Recent content by bifodus

Sorry matt, I must be having trouble parsing the sentences "I think my issue with these attempts to teach proofs by truth tables are that the students get good at showing some logical rules but..." and "There is a book with the same name as Polya's that appears to think explaining what truth...

You're welcome. I can see where you're coming from. I think why a lot of students might be seeing the technique as the holy grail of proof-writing (which obviously leads people of higher stature to scoff at the book) is because it makes all the logic they've learned (which often comes far...

I would possibly agree that Velleman takes a very pragmatic, and seemingly mechanical approach. But it just gives you a way to think about getting started, and how to understand the form of proofs. But seriously..."How to Solve it"? As I recall, that book has nearly nothing relating to the...

"How to Prove It: A Structured Approach" by Daniel J. Velleman is brilliant. It starts off with sentential and quantificational logic, which are absolutely necessary in really understanding how to write a proof, and then it gets into building blocks of analysis with relations, and functions...

So let p1 and p2 be elements of P2 Then T(p1 + p2) = (p1 + p2)(f) = p1(f) + p2(f) = T(p1) + T(p2) and T(cp1) = cp1(f) = cT(p1) Is this sufficient to show that T is a linear transformation or am I leaving something out?

Let f: R --> R and let T: P2 --> F, and T(p) = p(f). Prove that T is a linear transformation. P2 is the set of polynomials of degree 2 or less, and F is the set of all functions. It seems to me that I can treat f as really just a real number, in which case it's no different from proving...

Let S:V --> W and T:U --> V be linear transformations. Prove that a) if S(T) is one-to-one, then T is one-to-one b) if S(T) is onto, then S is onto This makes intuitive sense to me, since S(T) maps U to W, but I can't figure out how to go about proving this. I would appreciate any help...

I'm taking a first semester electricity and magnetism class and my teacher is quite a bit more rigorous than the textbook that he requires (Physics V2 by Halliday, Resnick, and Krane), so, in other words, my textbook is insufficient for the class. Does anyone have any recommended outside...

Ahh, thanks guys. For some reason I was attaching the unit vector to the equation for the magnitude of the force, which obviously removes the signs from the charges. Major brain fart. Thanks again.

To find the magnitude of a force between two charges is very simple, but to get the direction of the force seems a little strange to me. The signs of the charges aren't included anywhere in the law, so does this mean that I literally have to think "the signs are opposite, therefore I will...