• #### Issa Rice 10:36 pm on November 29, 2018 Permalink | Reply

I don’t mention this in my daily updates, but part of my routine as I study is to make Anki cards on the material I am learning. I also review the new and “due” cards daily, which usually takes about 30 minutes in the evening.

If you are curious about Anki or spaced repetition, as of 2018 I think Michael Nielsen’s article is the best introduction. However, since it is somewhat difficult to use “correctly”, I’m not sure I would recommend this sort of software to everyone.

I plan to write more about Anki at some point (probably not on this blog, as I want it to be in a more permanent location).

## 2018-11-29: more analysis

I continued working through Tao’s Analysis I. I worked through sections 10.2 (local maxima, local minima, and derivatives), 10.3 (monotone functions and derivatives), and 10.4 (inverse functions and derivatives). I got stuck on exercise 10.4.3(b) so I will resume there tomorrow.

I also spent time working on the page for little o notation again.

I also looked a bit at this study skills PDF (Cambridge University) as well as Lara Alcock’s How to Study as a Mathematics Major. The latter was actually better than I thought (based on the title) but I don’t think it contained insights I wasn’t aware of, so I skimmed a bit and stopped reading.

## 2018-11-28

I continued thinking about the chain rule and working on the page for it (in particular, adding the limits of sequence proof).

I also returned to thinking about proving the continuity of $f(x) := a^x$ (for fixed $a > 0$). (I know there is an $(\epsilon, \delta)$ proof to show continuity at zero, but I was wondering if I could do it using the squeeze theorem for sequences. I wasn’t able to find a satisfactory proof for this.)

I also thought a bit about the method of finding the inverse of a matrix by solving equations $Ax = e_j$.

I also asked a question on Math Stack Exchange.

I also posted a comment on LessWrong about an exercise in volume II of Analysis.

## 2018-11-27: more analysis

I continued thinking about the linear approximation interpretation of differentiability, and looked a bit at Caratheodory’s definition of differentiability.

I worked through the exercises in section 10.1 (basic definitions of differentiation).

I started a page on the chain rule for differentiation. For some reason I’ve always found this result slightly unintuitive, so I wanted to understand it “once and for all”.

## 2018-11-26: more analysis

I continued working through Tao’s Analysis I. I worked through section 9.9 (uniform continuity) and section 9.10 (limits at infinity), and read section 10.1 (basic definitions for differentiation).

I spent time thinking about the “best linear approximation” definition of differentiability. I started a page on little o notation.

## 2018-11-25: more real analysis

I continued working through Tao’s Analysis I. Specifically, section 9.7 (intermediate value theorem) and section 9.8 (monotonic functions).

I also began work on a timeline of my mathematical education. The timeline is kind of a way to make up for the lack of regular updates up to this point, but also a more compressed version of my progress.

I also posted a question about the use of “covariant” and “contravariant” in definitions.

I found a useful summary table for linear algebra (created by David Jekel), and thought about it a bit.

I did some preliminary research into finding a math tutor for myself. My current feeling is that having a tutor might help me learn faster (or better), but since I haven’t enjoyed too much working on math in person with people, it might not be worth the trouble. Also, I suspect that tutors at my level and personality fit are too expensive for what I am willing to pay, so I am pessimistic about finding someone. (It doesn’t help that search results are polluted with lower level/test prep tutors.)

## What this blog is about

The goal of this blog is to publicly make available updates about what I’m working on. Previously, this was not as important, since most of my work was already available publicly (via public activity feeds). However, since the main thing I am focusing on now is studying related to AI safety, most of what I’ve been up to recently has not been explained publicly. I wanted to fix that (as I care about individual transparency and public accountability), hence this blog.

Thanks to Vipul Naik for giving me the idea for this blog via his daily updates repo.

I chose WordPress because I am familiar with the service/interface (from using it in the past), because it has LaTeX support (which GitHub doesn’t), and because I want to allow comments (so that excluded doing this on my own website).

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