nickbros123

he didn't really have me in mind when he chose the topic per se. I needed to do a minor project for credits (minor being physics) and I approached him for something; it was just math he wanted to understand earlier, but he didnt spend much time on it before, so he figured now is a better time than any, so he thought he would give me this paper to read, and present it to him and his cohort.

The applications that he cares about are in string theory, certain counting problems in black hole physics and so on, but my work isnt in physics, I just have to understand the math that goes into it- mo…

before I ask this question, a bit of background: Im in my 4th year in a 5 year BSc+Msc in mathematics, and my 5th year is the final project year.

Now, a physics prof has (surprisingly (?)) given me some rather interesting reading work in number theory, that will effectively take up around 9 months (its to do with modular forms / mock modular forms, jacobi forms, hecke operators etc), and I know very very little number theory so it will demand quite a bit of my time. Now I am not entirely sure if NT will be my interest of masters thesis topic, it might be some other field, maybe functional …

some tinfoil hat speculation incoming:

we know via some fact about the natural numbers that for any field $F^{\infty}$ is uncountable dimensioned. Suppose $U$ is a subspace such that each sequence in $U$ only has finite non zero coordinates. The first fact would show that $F^{\infty}/U$ is infinite dimensioned, (since if it were finite, $F^{\infty}\sim U \times F^{\infty}/U$) via some cardinality argument.

My question is, could I reverse engineer this proof in some fashion such that I begin with the fact that $F^{\infty}/U$ is infinite dimensioned (I can generate an infinite linearly inde…

Stein "and" Shakarchi says the following: "a function $f:\mathbb{R}^d \to \mathbb{R}$ (finite valued) is measurable if and only if it inverse maps open sets to measurable sets", this is fine but in order to generalise the result to extended real valued function $f$, he says extra assertion $f^{-1}(\infty), f^{-1}(-\infty)$ must be measurable, but wouldnt working with the order topology on $R \cup\{-\infty,+\infty\}$ solve the issue,
as in it wouldnt be required to assert $f^{-1}(-\infty), f^{-1}(\infty)$ be measurable?

5 may not be far from the truth, more like 6 hours lol. also, this TA-ship is only hosting problem solving sessions, curating quizzes and generally clearing students' confusion, no grading on my part. I have a slight hedge I can handle all of this, well see. Not sure if the same professor will take the same course in a different semester, though

with regards to the course, the course is actually on the applied side of thhings, prereqs being real analysis, and probability (and stochastic processes), 10 hours of the module is devoted to revising markov chains, and various processes and brown…