed outline with length estimates so + I can sanity check with somebody in the physics department. +
Feb 28? + Have something resembling a draft and be working out details, + getting comments from professors and other students. At least + one interesting application should be demonstrated. +
??? + Spring break week +
??? + Final due to department +
+

Journal Entries

References

-

Summary

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Summary/Abstract

+from proposal: +

+I propose to implement a geometric formulation of curved space time in a +functional computer programming language, and to explore the space of +simulations +and manipulations made possible by such a formulation. A primary motivation +is to state the foundations of General Relativity in a non-ambiguous manner. +

+This work follows several attempts to formulate curved spacetime on +computers for the purpose of numerical calculations and algebraic manipulation. +Most of these packages are specially designed for the tasks of tensor analysis +and/or efficient numerical calculation, as is appropriate for use in +calculations. +A crucial difference of this proposed work will be to carefully build up the +geometric and analytical tools in a general purpose functional programing +language (mit-scheme). As a learning and reference tool, this will allow users +to explore +the inner workings and structure of the system, which I believe is essential to +understanding the system as a whole. +

+ The frame field representation will be used to emphasize the geometric +properties of curved space time, as opposed to the more traditional coordinate +heavy tensor analysis approach. +

+ The resulting work will include a full implementation with source code and +documentation, as well as example problems and qualitative comparisons with +existing packages and software systems. + -- cgit v1.2.3