Paper, astrolabe, ruler, compass: a short introduction to the math behind general relativity

I’m going attempt to give an accessible introduction to general relativity for non-mathematicians without glossing over the mathematical objects one must to get a feel for to be able to follow research in the area. Let me know how successful I am!

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Road To Reality–Part I

This past year I read Roger Penrose’s The Road to Reality: A Complete Guide to the Laws of the Universe

The tome is definitely the read for anyone interested in our current understanding of reality from the ground up. It doesn’t shy away from mathematics like most popular science accounts. Rather, as mathematics is the gasoline to travel the Road, it fuels the reader up along the journey. Yet the mathematics quickly progresses from exploring what a number exactly is to a graduate level textbook equivalent and this whirlwind journey is not to be taken lightly. Rather than a Road, I actually consider The Road to Reality to be more of a Roadmap indicating a path to reality without fully providing the reader with the tools to travel it. It worked for me–a Physics PhD student–as most of the book was putting familiar things in a grander context. However, for those not on the Road as a career, supplemental work is probably needed to get the most out of the book. In the that spirit I am presenting a condensed Roadmap in chunks of 6 chapters (there are a whopping 34 chapters covering 1123 pages) with additional links to online courses (primarily sourced from the wonderful Khan academy, Coursera, and MIT OCW).

Without further ado, I present the Roadmap I of VI of Chapters 1-6 of The Road to Reality:

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Dynamic Bayesian Combination of Multiple Imperfect Classifiers

Using the new Voxcharta.org system, I was the only physicist at my institute to upvote this paper, Dynamic Bayesian Combination of Multiple Imperfect Classifiers (pdf), more in the realm of machine learning or computer science than traditional astrophysics or astronomy. As such I was nominated to discuss it at our weekly journal club. Here I give a brief review of concepts needed to follow the paper, and then go in depth into how we can use the opinions of multiple lay people as to whether an object is a supernova or not to achieve a highly accurate classification at the expert level.

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Green’s functions

Some of the most important equations in physics can be solved by constructing a beast with a curious set of properties, called a Green’s function. This post contains some interesting nuggets from a lecture I gave on St. Patrick’s day about Green’s functions to the course I assist, Mathematical Methods in the Physical Sciences II. I’ll […]

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