Kevin Reid's blog

I blame a certain English teacher last year for introducing “FAIL” into my vocabulary.

Both of the non-internet-based computer-related classes I'm taking this semester are (only offered as) once-per-week night classes, nominally ending at 9:30. So I'm talking with someone after class — — gee, it's bedtime already.

Late update on Caja-CapTP:

Google Summer of Code is over. I passed based on revised goals, but I'm not happy with the state of the code and I did not complete any significant part of the original plan.

Regarding the items mentioned in my last update:

• Write more documentation/comments.
• Commit as much of the work-in-progress as I can.
  • ...including the incomplete CapTPConnection, even though its tests don't pass yet, so that the partial work can be counted.

I committed CapTPConnection, and found and fixed enough infrastructure (whenResolved, CommTable, SwissTable, deSubgraphKit, etc.) bugs that it starts up and can do a basic operation or two. It's not useful for anything, but it's a lot closer to running than it was at the time of my last update.

Also, I removed dependencies on 'window' so in principle it will operate on a non-browser (server) JavaScript implementation. This has not been exercised because there is no browserless driver for the test scripts yet.

I stated that I would continue working on Caja-CapTP past the GSoC work period; however, with the time occupied by schoolwork, I have not had time or brain space to do so yet. I am not going to abandon the project.

As I wrote before, I am currently attending MVCC, a two-year college, and need to choose a college to transfer to (for a bachelor’s in computer science).

So, tell me what college(s) I ought to consider.

(I have of course also heard the advice that it doesn’t matter that much, but I've got to choose from some short-list...)

I am willing to consider any location in the contiguous US, but have been looking mostly at New York choices as a way to make the research list manageably short.

I am not looking for vocational training; I can learn this year’s or last year’s hot technologies just fine by myself, thank you. I’m looking for general education (“well-rounding”, shall we say), useful theory, and practice in thinking. I wish to avoid a high-pressure or competitive academic environment. Also, at MVCC, I have greatly appreciated the instructors’ approachability, availability, and even willingness to acknowledge mistakes.

Outside of education, I am particularly interested in there being social opportunities for the socially awkward; chances to talk to like-minded people (i.e. total geeks), and opportunities to talk to unlike-minded people (for the practice!).

Please give me your recommendations. Just a name, your personal experience, comments on others’ recommendations, whatever info you’d like to share.

(On the other hand entirely, I’d also consider going directly from MVCC to a full-time job given the right opportunity. This will be the topic of an upcoming post.)

I get the feeling the textbook writers had a list of everyday objects which they randomly picked from to avoid saying “an object” in each exercise. The results are mostly just distracting or mildly amusing, but sometimes they're a bit too much:

— Halliday, Resnick, Walker, Fundamentals of Physics, 8th ed., page 215

(This is (finally, now that the semester is over and I have some free time, heh) one of those posts-related-to-schoolwork I mentioned before.)

Does the infinite series converge?

First, rewrite it to have n = 1 as , and discard the constant term since it does not affect convergence. The terms of this series are strictly less than those of ; therefore, there is some x such that

Let k be the upper bound of the sum as we take the limit: .

Since is a continuous function of p, for any k there is some p greater than 1 such that

Since is a p-series which converges, i.e. has a finite sum, and the series under consideration has a lesser sum by the above inequality, it converges.

Furthermore, the above may be generalized to a proof that any series whose terms are eventually less than those of the harmonic series converges.

However, it is invalid, and in fact diverges.

I managed to convince myself and my calculus teacher with it, but we realized it must be invalid after he presented a counterexample to the general case. I then realized which step was invalid.

You can't use the same k for all three series in the second inequality; each infinite sum has its own independent limit, and what this proof is doing is along the lines of ∞ - ∞ = 0 — assuming that “two infinities are the same size”. Or rather, the inequality itself (among partial sums) is true, but that fact has nothing to do with the properties of the true infinite series.

I would be mildly interested in a more formal description of this sort of failure: how the k inequality is true yet the independent series do not have the same relation.

Update: I have received many informative comments and replied to some; one pointed out an earlier mistake: is bogus because we can't compare the series until we know they converge.

Up until now, I've pretty much had an Online Life and an Offline Life (not much of one), and not made any connections between them. It's time to change that.

I'm 25, and my current phase of the Standard Life Plan, in which I am running a bit late, is “college”. I am currently attending Mohawk Valley Community College in New York, and planning to transfer to a four-year school, with the goal of a bachelor's degree in computer science.

It's taken me far too long to get around to posting this. A short todo list of further items:

1. Update my web site.
2. Post about transfer.
3. Post about employment.

(One of the reasons for this post is to provide context for if I later post something related to schoolwork; another is getting around to the third item on this list.)