Source
r/UniversityofReddit•
sheafification

PhD celebration: what math course do you want?

I'm set to graduate this May with my PhD in mathematics (hooray!). To celebrate I thought I would put my new degree to use at UofReddit by taking requests for what math course ya'll would like to be involved in. What do you want to see offered?

My specialty is commutative algebra, but I should be able to do any undergraduate level class (and some graduate level) given enough prep time, so don't hold back on your requests. It can be a traditional class topic, a "topics course" that highlights some things in a particular area, a course on cross-disciplinary connections, whatever. Vote up your favorites and I'll try to figure out the most popular thing that I can reasonably do.

This is a long term plan here: my aim is to run the course this coming summer, perhaps starting as early as May if I'm not wiped out from dissertation work. The latest that it would go is August since I'll be starting a job then if I'm lucky.

I haven't decided on how the course would go at this point. I'm fond of a Moore method style of teaching where I provide guidance in what to prove and how, and you guys do the proving and presenting, but I don't know how well that would go online since it requires some level of synchronization. If you have any ideas on the best way UofReddit classes should be organized feel free to toss those out as well.

UPDATE: It looks like the top three choices are algebraic topology, cryptography, and some sort of linear algebra. Right now I'll plan on topology and algebraic topology, but will continue to monitor to see what people think. Look for the official course announcement sometime late winter/early spring.

Posted Oct 29, 2010, 6:01 PM UTC · edited

3440
kunjaan•

Since I am a CS grad, I would love these courses

  1. Linear Algebra with applications to Computer Science

  2. Combinatorial Optimization Techniques or Anything from Optimizations

  3. Statistical Learning Theory

  4. Theory of Computation

  5. Graph Theory

Any thing related to problem solving, counting, optimization, discrete structures.

21
fas2•

Seconded.

I would also be interested in vector calculus (curl, divergence, Laplacian, gradient/green's/stokes'/divergence theorem).

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[deleted]•

[deleted]

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sheafificationOP•

What do mean by "hardcore"?

Modern algebraic geometry has a lot of background to it before you can really get going. If we don't have to build up background we could probably get through a chapter or two of Hartshorne, or some equivalent. Alternatively, if people need the algebra background we could go through (most of) the algebra necessary to get started on Hartshorne. Or if "hardcore" means you're comfortable with the basics we can do some topic like toric varieties.

Algebraic topology has less baggage to get it going. We could run through some point-set topology quickly and hit homology and homotopy in something like Hatcher no problem. If people are sketchier on point-set topology we would probably have to limit to one of homology or homotopy. Again, if "hardcore" means you know the basics then we can do something like K-theory or derived categories or something.

I'm guessing most people here fall into the realm of not having seen much in either subject before, but correct me if I'm off-base.

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[deleted]•

[deleted]

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[deleted]•

Cryptology.

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slaughter5500•

Never before has one word caused me to spend (waste?) so much time on wikipedia. Thanks for that.

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[deleted]•

hahahahahahahaha this is great.

1
invadermonks•

Number Theory? I haven't found a good book for learning number theory, and I had a very poor graduate number theory course in college (undergrad level is fine too, as long as it's more than just the prime number theorem & fluff like the only undergrad number theory course at my college was).

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St4ud3•

I would probably participate in anything related to: Analysis, Cryptography, Linear Algebra or what I would really like is a class consisting of introductions to multiple advanced branches of mathematics explained with reasonably easy examples (undergrad style).

I'm a EE major in Germany and we have basic math courses, that cover basic Algebra, Analysis and everything that is needed for enginnering related topic, but I would really love an insight into more advanced topics. Unfortunately I'm not a math wiz, so the math used would need to be at an undergrad level, if that is possible.

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Dercraig•

Whats commutative algebra?

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sheafificationOP•

It deals with things called commutative rings which are objects that are supposed to capture the essential properties of the operations of addition and multiplication. Polynomial rings are the simplest interesting example: when you add and multiply polynomials together you get a polynomial as a result. So the idea is: what interesting things can we say about some polynomials like x^2y-3xy^3 and y+xy^2? Is there any relation between these polynomials? Etc.

You might be familiar with this kind of thing from high school algebra. The graph of x^2+y^2=1 is a circle of radius 1. But what the heck does the graph of y^3-x^2y+x=0 look like? Is there anything we can say about it? This is starting to head more towards the realm of algebraic geometry, but modern treatments are of algebraic geometry are built on top of commutative algebra so there's lots of overlap.

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Dercraig•

Wow thanks for this straightfoward yet enticing explanation. I really do forget how deep math can go and how much I don't know. I would love to take more advanced math classes (I only have a standard high school education at this point.) But have no idea where I would begin.

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esmooth•

you should check out r/math

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thecolossusjade•

xy == yx

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Dercraig•

I'm familiar with the commutative property, what I don't understand is how there is a whole branch of algebra associated with this. What is its application?

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esmooth•

What is its application?

algebraic geometry.

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unkz•

I wouldn't normally point it out, but you used it twice in a row.

It's commutative, not communtative.

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Dercraig•

Thanks for the correction.

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[deleted]

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Spicyice•

advanced topics in graph theory with applications :) please?

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Spicyice•

btw congrats! I am excited to graduate with my ugrad in math in May

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sr3yas•

Linear Algebra Please :D

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nolsen01•

Game Theory

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dirtymick•

Pre-Algebra. For reals.

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Quicksilver_Johny•

That doesn't seem like a very rational idea.

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dirtymick•

Pour quois?

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Paiev•

Point-set topology. Or pointless topology. Pointless topology does have the advantage of having a great name.

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itsMalarky•

Honestly? Basic Algebra lol.

I could use a refresher. haha

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a_dog_named_bob•

Hilbert Spaces! please! :(

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Banach_Space•

Hilbert Spaces, Hilbert Spaces, Hilbert Spaces, that's all anyone ever talks about. :-(

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a_dog_named_bob•

They're useful :p

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Banach_Space•

And I'm not? How typical. :-(

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lazeyasian•

Tensor Calculus?

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reeve512•

Differential Geometry, Complex Variables, Advanced Calculus, Topology, Abstract Algebra. Basically, any of the remaining classes I need to complete my BS and get into an elite grad school. And congratulations! :)

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[deleted]

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[deleted]

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pedro3005•

I'd like to add that it is a great idea, I would love any class. But these look a little bit too hard! I'm just a kid :) Ignore me if I'm interfering, but maybe something not too easy not too hard? Linear algebra sounds good. And +1 to the CS guy somewhere else in this thread, I love CS.

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emkat•

What's the highest level of math that you are comfortable with/know?

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pedro3005•

Honestly? Beginning of trigonometry, up to the graphing of sine, cosine and tangent functions.

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emkat•

Is that gr 10? gr 11?

I think it would be better if we used a phd to teach a more advanced course. there's a few ppl teaching pre-calc i think.

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pedro3005•

Well, I see a lot of people suggesting linear algebra. I'm not sure if I could follow but I'd try. Do you think that's not advanced enough?

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pwncore•

One that will enable me to pass the math entrance exam at college.

I never finished high school you see, and to partake in any science course I need to pass the math entrance exam.

Please hear my plea, good human.

Oh and, congrats.

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NJpalms•

Linear Algebra or Tensor Calculus

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