Real Analysis at Columbia University summer session

[Hello, world]

Hi all,

I have been contemplating taking analysis over the forthcoming summer, and have had trouble locating schools that offer any variant of analysis during the summer. It seems that Columbia University may be my only choice? If anyone knows of other rigorous analysis summer courses, could you please let me know.

Analysis I has two options. One runs for 5 weeks, and one runs for 10 weeks. If I were to take the 5 week version, I could potentially do Analysis II, which runs the second 5 weeks. Several people have suggested to me that analysis from Rudin Principles at Columbia in 5 weeks is a death wish. Does it sound realistic to hope to solidly learn this material in 5 weeks? Has anyone taken this Columbia summer course that could provide me with some insight? I do not have much experience constructing proofs, but plan on doing some prep work on my own this spring semester. Again, does a 5-week turbo charged analysis course seem like a bad choice for my first real proof-writing experience? To provide you with some background, I have taken Calc I-IV, Linear Algebra, and Diff EQ, done well in all of them, but they were mostly computational in nature.

Any help/suggestions would be very much appreciated. Thank you, and good luck to all those putting out applications this year!



Description of Analysis I from Columbia website: "Elements of set theory and general topology. Metric spaces. Euclidian space. Continuous and differentiable functions. Riemann integral. Uniform convergence."

[zurich_econ]

I'd say its by no means impossible, but certainly a bit harsher than if you'd do it in a longer period of time. After all, doing proofs all day long is what maths majors do, so why shouln't you be able to?

But I think you're well advised to grab some real analysis book and try to do some of the easier exercises (e.g. proof that every differentiable function is Lipschitz-continuous).

[Gecko]

ho ho I would recommend the 10 week version no point taking the risk of a negative mark right ?

[hulk86]

real analysis takes a lot of time to get the hang of. 5 weeks sounds like murder.

[JohnMcClane]

If you don't have any experience with proofs and some form of abstract mathematics, I would suggest you to not do it. Here are three reasons why.

1) You will get a bad grade.
2) You will not learn anything.
3) You will never know how fun Real Analysis can be.

[Ludwig]

I would also recommend avoiding the 5 week course, unless you know you will be dedicated to it 100% - meaning you're willing to put in hours daily of study. I'm assuming you're going to cover what's normally covered in 18 weeks in my RA course, and I know that between weekly quizzes, homework assignments, and exam cram weeks, I put in on average at least 8 hours per week of independent study time (+3 hours of course time). So 200 hours over 5 weeks means an average of 40 hr/week.

Also, the main advantage of doing the 5 week analysis is that you get to take analysis II, but I'll bet you after finishing analysis at that intensity you're going to want to enjoy your summer for a change.

[Hello, world]

Thanks so much everyone for your comments! I will definitely be staying away from the 5 week variant.