mark-t

It was on the live video feed.

I've never come across a keypad lock that would be vulnerable to this. You either have to press # at the end of the code, or the codes are significantly longer than 4 digits. Of course, even in the first category, entering 24 codes (50% chance of entering 12 or fewer) isn't a huge barrier once you know the four digits.

Why don't they just increase their margins on the thing that people actually want?

I use Google Gears, so I can still access all of my mail. I'm sending e-mails from a mail server on my laptop, but I could just as easily use a different e-mail service while gmail is down. Yes, Google is a big company with lots of technical prowess, but you can't reasonably expect 100% uptime. If it's that important to you, you should have a backup plan.

Nope. I'm well aware that people still study analysis. I just meant that one doesn't necessarily need to learn calculus before taking the plunge into serious mathematics. Even in analysis, there's quite a bit you can do without knowing the stuff from a standard calculus class (though it certainly helps).

That post does not contain any advice. It contains facts, none of which were contradicted by your post (a typical property of facts). I never told him not to study calculus. Given our current education system, that would be impossible anyway. I guided him more toward real analysis and suggested some other areas of math that might interest him. Since his only background is high school math, I felt it would be best to introduce him to something where proofs play a central role. If he can't stand that, then he probably shouldn't go into math.

I'm aware of their applications; by "practically", I meant "almost". There are certainly compelling uses for number theory and combinatorics (though I'm not convinced the study of algorithms is one of them), but they're nothing compared to calculus.

No. Many pure math classes require no (or very little) calculus. Abstract algebra, number theory, combinatorics, and graph theory certainly fall into this category. Topology does, too, depending on which area you study and what you consider calculus. Sure, there are obviously fields that do rely heavily on calculus, as well as certain branches in the above fields, but my point was that it's nowhere near universally needed. I'm a graduate student at UCSD, and I can't remember the last time I used calculus in my research.

Putnam problems are not considerably harder than AIME problems, and AIME is definitely the next step from AMC12. Anybody who can solve a few AIME problems can certainly solve A1 on the Putnam of almost every year.

No, x = -1/4 is correct. Perhaps you should look up the order of operations.

I'm not willing to concede his point yet, but even if he's right, this should be implemented by the browser, not the website. And if you consider taking his advice, I suggest masking the password as soon as the input field loses focus.

Me too, but I use more like 20 minutes per month. (Seriously, who needs a phone? That's what the internet is for.) The great part is that I can buy $10 worth of minutes at the end of the year, and all my minutes last another year. So, after four years or so, I will have paid maybe $160 including the phone. You can't come close to that kind of deal with any other provider.

I agree, up to perhaps a log-log scale. My grammar isn't likely to be significantly better in 30 years. However, when comparing among groups with similar English experience, grammar is likely to have a reasonable correlation with well-structured arguments. Also, the amount of time since learning English is not under your control; adherence to the rules of grammar is.

> ah right, judging someone from grammar is a very rational thing to do

I think you just turned "rational" into a label. Apart from your attempt at sarcasm, this statement is probably true. Like it or not, your ability to structure sentences reflects your ability to structure thoughts.