An Autodidact’s Topology Curriculum

My topology curriculum is an example of How To: Learn a New Discipline.

0. Build the map.

The map is a high level representation of important concepts and connections — the threads that compose the subject.

I started by working through these two:

Screenshot from 2014-07-25 18:43:02Screenshot from 2014-07-25 18:44:32

Where “work through” $\equiv$ read carefully and annotate the text, take notes on important concepts, and complete a few exercises from each chapter.


“Catherine, you said you’d teach me math. Why are you drawing squiggles?”

Screenshot from 2014-07-25 18:58:39Screenshot from 2014-07-25 18:59:21

“Math is formalized art! I get to draw these squiggles on a page, describe them with symbols, and call it math.”

1. Learn by working through complementary perspectives in parallel.


2. Give weekly lectures on what you’ve learned.

I’m giving informal lectures to a small group of people on what I’m learning. These people ask questions and tolerate pauses to look things up.

Don’t forget to ask for help when you get stuck!

If you can’t find a satisfactory explanation online:

My Todo System

I used to overcomplicate my todo system.

My todos were scattered across workflowy, email, various plain text files, a weekly planner, my white boards,  and Dropbox. This doesn’t include the post it notes covering my desk, reminding me to check whichever planner, and notes to self on various topics. I would then write down my immediate todos (4 items) on a post it note to begin working, I would inevitably lose that post it and write another one with the same content.

My weekly planner is located on my tablet, and I would keep this open always. I’ve since begun using my tablet for project design and documentation*, and can no longer keep my todos continuously visible (which led to the aforementioned mess).

I find it is useful to have my todos to be immediately visible, this frees up my mental cache to focus on brainstorming by eliminating the need to actively keep in mind the mundaneties of everyday life. Thus, without structure to organize them spatially, post it notes grew colonies and conquered my desk.

Finally, I realized that considering self betterment an ongoing project is a productive perspective. It allows for more focus, and less guilt maintaining your physical and mental health when you could be working on a project.

With this mental freedom, I sat down and unified my todo system. I’ve finally settled upon a simple routine that works wonderfully for me.

The board is broken up into (annotated below)
0. Self improvement & documentation
1. Development of math & physics intuition
2. Low priority
3. Today (indexed 0,1,2,3 by order of planned completion — indexes adjusted throughout day)
4. Done

If I’m not at home, I email myself todos to add to the board.

*I maintain a writeup for each one of my active projects (linked to relevant files in dropbox) in One Note. These writeups include an “in progress” tab for detailed, longer term, project specific goals.

Todos requiring temporal synchrony with another party are listed on Google Calendar (i.e. calls to professors, doctor’s appointments)

Introduction to Algebraic Structures

This post is an experiment in explaining math concepts via colorful hand-drawn diagrams.

At the recommendation of a few friends, I will likely add examples in the near future. If you find this post uninteresting/difficult to connect to ideas that you already have, I highly suggest you check out this post by MathIsFun.


Now that we’ve got that out of the way — we will delve into rings, fields, lattices, and categories.

Only then, once we’ve built your intellectual tool kit, we approach will the applications of groups in physics and biochem. Here’s a sneak peak of the introduction to lattice structures:

Generate CSV of Google Music Playlist

I recently switched my music vendor from Google Music to Spotify. To avoid manually searching for each song, I semi-automized the transition as follows.

1. Generate a CSV (artist, title) from your Google Music Playlist. Zoom your window out all the way (querySelectorAll will only load a static list of currently active rows).

// Run in Chrome's Developer Tools Console: Crtl+Shift+I

var playlist = document.querySelectorAll('.song-table');
for(var i =0; i<playlist.length ; i++) { 
  var l = playlist[i]; 
  var title = l.querySelectorAll('td[data-col="title"] .content')[0].textContent;
  var artist = l.querySelectorAll('td[data-col="artist"] .content')[0].textContent;
  console.log(artist.replace(","," ") + ',' + title.replace(","," ")); //take out "," to clean up CSV

Scroll and rerun until you have all entries.

2. Open your CSV in vim to remove the VM290:8 at the end of each entry. For example:
Clamavi De Profundis,Far Over the Misty Mountains Cold VM290:8


Now you have a CSV file of arists, titles to do with what you wish.
To proceed with migrating this playlist to Spotify specifically, continue to steps 3 & 4.

3. Copy/paste into Ivy.

4. Paste Ivy results into desired playlist.