Real Analysis

[ComicBookDude]

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So it turns out that the only math class I could take this fall semester as a sophomore is Real Analysis (I'm only 6 credits short of a math major, so my options aren't to plentiful). I've heard rumors about this class being near impossible. Anyone here take it? Any advice?

 

[DoctaJay]

Man if its that hard, you dont' want that bringing down your GPA too much, or the stress. Wait until spring semester to take a class. As long as you are planning on taking it, its alright.

 

[dwigt]

I'm not sure if it's like this everywhere, but at my school it is the hardest math class an undergrad can take. Unless of course you take Real Analysis 2.

 

[novawildcat]

to be blunt-Real analysis is THE class that separates the real math majors from the wannabies. take all the calculus you learned and throw it out the window right now, because you have to start from scratch . the central idea real analysis is the idea of a limit. sure you have done limit problems in calc before, but you never actually proved what a limit was. you will not be doing problems you will be doing proofs the entire time. google what an epsilon delta proof is because you will be doing them the entire semester. your prof might even give you only 1 or 2 homework questions to prove for entire week. people either seem to completely fail this class/withdraw or get an A. there really is no middle ground, either you get it or you don't. The only way i can explain how i got an A in that class was that it just made sense. I tried to help other people in class who were struggling, but they would never understand what I was trying to explain to them. I'm not joking when i say that analysis is probably the hardest class that any university can offer. even stellar engineering majors completely bombed in this class. don't be intimidated though. i would highly recommend you read what real analysis is about and try to read through some basic limit proofs before you sign up. if you can understand them then you should be golden. if you are trying to get the math degree than analysis is a must. no one can get a BS in math without taking at least 1 class on analysis.

 

[Ari Gold]

another option is to take it pass/fail if you have done that too much in the past. it wouldn't hurt bc its not a pre-req

 

[MeBeans]

Not too bad. By real, they mean on the real numberline. This is actually a good thing, since it means you don't have to worry about complex numbers and the twisted logic they use.

 

[dwigt]

Not too bad. By real, they mean on the real numberline. This is actually a good thing, since it means you don't have to worry about complex numbers and the twisted logic they use.

No, by real they mean "real f*@#ing hard." (joke)
Make sure you have all the pre-reqs to take it before you worry about whether or not you will. At my school you have to have taken discrete math, Calc 3, and linear algebra.

 

[TarHeelBorn]

No, but I did take Fake Analysis. We looked at items that are commonly forged and determined whether or not each particular specimen was fake.

 

[ComicBookDude]

to be blunt-Real analysis is THE class that separates the real math majors from the wannabies. take all the calculus you learned and throw it out the window right now, because you have to start from scratch . the central idea real analysis is the idea of a limit. sure you have done limit problems in calc before, but you never actually proved what a limit was. you will not be doing problems you will be doing proofs the entire time. google what an epsilon delta proof is because you will be doing them the entire semester. your prof might even give you only 1 or 2 homework questions to prove for entire week. people either seem to completely fail this class/withdraw or get an A. there really is no middle ground, either you get it or you don't. The only way i can explain how i got an A in that class was that it just made sense. I tried to help other people in class who were struggling, but they would never understand what I was trying to explain to them. I'm not joking when i say that analysis is probably the hardest class that any university can offer. even stellar engineering majors completely bombed in this class. don't be intimidated though. i would highly recommend you read what real analysis is about and try to read through some basic limit proofs before you sign up. if you can understand them then you should be golden. if you are trying to get the math degree than analysis is a must. no one can get a BS in math without taking at least 1 class on analysis.

I took linear algebra (proof based) and did very well (Once I got the hang of proofs, they were actually quite fun). Would this be any indicator of at least having a chance at succeeding in the class? I did awesome in linear algebra, but am worried I'm going to completely bomb Real Analysis. Also, has anyone here taken advanced linear algebra?

 

[seadizzle]

I agree - analysis separates the men from the boys. I absolutely loved it [I'm a man 🙂]

If you are good at proofs, analysis should be quite tenable for you. Of course, you need to spend time understanding the methods of proof and memorize the definitions and theorems. Honestly though, you either get it or you don't. You can have everything memorized, but if you don't have the horsepower to put together an airtight proof on the test, you aren't going to do well. Another thing to remember is that you will be competing with mostly math majors in the class, physics/econ/compsci people take linear algebra, but you are entering relatively pure math, and although it's useful in phd level econ, it's definitely not as useful as linear algebra for applied pursuits.

I found analysis to be more intuitive than abstract algebra, if you've had any experience with that. I also found it to be very rewarding (I'm a math major and love this stuff), it gave me a better understanding of the limit and the integral. It develops mathematical maturity - familiarity with the language of math (definition,theorems,proof) which is invaluable if you want to learn anything math related outside of class (game theory, cardiovascular fluid flows, MRI math!).

 

[Aurora013]

Look back at your calculus textbook and read the few proofs they give there. Think you could do stuff similar to that but a hell of a lot harder? I was pretty good at proofs (or at least had been in prior classes with the more simplified stuff I had done), but was completely lost in Analysis. My advice though is if you think you can do it, by all means give it a try, but find a friend to take it with you so you can help each other out. Good luck!

 

[Oculus Sinistra]

I'm not sure if it's like this everywhere, but at my school it is the hardest math class an undergrad can take. Unless of course you take Real Analysis 2.

Or the third one where they fight the equation in outer space.

 

[novawildcat]

I took linear algebra (proof based) and did very well (Once I got the hang of proofs, they were actually quite fun). Would this be any indicator of at least having a chance at succeeding in the class? I did awesome in linear algebra, but am worried I'm going to completely bomb Real Analysis. Also, has anyone here taken advanced linear algebra?

The proofs in real analysis are a lot different than what you proved in LA. you did well in LA which is good since it gets you in the mindset to start doing proofs. I took a graduate class on linear algebra (which you could consider advance linear algebra) and it is a lot harder than the undergraduate version. Real mathematicians hardly ever use matrices and you will probably not use any matrices in advanced linear algebra. Instead you will use the more abstract version-the linear transformation. here are some ideas that you will encounter in real analysis, see if you can follow what is going on:

-read the idea of what a cauchy definition is of a continuous function
http://en.wikipedia.org/wiki/Continuous_function

-here is what a cauchy sequence is. real numbers can be defined as a cauchy sequence, so you will be doing a ton of these.
http://en.wikipedia.org/wiki/Cauchy_sequence

-here is an epsilon-delta proof. you will be doing a TON of these proofs. this is probably the only thing you must read in this thread if you are going to take analysis
http://mathworld.wolfram.com/Epsilon-DeltaProof.html

 

[akaz]

I have taken it. It is very abstract and proof oriented. I loved it and hated applied math. However others are the reverse. It is more a question of what you are good at.

The proofs in real analysis are a lot different than what you proved in LA. you did well in LA which is good since it gets you in the mindset to start doing proofs. I took a graduate class on linear algebra (which you could consider advance linear algebra) and it is a lot harder than the undergraduate version. Real mathematicians hardly ever use matrices and you will probably not use any matrices in advanced linear algebra. Instead you will use the more abstract version-the linear transformation. here are some ideas that you will encounter in real analysis, see if you can follow what is going on:

-read the idea of what a cauchy definition is of a continuous function
http://en.wikipedia.org/wiki/Continuous_function

-here is what a cauchy sequence is. real numbers can be defined as a cauchy sequence, so you will be doing a ton of these.
http://en.wikipedia.org/wiki/Cauchy_sequence

-here is an epsilon-delta proof. you will be doing a TON of these proofs. this is probably the only thing you must read in this thread if you are going to take analysis
http://mathworld.wolfram.com/Epsilon-DeltaProof.html

 

[ComicBookDude]

I have taken it. It is very abstract and proof oriented. I loved it and hated applied math. However others are the reverse. It is more a question of what you are good at.

However, if I am decent at abstract math (only took linear algebra thus far), is there still a chance at a B, or even an A? I know I'm not completely dumb, but can on still put in time and see results?

 

[_ian]

stuff

This is pretty much the truth. I wouldn't say it's the hardest course a university can offer by any means, but I would say you have to have a certain way of thinking to be able to stay afloat in it. Some people simply will not be able to handle real analysis, regardless of the amount of time and effort they put in. I took it freshman year and did well, but I didn't find it much fun.

I took linear algebra (proof based) and did very well (Once I got the hang of proofs, they were actually quite fun). Would this be any indicator of at least having a chance at succeeding in the class? I did awesome in linear algebra, but am worried I'm going to completely bomb Real Analysis. Also, has anyone here taken advanced linear algebra?

Depends on your linear algebra course, really. Mine was just the next step after differential equations in the standard calculus sequence, and it was a joke. That said, having any experience in proofs before going into the class is only a good thing.

[edit: boy do I sound like an dingus in this post; sorry]

 

[PerpetualBurn]

Can you list the maths you've taken so far? I think any response would be more helpful based on that.

 

[ComicBookDude]

Can you list the maths you've taken so far? I think any response would be more helpful based on that.

Calc I
Calc II
Calc III (Multivar)
Diff EQ
Intro to Statistics
Linear Algebra

Got an A in all the classes.

edit *I know that Abstract Algebra is usually taken after linear algebra, but there is a scheduling conflict with it and orgo, so I have to take Real Analysis this semester (I don't want to deal with any tough math classes as a senior), and Real Analysis I is only offered Fall sem.

 

[firebody]

is real analysis and applied analysis the same thing??

 

[grapeflavorsoda]

So it turns out that the only math class I could take this fall semester as a sophomore is Real Analysis (I'm only 6 credits short of a math major, so my options aren't to plentiful). I've heard rumors about this class being near impossible. Anyone here take it? Any advice?

real analysis is really fun class. i switched from biochem to math because of the analysis course.

if you have a good amount of experience with def/proof format, then you should be more than fine.

just buy rudin's book right now from amazon or whatever and indulge yourself.

you might hate it in the beginning but you will eventually fall in love the "baby" rudin(there are plenty of reasons why almost all the colleges use rudin's for real analysis).

 

[DoctorPardi]

I am glad I am not a math major. That is all I have to add to this thread.

 

[novawildcat]

is real analysis and applied analysis the same thing??

probably not, but it may just depend on your school. real analysis is theoretical/pure math. your applied analysis class might skim over the details that you would normally spend a lot of time on in real analysis in favor of doing applied problems. i know electrical engineers and physicists use some pretty hardcore functional analysis for some types of applied problems.

 

[grapeflavorsoda]

Calc I
Calc II
Calc III (Multivar)
Diff EQ
Intro to Statistics
Linear Algebra

Got an A in all the classes.

edit *I know that Abstract Algebra is usually taken after linear algebra, but there is a scheduling conflict with it and orgo, so I have to take Real Analysis this semester (I don't want to deal with any tough math classes as a senior), and Real Analysis I is only offered Fall sem.

hmm should have read this post before posting my previous post.

how can you be only 6 credits away from being math major?

all the courses you took are all low level. if you did use book like axler's intro. linear, you could be fine. but how comfortable are you with def/proof fomats?

when you took calc 3, were you exposed to k-forms, modern stokes, etc?

 

[novawildcat]

if you did use book like axler's intro. linear, you could be fine.

that was one excellent text book.

 

[ComicBookDude]

hmm should have read this post before posting my previous post.

how can you be only 6 credits away from being math major?

all the courses you took are all low level. if you did use book like axler's intro. linear, you could be fine. but how comfortable are you with def/proof fomats?

when you took calc 3, were you exposed to k-forms, modern stokes, etc?

I meant 6 classes (Real Anal 1+2, Abstract Algebra 1+2, 2 upper level electives and maybe an intro to comp programming)

 

[grapeflavorsoda]

I meant 6 classes (Real Anal 1+2, Abstract Algebra 1+2, 2 upper level electives and maybe an intro to comp programming)

no mathematical history class? 😱

j/k.

anyway, if you took linear class using decent text such as hoffman and kuntz or axler and did well in that class, you probably will not have alot of problems with the intro. analysis. but if you took linear with sparse proofs or brute(calculation heavy) force proofs, you might suffer due to lack of familiarity with the higher math text format/proof.

typically undergrad. offers two linear courses; a service course and the actual math major-intended linear algebra. it's like intro physics course where there are algebra based and calc. based one.

if you took the "service course" you might not have experienced enough proofs and will need to take other proof heavy courses such as abstract, number theory, topology, etc, before venturing into analysis course.

in my personal opinion, one of the best way to test whether you might be ready for a course or not, is buying the text and read it and see whether you can follow the material clearly. if you could do that for at least 4 or 5 chapters(approx. 1/4 to 1/3 of the whole text), you are good to go.

 

[_ian]

if you took the "service course" you might not have experienced enough proofs and will need to take other proof heavy courses such as abstract, number theory, topology, etc, before venturing into analysis course.

I'd guess this depends quite a bit on the school and the course description in particular, as the course I took was suitable for someone with limited experience in proofs. The advisory prerequisite is linear algebra, but it's entirely academic, as it was far from necessary and I hadn't taken it prior to this course.

http://www.lsa.umich.edu/cg/cg_detail.aspx?content=1610MATH451002&termArray=f_06_1610

 

[PerpetualBurn]

Calc I
Calc II
Calc III (Multivar)
Diff EQ
Intro to Statistics
Linear Algebra

Got an A in all the classes.

edit *I know that Abstract Algebra is usually taken after linear algebra, but there is a scheduling conflict with it and orgo, so I have to take Real Analysis this semester (I don't want to deal with any tough math classes as a senior), and Real Analysis I is only offered Fall sem.

Based on your performance on these, I think you'll do fine. It will be your hardest math thus far, so if you like, review Calc. I and II a bit for Real Anal I. I don't even think that's necessary, provided you go into the class expecting to work more than you have for your other classes. I'm betting you'll get an A.

 

[dwigt]

Also remember that it's a hard class for everyone, not just you, and if you have a decent prof they will be more lenient as far as grades go. Last fall my friend took Analysis and the distribution was something like 4 A's, 4 B's, 3C's. No D's or F's.