Should I drop this course and take it next year?

[flyingpig]

PLease ask me questions if I am unclear.

So here goes. It was a few months ago I asked this, I am taking an analysis course that basically is killing me.

Months and months ago, just before the spring term ended (near the end of April), I asked the professor who was teaching the course (analysis course) and the prerequisite (a proof course) if it was alright to take them together (the same person). He gave me a laconic response, "yes".

To be more concise, here is what the analysis course is. It's entitled "real analysis" and we use this book (the file was too big, I couldn't attach it).

The syllabus says we will do parts of ch2, ch4, ch5, ch7, and ch8.

Now I will talk about the proof course which was a prerequiste. We use http://www.amazon.com/dp/0321390539/?tag=pfamazon01-20.

We do ch1 - ch12 (excluding ch7 and ch11)

We had our first class yesterday (both proof and analysis) and my head already exploded. I spent last night drilling the proof course like reading the entire chapter (which is really big) and I still have trouble keeping up with the one page note my professor wrote in the analysis course. In other words, the proof course is not keeping up with the analysis course.

I have not talked with the professor yet because I had to catch the bus last night and it's Saturday which means I can't talk with him in person until Monday which he does not have office hours yet I still plan to see him.

Now here is the problem

I don't know how it's going to turn out after we talk.

1. If he convinces me to stay, it's going to be hell for me because the analysis course is going at a fast pace and all (and I mean ALL except me) my classmates nod when he writes something convoluted (to me at least) and I sit there wondering what heck is he on about.

2. If he somehow says "he made a mistake" and I should drop out (I won't get a W I believe), would it still be bad because I would still be in his proof course?

EDIT:

If anyone is wondering, I am going to replace that course with something I HAVE PREREQUSITE for.

 

[flyingpig]

Actually is it even a good idea to see him in person...? Like he could just say "drop the course" and I leave his room awkwardly.

 

[micromass]

Talk to him in person and see what he advises you. You're hitting a wall now... hard. But this is normal. Dropping out is one option. Studying your proofs hard is another option. Talk to him to see which is better.

My advice: judging from the threads you make in the homework section, you are not ready for real analysis. So I would drop the course. This is just my impression though.

 

[flyingpig]

Talk to him in person and see what he advises you. You're hitting a wall now... hard. But this is normal. Dropping out is one option. Studying your proofs hard is another option. Talk to him to see which is better.

My advice: judging from the threads you make in the homework section, you are not ready for real analysis. So I would drop the course. This is just my impression though.

Remember four months ago (or was it five?) that I talked with you and sent you the book? DId i? I could send it to you...

This is what happened...

 

[flyingpig]

What do you want from us? It sounds like you're asking us to a) predict what he is going to say, and b) tell us what he really means if he doesn't say what he means.

I am asking for b) mostly and if my decision is right. It's a little painful for me though...I actually went ahead and bought the book and I have to make the decision quickly before the refund period ends (including late course fees etc...)

 

[micromass]

Remember four months ago (or was it five?) that I talked with you and sent you the book? DId i? I could send it to you...

This is what happened...

You never sent me a book...

 

[flyingpig]

You never sent me a book...

May I send one to you now? PMing allows larger uploads right...?

 

[micromass]

May I send one to you now? PMing allows larger uploads right...?

Uuh, I'm not sure if the mentors are ok with that... What's the name of the book maybe I have it somewhere?

 

[flyingpig]

Uuh, I'm not sure if the mentors are ok with that... What's the name of the book maybe I have it somewhere?

http://www.springer.com/mathematics/analysis/book/978-0-387-98097-3

It was hyperlinked on "this book"

 

[flyingpig]

And we use this book for the proof course

http://www.amazon.com/dp/0321390539/?tag=pfamazon01-20

 

[micromass]

Hmmm, I don't seem to have these books

 

[flyingpig]

Okay I managed to break my book into sections.

I hope it shows.

It's basically the first chapter we did.

Do you want me to write out the notes he wrote?

I couldn't get the proof book, sorry

Edit by Borek: attachment deleted, this was a copyrighted material.

 

[micromass]

Okay I managed to break my book into sections.

I hope it shows.

It's basically the first chapter we did.

Do you want me to write out the notes he wrote?

I couldn't get the proof book, sorry

OK good. But what do you want us to do with it??

 

[flyingpig]

OK good. But what do you want us to do with it??

Basically we just started 2.1 and as I looked at the sections following, I do not have a clue of what it is.

The proof in https://www.physicsforums.com/showthread.php?t=528879 I had here was part of his notes and I had to ask you about it lol

I should also mention that while I could wait out and see (and hope) that the pace between the proof and analysis course balance out, it would also cut off any hopes of getting into any other course once the deadline passes.

 

[micromass]

Basically we just started 2.1 and as I looked at the sections following, I do not have a clue of what it is.

The proof in https://www.physicsforums.com/showthread.php?t=528879 I had here was part of his notes and I had to ask you about it lol

I should also mention that while I could wait out and see (and hope) that the pace between the proof and analysis course balance out, it would also cut off any hopes of getting into any other course once the deadline passes.

The thing is, if you don't understand that proof, then you're not read for real analysis. Why?? Because you will meet proofs in there which are 1000x harder.

If you would ask me, then I'd say to drop the course and take another one. You'll find the course more easy once you've had a basic proof course.

But do talk to your professor first and see what he says.

 

[flyingpig]

The thing is, if you don't understand that proof, then you're not read for real analysis. Why?? Because you will meet proofs in there which are 1000x harder.

If you would ask me, then I'd say to drop the course and take another one. You'll find the course more easy once you've had a basic proof course.

But do talk to your professor first and see what he says.

Was my question (in that thread) about n_1 or n_2 not being 0 way too trivial because I didn't understand the def of Q?

In any case, I will have to talk to him...

 

[micromass]

Was my question (in that thread) about n_1 or n_2 not being 0 way too trivial because I didn't understand the def of Q?

In any case, I will have to talk to him...

I'm not saying that it was trivial. It's ok not to understand the definition. But once you start real analysis, then you should understand things like the definition of Q and things like $\{a,b\}\in \mathcal{P}(\{a,b\})$.

Everybody struggles with those things. But you should struggle with those things in a proof class. Not in a real analysis class. All these concepts should be clear by the time that you start a real analysis class.

Right now, you indicate that those elementary concepts are not clear to you. This indicates that you're not yet ready for real analysis. The proof course will help, though...

 

[flyingpig]

I'm not saying that it was trivial. It's ok not to understand the definition. But once you start real analysis, then you should understand things like the definition of Q and things like $\{a,b\}\in \mathcal{P}(\{a,b\})$.

Everybody struggles with those things. But you should struggle with those things in a proof class. Not in a real analysis class. All these concepts should be clear by the time that you start a real analysis class.

Right now, you indicate that those elementary concepts are not clear to you. This indicates that you're not yet ready for real analysis. The proof course will help, though...

I don't think it is the real real analysis class. We talked bout it a few months ago. Here is the name of topics we are going to do

ch2.

The set N of natural numbers, the set Q of rational numbers
The set R of real numbers
The completeness axiom
Limits
Limits theorems of sequences
Monotone sequences
Subsequences (the Bolzano-Weierstrass theorem)
Cauchy sequences
Limsup and liminf of a sequence

ch4.

n-dim space
Convergences and completeness
Closed sets and open sets
Compactness sets and the Heine-Borel theorem

There are more, but a bit lazy to type them all out

 

[micromass]

What do you want to hear from me?? That you'll do good in the class? I've already told you my opinion.

 

[micromass]

If you do continue the course, be sure to buy "Understanding analysis" by Abbott. You'll find that book a huge help!

 

[ahsanxr]

PLease ask me questions if I am unclear.

So here goes. It was a few months ago I asked this, I am taking an analysis course that basically is killing me.

Months and months ago, just before the spring term ended (near the end of April), I asked the professor who was teaching the course (analysis course) and the prerequisite (a proof course) if it was alright to take them together (the same person). He gave me a laconic response, "yes".

To be more concise, here is what the analysis course is. It's entitled "real analysis" and we use this book (the file was too big, I couldn't attach it).

The syllabus says we will do parts of ch2, ch4, ch5, ch7, and ch8.

Now I will talk about the proof course which was a prerequiste. We use http://www.amazon.com/dp/0321390539/?tag=pfamazon01-20.

We do ch1 - ch12 (excluding ch7 and ch11)

We had our first class yesterday (both proof and analysis) and my head already exploded. I spent last night drilling the proof course like reading the entire chapter (which is really big) and I still have trouble keeping up with the one page note my professor wrote in the analysis course. In other words, the proof course is not keeping up with the analysis course.

I have not talked with the professor yet because I had to catch the bus last night and it's Saturday which means I can't talk with him in person until Monday which he does not have office hours yet I still plan to see him.

Now here is the problem

I don't know how it's going to turn out after we talk.

1. If he convinces me to stay, it's going to be hell for me because the analysis course is going at a fast pace and all (and I mean ALL except me) my classmates nod when he writes something convoluted (to me at least) and I sit there wondering what heck is he on about.

2. If he somehow says "he made a mistake" and I should drop out (I won't get a W I believe), would it still be bad because I would still be in his proof course?

EDIT:

If anyone is wondering, I am going to replace that course with something I HAVE PREREQUSITE for.

I haven't taken Analysis yet, but I was about to this semester, so maybe I can share my experience with you. I didn't have a proofs class either, and was considering taking an Analysis course using Rudin this semester. After some thinking I realized that I'm not prepared for this class, and even if I work as hard as I can, I may not get a good understanding of it, because I would also be learning proofs side by side, supplementing it with other easier texts, all while trying to keep up with the class, and if I put that much time into one class, my other grades would suffer. So I'm taking a proof based Linear Algebra course and a Differential Geometry course instead. Proof based Linear Algebra, I'm finding very manageable, and feel like it may be a good class to get comfortable with proofs. The semester after this I'll probably be taking Abstract Algebra, and then during the summer, I'll read a book like Understanding Analysis by Abott as per micromass' recommendation. Then take Analysis after that. If you do something similar to this, I feel you'll be MUCH better prepared. So drop the class while you can, without getting a W, and replace it with something you think you can manage. Would you agree micromass?

 

[micromass]

I haven't taken Analysis yet, but I was about to this semester, so maybe I can share my experience with you. I didn't have a proofs class either, and was considering taking an Analysis course using Rudin this semester. After some thinking I realized that I'm not prepared for this class, and even if I work as hard as I can, I may not get a good understanding of it, because I would also be learning proofs side by side, supplementing it with other easier texts, all while trying to keep up with the class, and if I put that much time into one class, my other grades would suffer. So I'm taking a proof based Linear Algebra course and a Differential Geometry course instead. Proof based Linear Algebra, I'm finding very manageable, and feel like it may be a good class to get comfortable with proofs. The semester after this I'll probably be taking Abstract Algebra, and then during the summer, I'll read a book like Understanding Analysis by Abott as per micromass' recommendation. Then take Analysis after that. If you do something similar to this, I feel you'll be MUCH better prepared. So drop the class while you can, without getting a W, and replace it with something you think you can manage. Would you agree micromass?

That actually sounds like a well thought-through plan! I'm sure you'll find that much better than taking Rudin right now. You'll enjoy it much more!

 

[ahsanxr]

That actually sounds like a well thought-through plan! I'm sure you'll find that much better than taking Rudin right now. You'll enjoy it much more!

Yes, I figured. Your advice certainly helped a lot. By the way do you think one can be fine without having a formal intro to proofs couse? For the Linear Algebra course, I feel like not taking an intro to proofs class hasn't affected me much, at least for the first two homeworks. It's just the process of thinking how I can prove something which takes me time, not the actual structure/format/techique of the proof, which most intro proofs focus on. I haven't had the need to consult Velleman. Would you say that it will continue to be like that?

 

[micromass]

Yes, I figured. Your advice certainly helped a lot. By the way do you think one can be fine without having a formal intro to proofs couse? For the Linear Algebra course, I feel like not taking an intro to proofs class hasn't affected me much, at least for the first two homeworks. It's just the process of thinking how I can prove something which takes me time, not the actual structure/format/techique of the proof, which most intro proofs focus on. I haven't had the need to consult Velleman. Would you say that it will continue to be like that?

Well, I don't know you personally of course, so whatever I say is based on what information you give me. But I'd say, if you're comfortable with induction, contradiction, contraposition, then you're good. Also (very important!) you need to be comfortable with sets. Sets play a major role in mathematics and lots of people have difficulty with them.
For example, if I would ask you if

$$f(A\cup B)=f(A)\cup f(B)$$

holds, then you should have no problem proving this. Linear algebra isn't set theory heavy, but later courses are.

So if you're not comfortable with sets, do self-study it! Although you will certainly be introduced with sets in abstract algebra and Abbott. But you might find Rudin hard in the beginning because of the heavy usage of set language...

 

[flyingpig]

I took Linear Algebra, well only the first semester

 

[ahsanxr]

Well, I don't know you personally of course, so whatever I say is based on what information you give me. But I'd say, if you're comfortable with induction, contradiction, contraposition, then you're good. Also (very important!) you need to be comfortable with sets. Sets play a major role in mathematics and lots of people have difficulty with them.
For example, if I would ask you if

$$f(A\cup B)=f(A)\cup f(B)$$

holds, then you should have no problem proving this. Linear algebra isn't set theory heavy, but later courses are.

So if you're not comfortable with sets, do self-study it! Although you will certainly be introduced with sets in abstract algebra and Abbott. But you might find Rudin hard in the beginning because of the heavy usage of set language...

I see, the meat of the course probably hasn't come yet. Anyway, as always your advice has been a great help and I'll be sure to study up on sets!

I took Linear Algebra, well only the first semester

Do not mistake the two! The fist course in Linear Algebra, is probably one of the easiest math classes I had, just learning algorithms and doing computations, with maybe one proof every other week, while this one, I don't think I've done a single silly computation with a matrix yet. It's all about proofs and theory.

 

[deluks917]

If you cover chapters 2,4,5,7,8 the course seems very reasonable. I think you should try to get through the difficulty. You might need a lot of practice to grasp these concepts. Two ideas I found tremendously hard to understand were "Induction proofs" and "Compactness." I just could not get a feel for what they meant. I spent two days trying to understand the proof of the binomial theorem and It just would not click. It wasn't until I did at least 20 exercises (all proofs some of which took me 1-2 hours each) could I understand. I now have intuition about these topics but it was very hard for me to get.

You need to just keep doing exercises, even if it feels like going through the motions at first. Eventually you will get it.

 

[Skrew]

I used that book as well, it's a little terse - doubly so for someone who hasnt done proofs as often steps are left out. Still I came to like it.

I don't feel it's a book for the inexperienced post calc student (even though it says no formal proofs course is needed). I would place this book between Abbot and Rudin on the difficulty scale.

In any event the proofs course will not teach you how E/delta arguments work but it will give you experience proveing things and general strategies. If you have trouble you might drop the class, do they offer the analysis course next term?

 

[Sankaku]

A good rule of thumb for ANY math course is, take the prerequisite courses BEFORE taking the course. Yes, you may be able to do it otherwise, but you will probably suffer. Why do you want to suffer?

Math is all about building on a solid foundation.

Profs will often be relaxed about letting you take the wrong course because math is usually self-correcting. If it is not working, people drop the course. Why prevent someone from trying? However, their answer "yes" that you can take the course does not mean that you should take the course.