Am I ready to take Real Analysis 1?

[SMA_01]

I'm a math major, and recently started taking upper level math classes. So far, the only upper levels I've taken in math are Abstract Algebra and Applied Combinatorics. To be honest, I didn't really work as hard as I should have in Abstract, and feel like my proof writing skills are not all that. The thing is I haven't had that much experience with proof writing. I mean, I can understand them when I read, but am just a beginner in actually writing proofs out. I'm registered for Real Analysis 1 this semester, and am really willing to work hard to master the material. Due to my weak proof skills, should I go through with it? Or will it be too much?


Thanks.

 

[Dembadon]

I'm a math major, and recently started taking upper level math classes. So far, the only upper levels I've taken in math are Abstract Algebra and Applied Combinatorics. To be honest, I didn't really work as hard as I should have in Abstract, and feel like my proof writing skills are not all that. The thing is I haven't had that much experience with proof writing. I mean, I can understand them when I read, but am just a beginner in actually writing proofs out. I'm registered for Real Analysis 1 this semester, and am really willing to work hard to master the material. Due to my weak proof skills, should I go through with it? Or will it be too much?


Thanks.

Weak proof-writing is going to be a major problem for the rest of your degree, especially in an analysis course. Simply understanding a proof is not enough. You must be able to put a pencil to paper and prove things by yourself. Trust me, I learned the hard way last semester. However, I was able to turn things around early enough.

Can it be done? Sure, but it's going to take you an excruciatingly long time to work problems if you have to learn analysis and proof-writing concurrently. I'd advise that you wait; take another semester and work on proving theorems from your abstract algebra textbook, if you still have it.

 

[SMA_01]

Thank you, Dembadon. I have to take it this semester if I want to take Real Analysis 2 before I graduate. I'm pretty worried, I was hoping this class I can greatly improve my proof-writing skills. Is Abstract Algebra harder than Analysis? I've heard Analysis is more intuitive. I had trouble grasping the concepts in Abstract.

 

[SMA_01]

I wanted to know, which class helped you better your proof writing skills?

 

[Dembadon]

Thank you, Dembadon. I have to take it this semester if I want to take Real Analysis 2 before I graduate. I'm pretty worried, I was hoping this class I can greatly improve my proof-writing skills. Is Abstract Algebra harder than Analysis? I've heard Analysis is more intuitive. I had trouble grasping the concepts in Abstract.

I've heard it both ways: some say algebra is harder while others claim analysis is. At my university, functional analysis is regarded as the most difficult undergraduate mathematics course by most everyone I've spoken with; one of them being a national merit scholar who has been doing math competitions since he was 10 years old.

In my opinion, the most significant factor regarding course difficulty is the instructor.

I wanted to know, which class helped you better your proof writing skills?

I took an "intro to proofs" course last semester. It touched on number theory, set theory, arithmetic in Z, functions, relations, combinatorics, and a few other things. The instructor made the problems quite manageable so that we could focus on our proof technique.

This will not be the case in real analysis; you will be expected to already be comfortable with writing proofs. It can be done, but you will need to devote extra time and have a lot of patience with yourself. And be humble (ask for help!).

 

[SMA_01]

Thank you very much!

 

[Snicker]

Proofs are prose: Be concise and clear.

 

[Dembadon]

Proofs are prose: Be concise and clear.

Isn't clear \subset concise?

 

[SophusLies]

Dembadon has some great advice. I'll say that my first analysis class was difficult and that was the pinnacle class that forced me to think and reason in a clear way. Even though I felt comfortable from an intro proof type course, the jump was very big to analysis so be warned.

 

[Visceral]

Thank you, Dembadon. I have to take it this semester if I want to take Real Analysis 2 before I graduate. I'm pretty worried, I was hoping this class I can greatly improve my proof-writing skills. Is Abstract Algebra harder than Analysis? I've heard Analysis is more intuitive. I had trouble grasping the concepts in Abstract.

I would say that generally course difficulty is more dependent on the professor than anything. With that being said, its hard to tell which undergrad course in those topics would be more difficult at your university. The best you can do is ask your advisor or students that have already taken both classes to give you their opinions.

I haven't taken abstract algebra yet, but I did take real analysis 1 with students who are now in abstract algebra. Everyone has said unanimously that analysis is much harder, but the semester has just begun, too.

I am currently in Analysis 2. The topics are no less abstract(actually technically they should be more abstract, seeing as we are now in n dimensions), but the course is definitely easier because the professor is more laid back and doesn't require weekly hard problem sets AND the course isn't required for the degree.

With all of that being said, I took analysis 1 right after I took the standard introduction to proofs course. Analysis was(and is) just on another level completely. You just get thrown into hardcore difficult proofs right from the get go. So if you do take it, my advise is be prepared for some intense work. When I got a B in that class, I was relieved, because the final exam was 3 hours long and there were over 13 proofs which made 3 hours seem like a joke(and hence, made me think I nuked the exam and got a C or worse).

Good luck, go for it, but be ready.

Edit: I realize sophuslies just said what I did basically but more concise, my bad.

 

[Robert1986]

Well, applied combo is probably just barely even a math class. Its kind of like comparing calc to analysis or something. So, you've basiclly had one class in writing proofs so, it is understandable that you might suck at it - you're not supposed to be really good at it. Chances are your prof knows this and expects it. There's no way to get good other than to write proofs - so start crackin'!