Dapthar

Senior Members

169

1. even and odd numbers

Whoa. So during the first trimester of Year 3, you have to take 11 classes? Crazy. Would you mind explaining how the scheduling works, since, in the US, the absolute maximum number of classes one can take during a semester is six, since most have three 50 minute lectures three days a week, plus a (two hour) lab or a (50 minute) discussion once a week, so six classes would be around 20 hours of class a week. On top of that, one credit translates to approximately four hours of study, and most classes are four credits, therefore, subtracting lecture and discussion time, that makes for about 12 hours of work outside of class per week, therefore six classes means about 72 hours outside of class studying/doing homework. Adding in the 20 hours for class, that makes 92 hours a week. Recall that there are only 168 hours in a week!
2. Why are you voting for Kerry?

Links: Nature's 15 Questions: http://www.nature.com/news/specials/uselection/index.html Science's Interviews with the Candidates about Science: (Click "Begin Manual Download") http://www.sciencemag.org/cgi/rapidpdf/1104420v1 Both are free of charge, and require no previous subscription to either magazine.
3. Math Help

Equations: $(x-x_0)^2+(y-y_0)^2=r^2$ $(x-x_0)^2+(z-z_0)^2=r^2$ $(z-z_0)^2+(y-y_0)^2=r^2$ The "centers" are at the points with the subscripts. There is the more general equation of a cylinder that is not parallel to one of the axes, however, it isn't particularly enlightening. The intuitive notion is that one picks two axes, and simply describes a circle in that coordinate system. Then, when one moves to the 3-D Cartesian plane, all the cross sections from the axes that was excluded from the initial equation are circles, thus one gets a cylinder. Alternatively, one could simply convert the equation of a cylinder in cylindrical coordinates to Cartesian coordinates.
4. College Majors...best..easiest..lucrative?

Yup. The CSci classes I have to take for my Engineering degree are interesting in the "broad scope of the subject" viewpoint, but the work is just minutiae and tedium to me. However, I agree with pulkit, when one gets far enough in their studies, it gets to be rather cool, however, I really don't have that much patience, or time. Math and EE is enough for me. Yeah, but it's not really that challenging of an area of Mathematics. Also, it's not much fun, and [old cliché]money isn't everything[/old cliché]. It's true that there's a ton of Applied Mathematics jobs in the US, however, most of them are with the Government, and frankly, I'm not too fond of their uses of Mathematics, to say the least. I'd rather keep my morals and stay in the more theoretical areas.
5. Report: U.S. losing ground in science education

True, however, you neglect to mention that one's tuition is usually paid in full for working as a TA or RA, and I doubt that this was included in the $19,000 yearly stipend you quoted. You stated that studying engineering will allow one to make around$60,000 upon graduation, and that is correct. However, when people decide to pursue a major that is not under the umbrella of Science, they generally do not go into higher paying majors such as Medicine or Business, but study something in the Arts, such as English, Political Science, etc. all of which pay less that any chosen engineering field (Electrical, Chemical, Mechanical, Biomedical, etc.). The bottom line is that people are shortsighted, and they forgo the immediate difficulties posed by Science majors for the later financial difficulties brought about by a poor (In the financial sense.) choice of major.
6. How fast can you count?

I got about 3 seconds, however, I think that is primarily a result of only counting to twenty once.
7. Maths Paper

When you get into more rigorous proof classes (Real Analysis, Topology, etc.), $\epsilon-\delta$ arguments will become the easiest type of proof you will encounter.
8. Zero to the Zero

False. It is undefined. Of course, you are free to devise your own number system in which this statement is true, however, you must re-derive any other mathematical results that you wish to use. You can't change a definition, and apply other results in Mathematics, as if nothing else had changed. Yes, for any given $b \ne 0$, the above statement is true, which proves that $0/x = 0$, for non-zero real $x$. Nope. Division of two real numbers is a single-valued operation, as I mentioned in my earlier post. Nope. Again' date=' division by [math']0[/math] is undefined so one cannot use algebraic operations on any equation that has such a term in it. Nope. Your argument isn't even true for real numbers, thus one cannot extend a fallacious argument to the complex domain. You're kidding, right? Do you realize that, in only 6 words, you've managed to contradict yourself? If something is undefined then it cannot be $\infty$ because it is undefined.
9. Why our own voices in our heads?

Yes. When I think, I do not "hear" a voice, just the words, most likely because thinking simply stimulates the part of one's mind that comes (temporally) after the "audio signal processing" section that lets one understand the spoken word. <sarcasm> Stop talking out loud when you think and the problem will stop. </sarcasm>

19. Is this equation always verified?

Then the equation you posted is correct, and this can be verified by simply adding $\frac{\partial w(t,y)}{\partial y^2}\cdot\frac{\partial u(t,y)}{\partial y^2}$ to both sides of the equation you posted.
20. Where does windows store the wallpaper settings?

In Windows XP, the directory where wallpaper is stored is C:\WINDOWS\Web\Wallpaper. Alternatively, you could put the file you want as wallpaper in your "My Pictures" folder, then right click on your desktop, click on Properties, go to the Desktop tab, and select the wallpaper you want.
21. Just some observations about the brain and time.

1.) Yes, I also find that time appears to progress more slowly when I'm concentrating on something, like homework. Also, I have found a way to reliably reproduce the effect you describe. Find a clock with a second hand that doesn't move smoothly, i.e. the hand jerks each second. Now, look at the clock for a moment, just to get the timing of the second hand down. Then, look away from the clock, keep counting, and look back at it right after a second ends. 2.) Nope, never happened to me.
22. Graph Calculator Question

I myself use a TI-86, and I would suggest that particular calculator since it does a great deal, with the exception of symbolic calculations. I find that using a calculator that does symbolic calculations tends to lead to mental laziness, and eventually one is solving one-variable linear equations with the calculator . However, if you can avoid this pitfall I suggest you get the TI-89, or the TI-92+, since they have a fair variety of advanced tasks, such as 3-D graphing. I recommend that you don't get a TI-83 or TI-84 since the syntax is rather arcane, and many Calculus operations that one may like to peform, such as numerical integration, are not possible to perform on either of these calculators. Unfortunately, I have no experience with HP calculators, so I cannot comment on them.

24. Quick LaTeX Tutorial

Just thought I'd post this link http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf. It's a relatively small, (approximately 2.3 MB) comprehensive set of symbol tables for $\LaTeX$ and some of its add ons. The page I got it from is here: http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf.
25. Zero to the Zero

Correct. Correct. Nope. It's due to the fact that $a/b = c \iff a = b \cdot c$, where $c$ is unique for a given $a$ and $b$. Note that if $b=0$ and $a$ is fixed, c can be any value, and therefore, it is not unique. Thus, division of any number by $0$ is undefined. Nope. Division of two real numbers is not a multiple valued operation. An example of a multiple valued operation is $\pm$. An example is the quadratic formula (i.e. if $f(x)=ax^2+bx+c, x=\frac{-b\pm \sqrt {b^2-4ac}}{2a}$). Assigning a numerical value to these concepts that does not conflict with the definitions of division is currently, and may never be, possible. Thus, the "undefined" moniker.
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