What's the difference between Adv. Calc and Real Analysis?

[poorboy44]

I'm trying to choose between Advanced Calculus and Real Analysis in the Fall.

Advanced Calculus (undergrad) is taught at the level of Fitzpatrick.
Real Analysis (graduate level) is taught at the level of Folland or Royden.

Two questions:
1) Will Real Analysis be too difficult without first taking Adv. Calculus? My math preparation is limited to Calc 1-3, DE, LA and Math. Stats.
2) Which one is more useful for Econ?
3) Can someone clarify the difference between Adv Calc and Real Analysis? Apparently Adv. Calc is also known as "Elementary Real Analysis"

I'm hoping to apply to an Econ PhD program eventually.

[treblekicker]

Originally Posted by poorboy44

I'm trying to choose between Advanced Calculus and Real Analysis in the Fall.

Advanced Calculus (undergrad) is taught at the level of Fitzpatrick.
Real Analysis (graduate level) is taught at the level of Folland or Royden.

Two questions:
1) Will Real Analysis be too difficult without first taking Adv. Calculus? My math preparation is limited to Calc 1-3, DE, LA and Math. Stats.
2) Which one is more useful for Econ?
3) Can someone clarify the difference between Adv Calc and Real Analysis? Apparently Adv. Calc is also known as "Elementary Real Analysis"

I'm hoping to apply to an Econ PhD program eventually.

I can't say much about the difference between Adv Calc and Real Analysis, but if you would be using Royden for your first RA class, it may be pretty challenging. Generally, Royden is used for a first course on measure theory and while it does touch on many of the topic from a first course on analysis, it glosses over a lot of them and omits a lot of stuff.

In many cases Adv. Calc is synonymous with undergrad RA. Based off of a amazon search for Fitzpatrick and Advanced Calc, if you are using: Amazon.com: Advanced Calculus: A Course in Mathematical Analysis: Patrick M. Fitzpatrick: Books
then that appears to be a pretty standard UG RA class; I can't see the table of contents so I don't know for sure, but I would say you are probably much better off taking the Adv Calc course before the Grad Analysis course.

[cooper]

I used Fitzpatrick for Adv Calc and based on my experience it is probably better to do this before the Grad analysis course. You will still have to prove things rigorously which is important.

Given your background, you may find it extremely difficult in the grad course since they would assume you are familiar with the 'epsilon-delta' arguments from Fitzpatrick. Also, in Adv Calc, you will learn basic topological concepts on the real line, which you should understand before generalizing to more abstract setting as you would in the grad course. Plus, there will more likely be a higher standard in the grad course since most students have studied analysis at the undergrad level already, while Adv Calc is usually the first course in Analysis,

More importantly, the Adv Calc course will provide the rigor that you need from an analysis course. You will have to think logically and you will get good practice constructing proofs so I think it is sufficient for first year Econ. In first year econ, you may have to think about function spaces or measure theory concepts, but not at a very deep level, and if you do well with Fitzpatrick, you will have the tools to handle these more advanced concepts on your own.

After the first year, you may need to think about more advanced math courses depending on your interests, but you can worry about that when you get there. Also, from a point of view of risk, it is probably better to get in A in Adv Calc than a B or even a C in Analysis.

[jeeves0923]

In my undergrad institution Advanced Calc was like elementary elementary real analysis. it was the prereq for RA. We used Abbott. Elementary Real analysis was with Rudin's Principles of Mathematical Analysis. And Graduate Real ANalysis I was with Royden. I would have been toast in Royden if I hadn't had either Adv Calc or Elem Real Anal. I strongly recommend you take Adv Calc

[econyun]

Originally Posted by jeeves0923

In my undergrad institution Advanced Calc was like elementary elementary real analysis. it was the prereq for RA. We used Abbott. Elementary Real analysis was with Rudin's Principles of Mathematical Analysis. And Graduate Real ANalysis I was with Royden. I would have been toast in Royden if I hadn't had either Adv Calc or Elem Real Anal. I strongly recommend you take Adv Calc

so usually people here say RA...are they referring Elementary Real analysis with Rudin's Principles of Mathematical Analysis or Graduate Real ANalysis with Royden?

[jeeves0923]

I'd say most people are referring to Rudin level real analysis. When they are talking about measure theory, they are talking about Royden level mathematics.

[ICECOLDECON]

At Florida State, analysis was considered the easier class (that math majors who had trepidations about taking adv calc would take). At South Florida, you dont have the option to take adv calc and analysis is taught with Rudin. At University of Florida, analysis is considered the tougher class.

My point (if I have one) is that there is considerable variation and flexibility in how these courses are taught (even within a state university system) and you should have opportunity in your application to explain the level and material your course was taught at (even if this amounts to nothing more than listing the text).

[argmax]

If you have the time try first for the advanced calc and then analysis as the first is generally a prerequisite for the latter. It would also help to form a base if you have not taken yet a proof based course in maths.
For your second question i would say both classes are useful for econ but in different levels. So if you want to apply for econ phd eventually both classes would be useful for admissions and for classes.

[Canuckonomist]

Keep in mind the topics offered under the course, too. @ Queen's, Advanced Calculus = Vector Calculus = partial/directional derivatives, dbl/trp/line/surface integrals, green, gauss and stokes.

I think this is mostly known as Calc III, but some schools, again, use different titles.


Canuck.

[vanRijn]

I remember that the Wired magazine had a Expired/Tired/Wired joke, where they used to write three things, one definitely passè, one representing the current standard, and finally the next thing in the field (usually referred to some technology).

If I had to apply the joke, tongue in cheek, to math requirements for econ PhD, I'd write multivariable/vector calculus = expired, basic Analysis/Advanced calculus (epsilon delta arguments) = tired, Advanced Analysis(measure theory, functional) = wired.

Or is it?