Recent content by mathwonk

watching the movie Ivanhoe today I was interested in the height of the famous fall off the castle by the great stuntman Paddy Ryan, reputed to be 100 feet into a moat. So I timed it at about 2.5 seconds. Given Newton's law (which goes back to Galileo) the distance fallen in 2.5 seconds should...

I think your new book is probably a good choice.

yes they meant what you said. however this is a strange definition, as property 3 follows from property 2, so is not needed. The book seems to be confusing two different characterizations. Namely given a topology on X, one wants to define a base for that topology, which is properties 1 and 2...

the fact that the natural numbers contain an infinite number of disjoint infinite subsets, implies for the arithmetic of infinite cardinals, that if A is the cardinal number measuring the size of the natural numbers, then A.A = A. On the other hand if 2^A denotes the cardinal number of all...

or, forgive me, maybe gently discuss it with her; after all, its another chance to spread the word, and that is what teaching is of course.

A family member in Tennessee, had a neighbor, an author, who once inscribed one of his books for her. Many years later, recognizing his name, I pulled that book off the shelf in a large used book store in Salt Lake City, and saw his inscription to her in the inside cover. Another time, while...

you seem to be asking for very extreme comparisons, but in the general direction of whether a significantly smaller boxer can win, I suggest you watch a film of the Jack Dempsey/Jess Willard fight; but only if you have a strong stomach for seeing the punishment absorbed by Willard, who...

In my opinion, one can teach to anyone at any age, anything that one understands oneself. Certainly one cannot teach anything one does not even know about. For this reason, I recommend that a teacher can never know too much. Anything he/she understands well, they can find ways to communicate...

I read about it enjoyably as an 8th grader, from the Universe and Dr Einstein, by Lincoln Barnett, (given to me by my father), but learned nothing of it, (nor much of anything else), in my extremely boring and less than elementary physics class as a h.s. junior.

@Andy Resnick : Some thoughts on the topic of post #10: https://www.math.uga.edu/sites/default/files/inline-files/onteaching.pdf

This has several excellent answers and I cannot improve on them. I just have this persistent nagging voice wanting to express this abstractly, if perhaps not actually usefully for a beginner. Namely, all answers point out, one way or another, that exponentiation is a function that changes...

@Surf_and_Sky: Have you talked to anyone at the U (in Salt Lake)? That is a very dynamic place, with lots of very bright people. That's where I think you are most likely to get relevant advice, and from people especially aware of the local options. If you cannot get help there, then maybe you...

Re: post #5. Here is the usual proof that every set has more subsets than elements. If S is any set (e.g. the set of rational numbers) and 2^S is the set of its subsets, and if S had as many elements as subsets, then there would be a surjective map f:S-->>2^S. We claim this is impossible...

Thank you for drawing attention to this. Many years ago, one of my friends told me as a joke on himself, that he had been referee for one of Faltings early 1980's papers, and had scolded the author for being bold enough to suggest that he hoped his work might contribute to a solution of...

by the way, if you decide to try this class, the fact that you know his source for the lecture material and for the exams, should make preparation for them rather straightforward. I.e. together with like minded fellow students, make sure you learn to do every single question on those MIT exams...