MHB What course should I take next after Real Analysis I?

[alyafey22]

This semester I have the first course in real analysis I . Basically , it discusses mainly construction of reals, sequences , limits , differentiation , continuity and integration. In the next semester I have many choices and I think I can only take one :

1. Complex variables
2. Modern algebra( abstract algebra)
3. Real analysis II (same as Real analysis I but with several variables)

If for me I want to take all of them :) but I think I'll have to choose one of them. So what course would suggest ?

 

[I like Serena]

Take all of them! ;)

 

[polygamma]

You probably know more about complex variables then I did after I took a class on complex variables 5+ years ago. Most of the stuff I know now is stuff I learned on my own.

 

[alyafey22]

You probably know more about complex variables then I did after I took a class on complex variables 5+ years ago. Most of the stuff I know now is stuff I learned on my own.

Indeed I agree with you but I have to have an evidence of the knowledge I have otherwise I wouldn't stand a chance if I apply for higher studies.

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Take all of them! ;)

I cannot because initially I am a computer scientist but I take mathematics as a minor so I guess the maximum I can have is two. I am thinking of abstract algebra and complex variables.

 

[I like Serena]

I cannot because initially I am a computer scientist but I take mathematics as a minor so I guess the maximum I can have is two. I am thinking of abstract algebra and complex variables.

I am a computer scientist myself. That didn't stop me from taking more courses than I was supposed to take.
Anyway, those courses should be easy for you.

 

[alyafey22]

I am a computer scientist myself. That didn't stop me from taking more courses than I was supposed to take.
Anyway, those courses should be easy for you.

Really ! what maths courses have you taken ?

 

[I like Serena]

When I started at university I went to a couple of study advisers, because I did not know what to pick.
One study adviser explained about rules and about pre-selected programs that allowed some combinations.
The other study adviser asked me: why not do all of them?
I ended up doing 3 majors at the same time (that admittedly had some overlap).

Of course that was in my country at my university.
I have no idea how things stand in your country.
My advice: try to think outside the box!

 

[I like Serena]

Really ! what maths courses have you taken ?

Hmm, let's see, the dedicated math courses in the first half year were:

1. Analysis 1
2. Linear Algebra 1
3. Abstract Algebra 1

Although, to be fair, I had already taken the Linear Algebra 1 exam before the university year started, so that does not count.
To compensate, I took a couple of 2nd year courses.
For math I did Discrete Math.

 

[Ackbach]

This semester I have the first course in real analysis I . Basically , it discusses mainly construction of reals, sequences , limits , differentiation , continuity and integration. In the next semester I have many choices and I think I can only take one :

1. Complex variables
2. Modern algebra( abstract algebra)
3. Real analysis II (same as Real analysis I but with several variables)

If for me I want to take all of them :) but I think I'll have to choose one of them. So what course would suggest ?

Of the list you have there, I'd say complex variables is probably the most immediately useful course, although they're all useful. If you have any plans for graduate school in mathematics, then I would strongly recommend taking all of them, as well as topology. Your background in computer science already gives you a computational edge (pretty much required for any applied mathematics program).

 

[mathbalarka]

As I have understood your mathematical capabilities, you seem pretty strong at CA. I'd then suggest you to take 1 and 3, leave Abstract Algebra for now.

I am thinking of abstract algebra and complex variables.

Hmm, you want to learn Abstract Algebra, then? Do you think you are quite strong enough to take it?

 

[alyafey22]

Hmm, you want to learn Abstract Algebra, then? Do you think you are quite strong enough to take it?

Here is the course description :

Review of basic group theory including Lagrange’s Theorem. Normal subgroups, factor groups, homomorphisms, fundamental theorem of finite Abelian groups. Examples and basic properties, integral domains and fields, ideal and factor rings, homomorphisms. Polynomials, factorization of polynomials over a field, factor rings of polynomials over a field. Irreducibles and unique factorization, principal ideal domains.

I think I can survive because I read about most of the concepts above but I didn't take that much exercises it was just plain reading of the definitions and proofs of theorems.I think it is pretty fun.

 

[mathbalarka]

I see that your course doesn't carry up to Galois theory. Not hard, though, that course, although I particularly had a very difficult time concerning solvability of groups.

And I agree with you, AA (WARNING : not Anti-Aircraft! ) is surely fun (not if you're airborne with AA's shooting at you (Sweating)) to learn.

Good luck with the AAs then!

Balarka
.

 

[alyafey22]

I never read about Galois theory but I think the foundation should be very strong before rushing into that mathematical concept. I even saw books on Galois theory . I think its discussed in a graduate course.

 

[polygamma]

Not too long ago I took a class on the theory of equations. We were supposed to cover Galois theory. But the class moved so slowly that we never got to it.

Something similar happened when I took abstract algebra. The class moved so slowly that it basically became a class just on group theory, which would have been fine if the second semester (which I haven't taken and is offered infrequently) actually continued from there.

 

[mathbalarka]

The fundamentals of Galois' result is not hard, although, in particular, Galois theory is indeed tough, which I realized several years ago when reading extensively on one of the research-level issues and my personal research subject, the inverse Galois problem.

Balarka
.

 

[I like Serena]

Seeing your activity on this forum, I believe that complex analysis is a free pass for you.
And multivariable analysis should be easy.
You haven't shown much activity in abstract algebra yet, so if you really want to learn more math that's the one to take.
You might take the others along for fun. ;)

 

[alyafey22]

Seeing your activity on this forum, I believe that complex analysis is a free pass for you.
And multivariable analysis should be easy.
You haven't shown much activity in abstract algebra yet, so if you really want to learn more math that's the one to take.
You might take the others along for fun. ;)

Just started reading about Abstract algebra this semester. It is fun but very long.

 

[I like Serena]

Just started reading about Abstract algebra this semester. It is fun but very long.

Doesn't have to be.
There's great fun in there.
Sometimes it takes a bit of time and effort for the dime to fall.
But when it does it tinkles.
And afterward, you may wonder why it took so long to see what may seem so obvious in retrospect.
That's when you know you've learned something valuable!

 

[Petrus]

Sometimes it takes a bit of time and effort for the dime to fall.
But when it does it tinkles.
And afterward, you may wonder why it took so long to see what may seem so obvious in retrospect.
That's when you know you've learned something valuable!

Hehe! I am waiting for that to happened to me in linear algebra! For some reason i find calculus a lot more fun and easy to understand ( especially when you can see with graph)... ! Maybe it's because I Dont see anything intressting with linear algebra (makes it harder and booring to studdy..):S

Regards,
$$|\pi\rangle$$

 

[I like Serena]

Maybe it's because I don't see anything interesting with linear algebra (makes it harder and boooring to study..):S

Yet!

 

[Deveno]

My advice would be (of course!) Abstract Algebra.

Seriously, if it's a well-taught class, the things you learn will be useful to you the entire rest of your career. So many topics in advanced analysis become so much easier when you have a grasp of the underlying algebraic structures (often not even presented as such).

One choice I do NOT see there, which you simply MUST take, as soon as you can, is Topology. A good grasp of topology makes much of complex and real analysis so much clearer.

I sense you have a deeper affinity for analysis-related topics, and I assure you, you WILL eventually "go deeper" in these areas, what I am suggesting first is establishing a little breadth. You'll have a broader mathematical vocabulary, which will help at the conceptual level (unfortunately, not so much with computation. Oh well).

@Petrus: I feel sorry for you, bro. Obviously you are in the "wrong" linear algebra class (it happens...linear algebra is required for so many fields that what often gets taught is just the dried-out husk of what it can be). Unfortunately, the standard curriculum is to teach linear algebra first, and abstract algebra second, so the more "interesting" parts of linear algebra (which rely on more abstract algebraic concepts) are never gotten to, and one is stuck in row-reduction and determinant-calculating hell. Seriously, I let Wolfram|Alpha do that stuff for me.

But...there is a bright side to the drudgery of linear algebra...when you do calculus of more than one variable, all of a sudden the usefulness of those linear-map matrix thingies becomes vitally important (for example, with a surface in 3-D, you don't have tangent lines anymore...it's tangent planes...hmm...sound familiar?). In physics, the fact that i, j, and k form an orthonormal basis gets to be pretty handy. And there are plenty of pictures to go around.

*******

Back on topic: in the end, however, Zaid, just do what you think you really want to. As Samuel Johnson once said (a paraphrase?): A man ought to read just as his inclination leads him, for what he reads as a task will do him little good.

 

[alyafey22]

@Petrus: I feel sorry for you, bro. Obviously you are in the "wrong" linear algebra class (it happens...linear algebra is required for so many fields that what often gets taught is just the dried-out husk of what it can be). Unfortunately, the standard curriculum is to teach linear algebra first, and abstract algebra second, so the more "interesting" parts of linear algebra (which rely on more abstract algebraic concepts) are never gotten to, and one is stuck in row-reduction and determinant-calculating hell. Seriously, I let Wolfram|Alpha do that stuff for me.

Seriously , the same thing was done in a class I took. It was just horrible with all computations and less concept. I was having the sense that Linear Algebra is much fundamental than the way it was taught. I assure you I didn't pay attention . I am planning to read it again on my own and taste the real beauty.

About Topology , I think I know what is needed to survive. I didn't read that much about general topology but I have shattered pieces of information here and there. I try every now and then to read about it.