Should I take Real Analysis?

[Parth Thakkar]

I was recommended by a T.A. to take real analysis (Course would cover: real analysis; real numbers, point set topology in Euclidean space, functions, continuity.) if I was going to pursue an MFE and especially if I was going to apply to an MFE program fresh out of undergrad.

For all the established Quants out there, is this a good idea?

Thanks

 

[Barny]

Yes. Not only for the material you will learn, but mainly for the fact that you'll learn how to think properly (rather than just learning and following methods) in maths.

 

[JDawg]

definitely take real analysis

 

[Parth Thakkar]

Awesome! Thanks So much guys! I just added it to next quarter's schedule =)

 

[DeltaVega]

Hi;
I am not a quant or anything right now (currently an engineer) but analysis was one of those courses that after you finish them you look back and say: "wow! i'm not going to think the same after this!!"
i want to give you a heads up by saying this course was notorious as being the toughest undergrad math course... nonetheless as the previous posters said, the course will change how you think, and will teach you how to be always rigorous in your analysis, and this is a very important quality to have!!

 

[olgenue]

Yes, trains you to go back to first principles and think rigorously and question assumptions previously taken for granted.

 

[Honey Badger]

Just do it.

 

[albo]

You should definitely take Analysis. It is a sophisticated math course, and you can learn a lot of things that you can later apply to Finance, if the course is taught correctly. I believe one of the finance-related topics that you learn in Real Analysis is Mandelbrot's Theory of Fractals. Even the concept of Brownian Motion that is used to model the markets today, is one of the cases of Random Fractals. However, this is just what I remember from my Analysis course. You might have exposure to more interesting stuff.

 

[ExSan]

Consider Terence Tao's books

 

[Zeuge]

I would be more reserved in recommending analysis. At many schools it is a notoriously difficult course, and if you are an engineering/statistics/physics major you'll probably be met with a level of abstraction you're not used to. Many/most of your classmates will be math majors who will be among the smartest students at your school. If you're not sure that you can stay ahead of the curve and keep up, it might not be the best decision.

 

[albo]

I would be more reserved in recommending analysis. At many schools it is a notoriously difficult course, and if you are an engineering/statistics/physics major you'll probably be met with a level of abstraction you're not used to. Many/most of your classmates will be math majors who will be among the smartest students at your school. If you're not sure that you can stay ahead of the curve and keep up, it might not be the best decision.

What is the point of getting a higher education, if we don't challenge ourselves through it?

 

[Zeuge]

What is the point of getting a higher education, if we don't challenge ourselves through it?

I am not recommending that he avoid analysis because of the challenge. After all, I went through the sequence as a lowly economics major (and survived). However, I have seen many people struggle through the class and have it affect their performance in other classes. I was only emphasizing the difficulty of the course.

 

[Barny]

I would be more reserved in recommending analysis. At many schools it is a notoriously difficult course, and if you are an engineering/statistics/physics major you'll probably be met with a level of abstraction you're not used to. Many/most of your classmates will be math majors who will be among the smartest students at your school. If you're not sure that you can stay ahead of the curve and keep up, it might not be the best decision.

The first reason is exactly why you should take it. The second is not a reason you shouldn't take it.

The whole point of learning is to learn stuff that is new and stretches you. What is the point of learning something you can do comfortably? It teaches you absolutely nothing.

 

[Zeuge]

The first reason is exactly why you should take it. The second is not a reason you shouldn't take it.

The whole point of learning is to learn stuff that is new and stretches you. What is the point of learning something you can do comfortably? It teaches you absolutely nothing.

I am not saying that he shouldn't try the introductory analysis course. What I am saying is that I've seen very bright students who are otherwise doing quite well in their majors (physics, chemistry, etc) have to withdraw out of analysis because they were failing. I want him to know what kind of time commitment the class is going to be. Then again, our math department likes to say that we have the toughest analysis sequence next to MIT, so his mileage may vary.

 

[bigbadwolf]

What I am saying is that I've seen very bright students who are otherwise doing quite well in their majors (physics, chemistry, etc) have to withdraw out of analysis because they were failing. I want him to know what kind of time commitment the class is going to be. Then again, our math department likes to say that we have the toughest analysis sequence next to MIT, so his mileage may vary.

Why do they trip up in analysis? Bad books? Not familiar with techniques of proof? Don't see the need for proving intuitively plausible results like intermediate value theorem and Rolle's theorem? Teaching is poor?

If a savvy student surreptitiously buys one or two back-up texts and gets a bit of guidance on what's important and what's not, undergrad analysis should be a piece of cake. For instance, one key idea is to understand different formulations of the completeness of the reals (Bolzano-Weierstrass property, convergence of Cauchy sequences, l.u.b. property, Dedekind cuts, and maybe I'm missing one or two others) and understand why completeness is so essential. Or becoming experienced with the delta-sigma style of proof. Maybe there are around ten to fifteen key notions, of which I've listed two. That's the skeleton of the subject. It's easy to not see the structure if using a bad text and/or being droned at by some nincompoop of an incompetent professor.

 

[Barny]

Agreed with bbw. You will struggle, that's the point. I spent 9 months studying analysis in my first year at uni, the penny didn't drop until a month before my exams and I came top of the year. Before that I hated, hated, hated it with a passion. The whole experience was stressful, but extremely worthwhile because I'm now a better mathematician because of it. As bbw says, there are a bunch of concepts you should learn, and once you've done that it's really easy - at first I thought it was just learning proofs and definitions ad nauseum, but then I realised that understanding a few proofs and concepts was enough to basically get you through the rest - they key is achieving that understanding in the first place which takes a lot of effort and struggle. But when you do get it, it's an amazing feeling and far more rewarding than just learning how to do 50 fourier transforms or whatever people do in maths degree these days.

As it is, I really don't buy the argument that you've seen "bright" students struggle with analysis - what you've seen is people who are good at memorising and regurgitating methods and information very well and getting good grades suddenly struggle when it comes to a subject that requires some actual thought. Modern day university mathematics education can be extremely process driven if you choose carefully - you can feasibly go through your whole time just learning methods and applying them. Analysis teaches you something better - it teaches you to think for yourself a little bit. And that's the effect you're seeing - separating people who have the potential to think (since being able to do introductory analysis isn't exactly Field's medal winning stuff) from those who can just learn and apply.

 

[Daniel Duffy]

After real analysis, then Functional Analysis that has many applications.

"Dedekind cuts" are/were used in 121 courses and they determine if you like pure maths (or not).

 

[bigbadwolf]

After real analysis, then Functional Analysis that has many applications.

After real analysis, complex analysis, which is aesthetically so much more satisfying, appeals to one's heart as well as to one's mind, and leaves one a richer and more complete human being. Though I concede that from the viewpoint of PDEs, functional analysis is of crucial importance.

 

[DMD]

Now I wish I took Real Analysis...

 

[Zeuge]

Why do they trip up in analysis? Bad books? Not familiar with techniques of proof? Don't see the need for proving intuitively plausible results like intermediate value theorem and Rolle's theorem? Teaching is poor?

If a savvy student surreptitiously buys one or two back-up texts and gets a bit of guidance on what's important and what's not, undergrad analysis should be a piece of cake. For instance, one key idea is to understand different formulations of the completeness of the reals (Bolzano-Weierstrass property, convergence of Cauchy sequences, l.u.b. property, Dedekind cuts, and maybe I'm missing one or two others) and understand why completeness is so essential. Or becoming experienced with the delta-sigma style of proof. Maybe there are around ten to fifteen key notions, of which I've listed two. That's the skeleton of the subject. It's easy to not see the structure if using a bad text and/or being droned at by some nincompoop of an incompetent professor.

Many of those concepts are covered in our honors calculus sequence which is a prerequisite to the real analysis sequence. In RA we go over things like metric and topological spaces, and the first class in the sequence ends in the p-adic completion of Q.