Should I Take Real Analysis I as a Sophomore?

[selig5560]

Hi - I am a second semester Sophomore, and am wondering what I need to know to succeed in Real Analysis. My background is in linear algebra, differential equations, and calculus. However, I have not had any real exposure to rigorous proofs which I hear what you do in RA. The prerequisite for RA at my school is an intro to proofs class, proof based linear algebra (I took the computational one), or honors calculus (Apostol). Should I hold off RA until I get more exposure to proofs or if I studied hard succeed in the course? If I were to take RA, I would only take that math course. Even though its for juniors or seniors, I really would like the course, but don't want to fail or get a bad grade in it.

~~Selig

 

[homeomorphic]

Hard to say. As far as formal prerequisites, you should be okay, but it's just going to be harder. Many people already find it to be a hard class, so for most people, it would be a better idea to do some other stuff first. That's the safest option. If you want to take the risk and go for it, I suggest trying to expose yourself to some proof-based math on your own to see if it scares you away or not. You can try to read an analysis book and see how far you get.

 

[selig5560]

Hi - I have already looked through Rudin and some other books on analysis. My worry is that I don't seem to easily get how to prove the proofs in Real Analysis. Is that something to be worried about? In terms of proofs, I've done induction, contrapositive, and proof my contradiction (This was in my linear algebra course) Course description: http://www.math.wisc.edu/521-advanced-calculus

 

[halo31]

Before you tackle Rudin's book i'd suggest get a book that is a step lower or more so a bridge between Calculus and advance calculus. Rudin's book is a bit too advanced for you right now. I'd recommend Elementary analysis by Kenneth Ross, there is another one by Lay, Spivak's Calculus ( I'd recommend working through this book), Advance Calculus by Fitzpatrick, or Serge Lang's book Undergraduate Analysis. Of course there are many more books. Self-studying one of these books should prepare you well for Rudin's Book.

 

[jbunniii]

The prerequisite for RA at my school is an intro to proofs class, proof based linear algebra (I took the computational one), or honors calculus (Apostol).

An honors calculus course using Apostol as the text would be excellent preparation for real analysis using Rudin. I would highly recommend taking such a course before real analysis if you have time. Linear algebra will help you to become comfortable with proofs in general, but not the epsilon-delta style of proof that is ubiquitous in real analysis (and in honors calculus).

 

[micromass]

Hi - I am a second semester Sophomore, and am wondering what I need to know to succeed in Real Analysis. My background is in linear algebra, differential equations, and calculus. However, I have not had any real exposure to rigorous proofs which I hear what you do in RA. The prerequisite for RA at my school is an intro to proofs class, proof based linear algebra (I took the computational one), or honors calculus (Apostol). Should I hold off RA until I get more exposure to proofs or if I studied hard succeed in the course? If I were to take RA, I would only take that math course. Even though its for juniors or seniors, I really would like the course, but don't want to fail or get a bad grade in it.

~~Selig

You haven't yet taken a proof based course? That indicates to me that you are not ready for analysis. I don't know anything about you, so maybe you can get a good grade if you work hard, or maybe you won't.

I recommend working through a rigorous book such as Spivak. Maybe you can try to self-study it. If you are able to do Spivak, then you're ready for analysis.

 

[selig5560]

Quick update, I found out that I can take "Intro to proofs" and Real Analysis without overriding any prereqs (a way of taking analysis is to take it concurrently with intro to proofs.) Any thoughts?

 

[BloodyFrozen]

It's great if you can keep up with the classes, but I would think Real Analysis already assumes a good grasp/knowledge with proofs.

EDIT: Oh - it's baby Rudin. It's not that bad then. At Princeton, Baby Rudin is used as a honors math track. It's rigorous, but if you commit to it, you'll do fine.

 

[selig5560]

Hi - THanks for the advice! However, the books used at my university are either Pugh or Rudin...What is baby rudin?

 

[BloodyFrozen]

Baby Rudin - Principles of Mathematical Analysis
Big Rudin are the actual 2 analysis ones

 

[BloodyFrozen]

If you look at this webpage, you can see some of the Analysis problems. If they interest you, you might want to take it.

https://web.math.princeton.edu/~adeptrep/lowerdiv/215/MAT215

 

[selig5560]

Thank you for the help! So my options this semester are either Vector Analysis (NOT calc 3, but actual vector analysis) and PDEs or Analysis I and Intro to proofs. As a math major (applied) would track should i take this sem?

 

[BloodyFrozen]

What is the description for vector analysis. I would guess PDEs are useful for appplied, but I'm not qualified to say it's true nor what you should take. I'd suggest for someone else's opinion. Ask your professors; they know the most.