Recent content by Axel Harper

Homework Statement Courant states that a convergent sequence is necessarily bounded; that is, for all n, the absolute value of term an is less than or equal to some number M. My question is does this apply to the sequence given by an = 1/(n-1)? Homework Equations As n approaches infinity, an...

I used to compete in math competitions in middle and high school and I've heard incredible things about the Art of Problem Solving series. Unfortunately, I never did get the chance to read them myself, but they cover everything from prealgebra to calculus. These books aren't cheap though, so I...

That's a good point. I think we could still interpret the problem in the same manner if NN is a woman because we still can't guarantee that her son's father is the same person as her father's son.

Homework Statement Problem 63 from Gelfand's book Algebra asks "are the father of the son of NN and the son of the father of NN the same person?" Homework Equations This problem is in a section about the square of a sum formula. (a+b)2 = a2+2ab+b2 The Attempt at a Solution If NN has a...

For a while, I thought I would apply to MIT, but earlier this year, I decided it wasn't the best school for me, so I appplied elsewhere. In general, there is no guarantee of being accepted to a top university, especially with admissions rates steadily declining, but I can tell you how to...

When I decided to teach myself some calculus, I used Thomas' Calculus with Analytic Geometry (blue cover with a lighthouse). It's a very straightforward and well-written book' and it's also cheap; I bought a copy for 1 cent. There are also great resources online. Someone already mentioned Khan...

It seems the others have covered your question well, but I want to speak more on memorization in math. I used to have the idea that math was memorizing a bunch of formulas and knowing when to use them, but of course, you'll run into a dead-end if you get a problem that doesn't fit any of your...

I'm honestly not a huge fan of modern textbooks, and maybe I'm too harsh on them, but my intended meaning was that I can't endorse anyone of the commonly used physics books over any of the others because they're essentially almost identical in terms of topics. I'm not entirely opposed to the...

The standard courseload for a bachelor of arts degree is 8 classes per year.In addition to this we have to complete two papers junior year involving independent research, and a senior thesis and oral presentation, which honestly sounds like fun (at least to me). I don't want to burn myself out...

Will do.

As a fellow self-studying student, I can give you some personal advice (some of which was probably already mentioned). I honestly can't endorse any of the more modern university physics books (Knight; Halliday, Resnick, Walker; Giancoli; Young, Freedman, Ford; Serway, Jewett; etc.). They all...

Thanks! I'm excited to be accepted to such a good school. I don't think I'll be the next Einstein, but I know I'll learn a lot! I've seen MATLAB mentioned a lot on MIT's OCW courses, so I should probably learn that. Princeton offers certificates instead of minors, and I'm considering one...

When I matriculate this fall, I should be able to find good professors. I'll also attend office hours and find a study group for problem sets. I'm trying to decide if I should take the honors multivariable cal/linear algebra sequence or try the introductory analysis sequence intended for math...

I've heard that a lot of physics majors get hired as "engineers" by industry, and your job prospects increase greatly if you can work with computers; now, whether or not that's your interests or desires, I'm not sure. I think that with a combination of physics and computer science, you could...

My proof-writing skills aren't quite as good as I'd like them to be, and I'm wondering if anyone can suggest particularly good books to help me develop better mathematical reasoning. I learned this the hard way by opening Spivak and struggling through the first few chapters. I understand the...