Back in high school, I sometimes wondered what all the big deal about ZFC and the Axiom of Choice was, but I never really understood what I read in the corresponding Wikipedia page. In this post, I'll try to explain what axiomatic set theory is trying to do in a way accessible to those with… Continue reading Set Theory, Part 1: An Intro to ZFC
Why do roots come in conjugate pairs?
This is an expanded version of an answer I gave to a question that came up while I was assisting the 2014-2015 WOOT class. It struck me as an unusually good way to motivate higher math using stuff that people notice in high school but for some reason decide to not think about. In high… Continue reading Why do roots come in conjugate pairs?
Arch Linux on a Mac Mini
This post briefly outlines the process of setting up a dual boot OSX and Arch Linux on a Mac Mini. This is mostly for my reference in the likely event that I will be doing anything similar in some years, so it assumes some competence; fortunately, the Arch Wiki's Beginner's Guide probably fills in any… Continue reading Arch Linux on a Mac Mini
What leads to success at math contests?
Updated version of generic advice post: Platitudes v3. I think this is an important question to answer, not the least of reasons being that understanding how to learn is extremely useful both for teaching and learning. [1] About a year ago [2], I posted my thoughts on what the most important things were in math… Continue reading What leads to success at math contests?
Writing Olympiad Geometry
I always wondered whether I could generate olympiad geometry problems by simply drawing lines and circles at random until three lines looked concurrent, four points looked concyclic, et cetera. From extensive experience you certainly get the feeling that this ought to be the case -- there are tons and tons of problems out there but… Continue reading Writing Olympiad Geometry
A Sampler of Harvard Math
I was in Boston over this weekend for the 2014 Harvard-MIT Math Tournament. Before the contest on Friday, I sat in a few of the undergraduate math classes. They were pretty nice; I was actually able to learn some higher math that just by sitting in, despite the fact that I didn't have the necessary… Continue reading A Sampler of Harvard Math
PDF Compression
I always scan copies of letters into my computer before I send them out. So I had a bunch of large PDF's sitting around hogging my Dropbox space. One day I found this blog post which claimed that simply running (in Bash) the commands $ pdf2ps original.pdf temp.ps $ ps2pdf temp.ps new.pdf would decrease the… Continue reading PDF Compression
Constructing Parallelograms
This is a reflection of a talk I gave today. Hopefully these reflections (a) help me give better talks, and (b) help out some others. Today I was worked from 6PM-8PM with the Intermediate group at the Berkeley Math Circle, middle school students maybe one or two standard deviations above the average honors student. My… Continue reading Constructing Parallelograms
Email, JetPack, and Wintermelon
So I guess I can resume blogging now, seeing that I'm done with college applications (at last!). I'm not sure what I plan to blog about in general, but I figured I might as well put this domain name to good use :) I also realized that writing things out helped me clarify my thinking… Continue reading Email, JetPack, and Wintermelon
Power Overwhelming 