Should I have learned real analysis before taking complex analysis

[stgermaine]

Hi I am taking summer class in complex analysis and I am having a horrible time.
I don't understand anything we've covered so far, e.g. Cauchy-Goursat theorem, Laurent series, series expansion, etc.

The prereqs was just Calc III, which I got an A- in.

The textbook isn't much help either, so I might see if it gets any better after I borrow a different book from the library.

Though not a prerequisite for this class, would real analysis have helped me understand the topics in complex analysis much better? How should I approach analysis? I am in need of dire help

Thank you

 

[mathman]

A usual course in complex analysis does not require a course in real analysis, although it might need advanced calculus.

 

[Office_Shredder]

Are you having trouble because it's a proof based class, or because you feel that you don't know the prerequisites, or something else?

 

[Hercuflea]

I was in your exact situation last fall. Took calc 3 but not real analysis and I took complex analysis. It's a tough class. I also found laurent series to be the hardest part of the course. My prof gave the class a big curve though because more than half of the class withdrew and the highest grade of the rest was like a B-. Good luck.

*ended up with a B

 

[EricVT]

Personally, I did not feel that I needed real analysis to succeed in complex analysis (I also took complex prior to real). The only benefit that I think real analysis would have offered is some additional experience with rigorous, proof-based mathematics (but I feel that complex analysis helped me with real analysis in this same way).

I do think the transition from your typical calculus course that focuses on problem-solving into analysis of any kind is difficult if you've never been exposed to that level of mathematical rigor.

 

[stgermaine]

Are you having trouble because it's a proof based class, or because you feel that you don't know the prerequisites, or something else?

No, I think it's just that I totally suck at analysis. I took algebra and linear algebra (300 and 400 level courses) which had plenty of proofs. I was also taking differential equations last semester but ended up dropping it.

Proofs I am fine with, but it just something about complex analysis I don't really get.

 

[micromass]

No, I think it's just that I totally suck at analysis. I took algebra and linear algebra (300 and 400 level courses) which had plenty of proofs. I was also taking differential equations last semester but ended up dropping it.

Proofs I am fine with, but it just something about complex analysis I don't really get.

Can you describe why you thought algebra and linear algebra were not so difficult and why complex analysis is difficult? What makes it hard?

I recommend you to get the book visual complex analysis by Needham: https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20

 

[hsetennis]

It was a prerequisite for me. I took complex after real and I didn't feel like I was benefitted in a major way, other than being able to breeze through some of the basic limits/continuity proofs.

Of course classes are taught differently everywhere, but the main thing that irked me about complex analysis was the number of topics. As opposed to real analysis, linear algebra, and algebra that focused deeper on a shorter list of topics, my complex analysis contained a much larger breadth of material without as much depth (my class used Brown and Churchill). I guess this is because certain results were generalizations of the already-well-covered topics in real analysis.

 

[stgermaine]

Can you describe why you thought algebra and linear algebra were not so difficult and why complex analysis is difficult? What makes it hard?

I recommend you to get the book visual complex analysis by Needham: https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20

I feel like algebra proceeded in a fairly step by step way. First you covered basic number theory. Then Euclid's algorithm, then you go into GCD and modular arithmetic, then Euler's totient theorem, etc.

Complex analysis I guess does go in steps, covering complex variables first, then learning about complex differentiation, Green's theorem, line/contour integrals, and moving on to Cauchy's Theorem and Laurent series. I guess it's that there is a lot of visualization involved, which is something I didn't really need for algebra.

For example, when learning about Euler's totient theorem, I had a fairly solid base that i could follow the proof without being confused too much. When I see the proof for Cauchy's Integral theorem, I feel like there are large 'gaps' in the proof, or rather my understanding of the proof.

 

[mathwonk]

don't despair. we all suffered with our first analysis course as this is where one first encounters super precise and picky arguments. it gets better.

 

[Chronos]

A good grasp of geometric proofs is useful.