Intereting Posts

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Infinite subset of Denumerable set is denumerable?
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Bayesian Parameter Estimation – Parameters and Data Jointly Continuous?
Can the same subset be both open and closed?
Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
$(\tan^2(18^\circ))(\tan^2(54^\circ))$ is a rational number
Singular Distribution
Can the Basel problem be solved by Leibniz today?
If $n\ge2$, Prove $\binom{2n}{3}$ is even.

I really wanna learn complex analysis but I don’t know where to start.

Basically I can do olympiad problems, but I don’t know calculus that well, so I would appreciate it if someone can post a list of topics (preferably in chronological order, if that makes sense) for me to learn before I am absolutely 100% ready to start learning the complex analysis, which I’ve read about and think is A-M-A-Z-I-N-G.

Thx for your time everyone! ðŸ˜€

- Determining holomorphicity
- Cauchy's Theorem vs. Fundamental Theorem of Contour Integration.
- What's the difference between $\mathbb{R}^2$ and the complex plane?
- Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
- On continuity of roots of a polynomial depending on a real parameter
- Maximal Ideals in the Ring of Complex Entire Functions

- Conformal mapping of a doubly connected domain onto an annulus
- Generating sequences using the linear congruential generator
- Is there any connection between Green's Theorem and the Cauchy-Riemann equations?
- Cauchy-Riemann equations in polar form.
- What is the radius of convergence of $\sum z^{n!}$?
- Integral $\int_0^\infty \log(1+x^2)\frac{\cosh{\frac{\pi x}{2}}}{\sinh^2{\frac{\pi x}{2}}}\mathrm dx=2-\frac{4}{\pi}$
- If $f$ is a non-constant analytic function on $B$ such that $|f|$ is a constant on $\partial B$, then $f$ must have a zero in $B$
- converse to the jordan curve theorem
- L-functions identically zero
- Is my proof correct? (Conformal equivalence of two circular annuli)

I’m told that the Stewart text is good for learning calculus for the first time.

If you’re looking for a challenge, Buck’s *Advanced Calculus* is rigorous. He even introduces complex variables at the end.

If you want a fun introduction without too much rigor, there are some popular books on complex variables, such as *An Imaginary Tale: The Story of $\sqrt{-1}$*.

This goes along with the excellent advice you have gotten so far. Learning calculus is, of course, an important step. Then you might consider learning real analysis. It is usually the transition to rigorous math, which is, in it’s entirety, as you say amazing.

This set of lecture notes by Fields Medal winner Vaughan Jones (like the Nobel Prize in math) are fabulous. A master, giving great insight as to how to think about things, starting from a position of no prior experience. So it’s great for self-learning. They are free for downloading. The last part is a rigorous presentation of a good deal of calculus – which will be invaluable in CA studies.

https://sites.google.com/site/math104sp2011/lecture-notes

I am sure once you actually start complex analysis you can get excellent recommendation for study materials here. But I might suggest Flanigan.

http://www.amazon.com/Complex-Variables-Dover-Books-Mathematics/dp/0486613887

It rigorous, but makes things very clear with the added feature of many examples and pictures, not to be underestimated as an aid to visualization (redundancy intended).

Good luck.

The most useful topics to cover, which relate directly to complex analysis are:

- integration (1 variable)
- differentiation (1 variable)
- and basic topology

email me at yoshayne95@gmail.com so that I can provide you with a pdf that contains most of the material you will need to cover before you can tackle complex analysis

Yaseen

- The Aleph numbers and infinity in calculus.
- Divide by a number without dividing.
- Understanding Strategy:Minimum number of weighing to find the faulty bag
- How to find $\sum_{i=1}^n\left\lfloor i\sqrt{2}\right\rfloor$ A001951 A Beatty sequence: a(n) = floor(n*sqrt(2)).
- Is there an alternative proof for periodic expansion of decimal fraction?
- What is the explanation for this visual proof of the sum of squares?
- Asymptotics of sum of binomials
- Positive part of the kernel
- Continuity on a union
- In how many ways can 40 identical carrots be distributed among 8 different rabbits?
- $A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
- Finding nonnegative solutions to an underdetermined linear system
- Uniqueness in the Riesz representation theorem for the dual of $C(X)$ in the book by Royden
- Prove ten objects can be divided into two groups that balances each other when placed on the two pans of balance.
- Number of words with a minimal number of repetitions