Upper level probability theory over summer

[malignant]

I need another class for a 6 week summer semester and I'm curious if probability theory is generally a class you wouldn't want to cram in 6 weeks with another class? The only college level probability I've done was in a discrete math course but I'm fine with other areas since I also took calc1-3, linear algebra, odes, pdes and some additional topics learned in upper division mechanics and e&m (not quantum yet).

The description is:

"A first course in probability. Introduces the basic concepts of probability theory and addresses many concrete problems. A list of basic concepts includes axioms of probability, conditional probability, independence, random variables (continuous and discrete), distribution functions, expectation, variance, joint distribution functions, limit theorems."

I have no idea what to expect in terms of difficulty in comparison to what I've already taken.

 

[QuantumCurt]

I've actually been wondering the same thing. I'm considering taking a Probability Theory class next summer, so I'm quite interested in the replies to this. The course I'd be taking at UIUC has an almost identical description, so instead of starting my own thread I'm just going to piggyback onto this one. In my case, the Probability Theory course would likely be online, which may present an extra layer of difficulty in taking it over the summer.

 

[micromass]

In the case of probability theory, the course description doesn't mean much. It is possible to teach those concepts in a very simple way. On the other hand, probability theory was definitely the hardest course I've ever taken (and the most fun one), so it can be made difficult. The reason for this is deciding which foundations to go from. One can do it pretty elementary (leaving some things unproved), but one can also do it very mathematically using measure theory. And one can also vary the amount of proofs and the hardness (because of generality) of the proofs.

You never took analysis and (I assume) are allowed to take the course. This would mean that the course contents will likely not be measure theoretical. So it will be on the easier side. This is good. In that case, I think that it should be doable to "cram" the contents in 6 weeks. You should expect a difficult similar to linear algebra or the discrete math course. But it is not the mathematical difficulty that is important here, it is the philosophical one. That is, there are many concepts that can be very unfamiliar at first and which need to be internalized. The amount of such concepts is probably higher than any course you have taken so far. That will be the most important difficulty. The actual calculations will be close to trivial.

Please do ask if something is unclear.

 

[Intraverno]

Nice new avatar btw Curt.

 

[QuantumCurt]

In the case of probability theory, the course description doesn't mean much. It is possible to teach those concepts in a very simple way. On the other hand, probability theory was definitely the hardest course I've ever taken (and the most fun one), so it can be made difficult. The reason for this is deciding which foundations to go from. One can do it pretty elementary (leaving some things unproved), but one can also do it very mathematically using measure theory. And one can also vary the amount of proofs and the hardness (because of generality) of the proofs.

These are very good points. Ultimately I'd prefer to avoid taking it in the summer. I'd rather avoid having any classes in the summer though for that matter. I'd rather allocate that time to research. At UIUC the math courses tend to be abstract and rigorous as I understand. The probability theory course is the more abstract and theoretical statistics course (as compared to a different Statistics and Probability course), so I imagine the workload wouldn't be easy. It might be necessary for me to take it over the summer in the interest of avoiding any overloaded semesters. I've still got quite some time to get this figured out in either case.

Nice new avatar btw Curt.

Thanks! It's a neutrino event from the Ice Cube Neutrino Observatory that was dubbed Big Bird, if you aren't familiar with the specific one. Although I rather get the impression that you may be.

 

[Intraverno]

Thanks! It's a neutrino event from the Ice Cube Neutrino Observatory that was dubbed Big Bird, if you aren't familiar with the specific one. Although I rather get the impression that you may be.

I actually wasn't, thanks for telling me! I figured that it was something similar to the higgs boson pictures at a particle accelerator like Large Hadron, I didn't think it would be neutrinos.

 

[malignant]

I've actually been wondering the same thing. I'm considering taking a Probability Theory class next summer, so I'm quite interested in the replies to this. The course I'd be taking at UIUC has an almost identical description, so instead of starting my own thread I'm just going to piggyback onto this one. In my case, the Probability Theory course would likely be online, which may present an extra layer of difficulty in taking it over the summer.

After the first week I can confirm that the course does not have measure theory (the teacher stated this). The students are mostly computer science and economics majors and two are phd students in economics. It doesn't seem bad but I can feel the discrete math knowledge helping a lot for all of the set theory that the teacher only spends one lecture on (6 week course so he has to go fast). The HW seems to have quite a bit of basic proof problems but it's nothing crazy.

 

[micromass]

You will be ok then! Have fun learning probability!