Archive for the ‘Math’ Category

Lacking Latex

Tuesday, March 21st, 2006

I tried to set up a plugin today that would allow me to embed Latex[1] equations in my posts, but to no avail. My hosting company doesn\’t have latex installed. I need to get this blog (and the rest of my data) moved to my other space, then get the DNS transferred, but I\’m really just too lazy.

Also, today is the second time I\’ve failed to receive any email in my account. That\’s really not ok.

[1] I don\’t write LaTeX because I don\’t have the ability (lacking Latex) to reproduce the logotype correctly and because gratutituous capitalization in general is anathema to me.

Adding Up Numbers is Very Fun

Tuesday, March 21st, 2006

So, Stevey used to be at Amazon, but now he\’s at Google. At Amazon, his blog was one of the high points, and it was a sad day when I learned he wouldn\’t be able to back me up in my battles anymore. Now his blog is public, and it seems to be catching on already. Not to be left out, I figured I\’d offer my own comments on his suggestions for learning math.


Reading Update

Monday, November 14th, 2005

I haven\’t gotten as far into the Topology and Algebra as I had been hoping to. Although, my focus has definitely helped a lot with my progress in general. I\’ve read Nietzsche\’s Why I am So Wise, I Think, Therefore I Laugh by John Allen Paulos, most of Thomas Paine\’s Common Sense, and getting a good way into Machine Learning.

Actually, seeing that it\’s been a month, I\’m now less happy with my progress. I\’ve definitely been devoting much less time to my reading over the past few years. Gotta step it up.

The Reading Plan

Monday, October 24th, 2005

I just want to let everyone know that I haven\’t fallen off the math track yet. I\’m just not so good at the blogging about it. I\’ve tried to optimize my reading by concentrating on fewer books at once. I\’ve got five right now. For those who don\’t know me, that probably sounds high, but really, it\’s like a four-fold improvement. I\’m trying to stick with one book in each category:

  • fiction: The System of the World, Neal Stephenson
  • non-fiction: Why I am So Wise, Friedrich Nietzsche
  • analysis: Introduction to Topology, Bert Mendelson
  • algebra: A First Course in Abstract Algebra, John Fraleigh
  • computer science: Machine Learning, Tom Mitchell

For each of the last three, I also have a nice little Moleskine journal to take notes and work through problems in. I\’ve only used the Machine Learning notebook so far. It\’s the subject most relevant to work, so it gets a bit more attention.

The Statistical Inquirer

Monday, October 24th, 2005

Woah, I can\’t believe I haven\’t published this one. Just noticed it languishing in the backlog.

Combining ideas from Edward Tufte and John Allen Paulos, I thought it\’d be a good idea to create a statistical supplement to the newspaper. Which newspaper? All of them. The supplement would be organized like a newspaper, but would have only statistics. It\’s not meant to replace a paper, but to fill in the blanks that are always left in stories. Of course, not every story can be covered, but sports, important national and world events, etc. can all be handled quite well. Each paper may leave out different pieces of the puzzle, and this supplement will help to fill them in for the people who are interested in seeing the numbers.

Ideally, it seems like this could be an insert included with the paper. I definitely want it to be printed. The Web is so coarse, graphically. One of the primary issues will be how to keep it up-to-date with the daily papers. Maybe it\’s a weekly supplement?

Wouldn\’t it be nice to open your newspaper and have a little sheet to keep at hand so that when you ask yourself \”3,000 people died? Out of how many?\” you have somewhere to look?

I wrote a Common Lisp sparklines library. Maybe I can tie it in with cl-typesetting, and make something from there.

It Begins

Thursday, October 13th, 2005

I\’ve been reading a bit of Introductory Functional Analysis with Applications, but with the knowledge that it\’d mostly be over my head until I went back and did some Real Analysis. Today the first two analysis books arrived, Introduction to Topology and Introductory Real Analysis. I expect the Topology book will be simple, but it will probably also fill in a few blanks for me. Also, these books are smaller than Functional Analysis, so I\’m more likely to carry them around with me, too.

I\’ll probably get into Topology tonight.

I\’m also waiting on delivery of Basic Category Theory for Computer Scientists, which should lead nicely into Types and Programming Languages by the same author. As much as I may enjoy math, my primary motivation here is being a better programmer, so being able to see direct applications is nice.

There\’s More to Life than Analysis

Sunday, October 2nd, 2005

So, as I mentioned yesterday, I\’m starting to study math more seriously. After yesterday\’s post, I was informed that the list I had was only one half of the landscape. Farus gave me a path (as requested) to Rudin. That path has no aspect of Algebra in it, so I need to create a parallel path. Here\’s what I have so far:

  1. A First Course in Abstract Algebra — John B. Fraleigh (I\’m already reading this one)
  2. Something in Category Theory (Basic Category Theory for Computer Scientists — Benjamin C. Pierce? I have TAPL, so I\’m guessing Pierce is a good bet)
  3. Something in Combinatorics

Any help fleshing this out?

Update: Apparently I should replace Fraleigh with Topics in Algebra — I. N. Herstein.

Maths on $50 a Year

Saturday, October 1st, 2005

So, as the result of a conversation on #lisp the other day, I\’ve come up with this potential course of study to gain some math knowledge. Please comment, let me know which books are good, and which aren\’t. Also, any general strategies for diving into this stuff.

With the exception of Apostol and Rudin, these books are all around $10. That\’s pretty awesome.

  1. Introduction to Topology — Burt Mendelson
  2. Calculus, Vol. 1 — Tom Apostol (can I skip this one, at least on my first pass?)
  3. Introductory Real Analysis — A. N. Kolmogorov, S. V. Fomin
  4. Infinite Sequences and Series — Konrad Knopp
  5. Elements of the Theory of Functions and Functional Analysis — A. N. Kolmogorov, S. V. Fomin, which I might replace with Introductory Functional Analysis with Applications — Erwin Kreyszig since I already own it
  6. Principles of Mathematical Analysis — Rudin

So, from that list, how do I get to Category Theory? Where does Abstract Algebra fit into this? What other topics are important to a programmer using lambda calculus and machine learning?

I\’m going to try to post semi-regularly about what I\’m studying as I go. Hopefully 1. I\’ll make progress and 2. I\’ll remember to post about it here.

Thanks to farus for giving me a good path, and luis for recommending I blog about this.

I Don\’t Know Enough Math

Friday, August 13th, 2004

A lot of my friends are of a more artistic bent, so when I mention something like Google\’s \”{ first 10-digit prime found in consecutive digits of e }.com\” hiring campaign, I usually get a response like \”What\’s e?\” It\’s the kind of thing that makes me think I\’m pretty good at this math stuff. Then something comes along that proves me wrong.