I proved some of the propositions in *Linear Algebra Done Right*.

I asked a question on Math Stack Exchange about the use of “conversely” in some proofs in *Linear Algebra Done Right*.

I thought about how to show that “divide the data points by the standard deviation” and “scale the data points by a constant so that the new standard deviation is 1” are the same.

I thought about some stuff related to composition of limits (in analysis), and did one exercise from Spivak’s *Calculus*.

I made some edits to the page Comparison of concepts in computability theory.

]]>I did problem 8 in chapter 8 of Spivak’s *Calculus*.

I did problem 1 in section 13 of Munkres’s *Topology*. I also started on problem 2 but after I got the hang of it I stopped.

I read some articles on the Tricki related to real analysis. I especially enjoyed this page.

I think I continued reading a bit of Rogers’s computability book.

]]>While reading about recursively inseparable sets, I realized that this pattern of words was similar to saying a series is “absolutely divergent”, so I made a page to track similar terms.

I looked a bit at Hartley Rogers’s text on recursive functions. I think this book goes into computability in more depth than the text by Boolos, Burgess, and Jeffrey, so I might want to look at this text more. (Fun fact: Rogers was Stillwell’s advisor.)

]]>I wrote a page called Tiers of learning in mathematics.

]]>I spent some time thinking about the intermediate value theorem, the boundedness theorem, and the extreme value theorem in analysis.

I started doing some conditional probability problems out of *Intermediate Counting & Probability* (David Patrick). This isn’t really material that is new to me (actually I think some of the material in this book is new to me) but I want to get better at solving these types of problems (especially under time pressure).

I continued reading Stillwell’s *Reverse Mathematics*.

I started working on a dependency graph of results in analysis. This was inspired by (1) reading different textbooks that all give different proofs of the main results; and (2) reading Stillwell’s book.

]]>I tried proving the Heine–Borel theorem for the real line again, which I learned a while back.

I made some edits to the page Understanding definitions.

I discovered John Stillwell’s book *Reverse Mathematics* and started reading it a little. The book seems pretty interesting but I don’t know if I should continue reading it (it might be tangential to my goals, but it might also strengthen me mathematically or cement my understanding of real analysis).

I also spent some time thinking about the nested intervals theorem.

I started reading James Munkres’s *Topology*. I finished reading section 1.1 (set theory and logic) and thought about/did some of the exercises (they are the kind of exercises I am familiar with from other texts, so I don’t plan to work through all of them). One particular exercise caught my eye, which was exercise 1.1.2(k)–(l); this is because I had seen the same exercise in Tao’s book a while back. Since I fell into the trap on my first attempt (when working through Tao’s book), I had wanted to “get back at” the problem by explaining it clearly (I didn’t find any excellent explanations online). This seemed like the right opportunity, so I started the page Conjunction of subset statements versus Cartesian product subset statement.

I finished the final problem in section 11.2 and worked through section 11.3 (did not finish working through the exercises).

I started a page called Understanding definitions.

I submitted some corrections for Tao’s book *Analysis I* (they were added to the page on 2018-12-05).

I read section 10.5 (l’Hopital’s rule) but didn’t do the exercises (yet).

Today was spent mostly relaxing and doing “first day of the month” bureaucracies (updating the front page of my website, updating Timelines Wiki pageviews table, submitting contract work hours to Vipul).

]]>As I stated at the beginning, this blog came about because I wanted to make available information about “what I’m up to” in cases where “what I’m up to” doesn’t naturally lead to public updates. So I think it’s not so important to record things on here when the same information can be obtained through other sources (i.e. my public activity on other websites).

However, I also want to have some kind of conceptual coherence about this blog. And since the overlap between “my activity that doesn’t naturally lead to public updates but where I would like to make public updates available” and “my AI safety learning” is nearly perfect, I think I will track the former by writing about the latter. What does this mean in practice? It means:

- There will be some AI safety-related stuff on this blog that
*can*be tracked elsewhere. For instance, for now I am planning to blog about wiki pages I update in the course of my studying. - Some stuff not related to AI safety, even in cases where they can’t be tracked publicly, won’t be on this blog. This will mostly be one-off projects that I think up one day and decide to work on for a few hours or a day. Will these ever be made available? I think if they lead to something interesting I will try to publish them somehow.

- Reflections on working through Tao’s Analysis
- Proof that assumes the trick
- Colon-equals allows directionality
- Tao’s notation for limits
- Chain rule proofs (added a note about splitting into cases in one part of the limit of sequence proof)
- Timeline of my mathematical education (looked up when I ordered some books and added rows for these)

I also asked a question on Math Stack Exchange about point-free notation for limits.

]]>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).

]]>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.

I also returned to thinking about proving the continuity of (for fixed ). (I know there is an 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 .

I also asked a question on Math Stack Exchange.

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

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”.

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

]]>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.)

]]>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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