Recent content by deluks917

How strong is your dissertation? The stronger it is the more "unusual" you can be in the citations. If possible give correct credit but unless you have great results I wouldn't include a wall of internet cites.

You only need to state that S is open. Or that ∅ is open. Since they are compliments of each other.

Can you prove that sqrt(an) is eventually less than 1/100 ? How about that sqrt(an) is eventually less than 1/(1000000) ?

In this case imo, it is probably not a good idea both to increase the difficulty and the number of the classes you are taking. My guess would be you are best off with CM + EM2 + thermo lab + 1 other class. But I agree you should talk to a faculty advisor.

Do you have any friends who enjoy mathematics. Possibly you could get one of them to teach you. Lots of people love to teach intelligent, motivated students. I for example met approx 4 hours per week with a group of 3 students who wanted to work through Spivak's calculus. As well as answering...

What has worked well for you in the past in terms of course load. I personally learn the most when I can focus on a small number of things. In theory this might mean I learn less overall. But if you focus on a topic you tend to pick up a bunch of generally useful things. As an example studying...

You do not have to think about angles to understand the idea of a directional derivative. Let x and v be in Rn, v be a unit vector and t in R . The directional derivative of f at a in the direction v is just the derivative of the single variable function h(t) = f(a + tv) at t=0 (that is h'(0)...

My first recomendation would be this course. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-00sc-introduction-to-computer-science-and-programming-spring-2011/ . The course has video lectures and problem sets (not so easy if you are new to programming!). Also included...

I personally had absolutely no understanding of proof structure or logic (in the sense you mean) and I was fine. I cannot personally attest that someone with no knowledge of calculating derivatives would also be fine but probably they would be. My knowledge of calculus was very weak and not...

Here is a Nobel Prize winner's Advice: http://www.staff.science.uu.nl/~hooft101/theorist.html

I also suggest computer science. If you know a reasonable amount of computer science you can do useful things in all sorts of domains easily. Formatting documents, coding simulations or coding games (this is a really bad career choice since its so popular but its fun as a hobby!). And by...

In fact I personally did this. I had some exposure to single variable calculus (though at a very low level) before reading Spivak. But I had absolutely no understanding of proofs. I explicitly remember thinking to myself "I don't really get what a proof is." When I read the chapters on induction...

I do not understand why you need any preparation. The book has no pre-requisites besides basic High School Algebra. What you probably need is a lot of time to think about the material and ponder the problems. In my opinion you are much better off skipping any prep work and instead giving...

Surely you can find him in person somehow? Does he teach anything? Does he regularly attend any seminars? Is there any door you can sit in front for a couple hours until he will come by with high probability (just bring physics HW)? f you know where he is I would go up to him and ask for the...

Spivak is not, to my knowledge, freely available. This e-book however is openly inspired by Spivak and free! Really well done text imo http://math.uga.edu/~pete/2400FULL.pdf