On Tuesday, topology suddenly got hard, and I realized I didn’t understand anything. After a bit of studying, I was able to understand most of yesterday’s lecture. I still have to learn what quotient spaces are. Hopefully I won’t have as much trouble with quotient spaces as I had with quotient groups. Ring theory is getting interesting.

I can’t log onto my Arrowhead water account. I need to start getting much more water desperately since I feel dehydrated almost all the time. It doesn’t help that the classrooms don’t have any ventilation.

I went to Rabbi Steve Cohen’s “State of the Union” speech yesterday. Unlike two politicians who are actively destroying the state and country in which I reside, the Rabbi has evidently made UCSB Hillel into a much better place. Apparently crowds of 200 were completely unheard of a few years ago, and now such crowds are normal.

One of the students in the AoPS MathCounts/AMC Counting class was kind enough to tell me of a very nice free LaTeX system that can generate PDF files. That is good news since PCTeX and Acrobat Distiller together don’t make proper PDFs. That will make my life much easier.

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## About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.

Oooh, quotients… I used to have a grudge against any construction with the word “quotient” in it, though I’ve become cool with them. Quotient topologies are not as fun as quotient groups, since you’re modding out with respect to an arbitrary equivalence relation instead of having yummy coset goodness. They do seem to be essential to algebraic topology from what (not too much) I know of the subject.

Okay, I know that’s not a definition, but I think MathWorld or whatever other books/resources you have would do a better job of explaning what they’re about.

Yes, quotient spaces are seen frequently in algebraic topology. I am not sure that I would agree that they are less fun than quotient groups; collapsing a subspace to a point can be very useful. I think that combining the two ideas with quotient topological groups (for example S^3 with quaternion group structure) is even more fun, though.

Cool! I think I just have more of a feel for quotient groups. I won’t deny the usefulness of quotient topologies, though.

What is this program of which you speak?

It’s called TeXnicCenter. You can find it here.

I can attest to TeXnicCenter’s utility. And it feels like using Visual Studio, which gives me a warm fuzzy feeling in my tummy.