favorite branch of mathematics

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I like set theory and basic combintorics at least and calculus. What are other people favorite branch.

Number theory. It's just plain cool.

The bigger question is what do you not like? I was never that fond of Differential Equations (too practical) and Graph Theory (bores me to tears).

Complex Variables, non-Euclidean Geometry, and Topology were more my favorite.

Reals and Matrix Theory were somewhere in between.

Topology and differential geometry.

ruveyn

I should have wrote differential geometry rather than non-Euclidean geometry. Or just Geometry.

Discrete mathematics, topology; set theory, mathematical logic and the foundations of mathematics.

Calculus and probability, cause I did engineering

Calculus is easy as well.

Yes and no. As a mechanical calculation, not hard although integration can be a bear at times.

Done rigorously the analysis of real and complex variables requires close attention and hard work.

ruveyn

I consider that real or complex analysis. Calculating integrals by the definition is really hard and tedious.

Algebra. It's very easy for me and I enjoy it. I get relaxed when doing algebra equations.

The research on various algebras prove rather deep properties of the algebra rather than focusing on the solution of this equation or that equation. For example it was proved by Abel and Galois that the general fifth degree polynomial (and higher degrees) do NOT have solutions in terms of radicals of functions of the co-efficient s That put an end to trying to solve the general quintic equation by taking roots. A similar analysis proves that using straight edge and compass one cannot trisect the general angle. It is these deeper theorems that are the glory of algebra.

ruveyn

I like linear algebra. Matrices and eigenvalues crop up everywhere in applied mathematics.

Complex analysis has that perfect balance of being both elegant and somewhat mysterious. There are a lot of fairly simple proofs of very non-obvious or very roundabout kinds of results. Analytic number theory in particular is quite mind-boggling. Euler's formula is also handy mnemonic shorthand for deriving rotations and angles/phase-shifts without having to constantly write down loads of tedious trig identities.

Mathematical logic, set theory, foundations of mathematics... you get the idea. This stuff I find the most interesting.

I find the proofs and more abstract course I took on linear algebra easier than the more computational course as easy to get sidetracked and make mistakes in the computational one with matricies.