Recent content by sin2beta

Yes, because of the subtraction before the left most parentheses. No it shouldn't. I don't know what I was doing. There will be coefficients on those two terms in the binomial theorem that need to be taken care of. Disregard my previous post.

A possible first step is to simplify (a+b)^n - (a^n + b^n) as (a+b)^(n-1). Likewise with the c and d terms.

This varies greatly. I have seen several studies showing differences in efficacy based on demographic. There seems to be fantastic outcomes for at-risk secondary students. However, for a lot of other groups, online learning just does not work. I have not seen studies based on subject, but I am...

I am a teacher and certified for high school mathematics, physics, and computer science. I also am a graduate student at Oklahoma State University in Mathematics Education (research in cognitive architecture (ACT-R) informing math reform). I did some experimental methods teaching for physics REU...

In order to do well in classes, I believe that study and going beyond the homework problems will suffice. A good study group is excellent as well. What the study group will do is act as a community to build on similar interests. However, I think a bad study group can be counterproductive...

I don't think that works. If nothing else just because one can not divide by 0 in that way. If one could then we would have the classic 1=2 proof as valid. http://mathforum.org/library/drmath/view/55792.html

This may be hijacking the thread, but why is x/0 when x \ne 0 not undefined. I'm not saying your wrong. I'm just wondering if there is something I am thinking about incorrectly since I haven't really revisited that aspect of math since middle school. However, for anything I can think of, in...

I believe that the investment whether borrowed or not is still considered an investment. But if I am wrong (which is quite possible, I don't know finance or economics) and short selling is not an investment, then the ROI formula makes no sense to use. It is return / investment. When the...

The first thing that comes to mind for me is Milliman. It's an actuarial firm. There is an office in San Diego. When I first left undergrad I worked at Milliman (not in San Diego) and the people there were great. It was like I never left academia in a way. I had worked on the BaBar project for...

The mean value theorem. A technique that I have found useful in many surprising instances is Gauss's trick. (See Knuth's Concrete Mathematics) It is not a theorem of course, but something that has been very useful in my bag of tricks and favored approaches.

From my experience, it should not cause problems down the road. I finished my undergraduate studies in math and physics and am now in grad school for math. However, I disliked algebra 1 and geometry severely. To this day, I am not fond of statistics. There will be areas that you dislike, some of...

Why is your investment 0? I would say that one invested $100 dollars. The initial stock sold was still worth $100 and was an investment. Does that make sense?

I would second Strang's Linear Algebra. Concrete Mathematics by Donald Knuth is very good. It doesn't pull any punches but doesn't require much after calculus. It is subtitled mathematics for computer science, but it is pure mathematics. The problem sets by themselves make it worthy of a...

If it interests you, absolutely! It would be very applicable to many fields of research. And an REU does not have to be in the field that you currently study. It helps, but is not needed. And discrete wavelet transformations will help in physics depending on what experiment you work on. But the...

A bit also depends on what grade you are. If you are near the end of your high school career and have taken physics, those lectures should be on par with your knowledge. If you are a freshman, you are probably ahead of the curve. The introductory lectures are exactly that, introductory...