I love Topology!

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It's the best undergraduate math course I've taken yet, although I've had a heck of a time trying to explain any of it to non-mathematicians. It gives me that feeling that I associate with growing new neural connections.

For some time I have been watching this forum, but when I saw this topic, I decided it was time to register

All I'd like to say is that I can understand your feeling completely, and I'm happy for your joy. Topology was what initially drew me to mathematics (firstly, a course in metric topology, after that a course in general topology), although I work in analysis now. It demonstrates the power of abstraction, while at the same time being very "tangible". Ultimately, as you are likely to see, it is closely intertwined with other areas of mathematics (ranging from set theory to probability and even statistics), for which it often provides a (sometimes less visible) basis.

Enjoy!

I intend to take Analysis next semester. I have heard that I'll need it in order to understand the proofs underpinning Statistics, about which I feel curious.

The abstraction in Topology has taken some work to comprehend, but it does seem like that way of thinking will help me in other areas of mathematics.

I haven't participated much in this sub-forum, since I come to WP mostly for light entertainment, but perhaps I will check in more often. Welcome, though, SweetTooth.

Thank you both for the welcome!

I don't want to "hijack" this thread by talking about my own subject, so I will just be brief. My interest is in dynamical systems. A dynamical system is a mathematical description of the time evolution of some quantity, for example the position of the earth in its orbit around the sun, the electromagnetic field inside a laser, the price of a stock or the number of individuals in a biological population.

Often dynamical systems are generated by (partial) differential equations, integral equations, maps or combinations thereof. My interest is particularly in their abstract, functional analytic properties, their rigorous numerical analysis and the interplay between these two aspects. Part of this is the investigation of how the qualitative (i.e. topological!) behaviour of systems depends on parameters. For example, for certain parameter values a system may settle on an equilibrium, while for other parameter values it may display periodic or even chaotic behaviour. Such a study is called a bifurcation analysis. Developing methods for this has my special attention.

I propose that WrongPlanet implements LaTeX in its forum, so we can all go on the loose now

Maybe we should talk! I have a minor obsession with the Mandelbrot set. There's a significant open problem concerning the local connectedness of the boundary of the set. Mathematicians seem to believe it's locally connected but there hasn't been a proof.

Thanks for that explanation, SweetTooth. There are people here who will understand and be enthusiastic about what you are researching.

The potential of this site for Autistics to collaborate and support each others advancement is tremendous and sadly underutilized.
I want to encourage all WP users to open up and lets advise, teach and support each other.

Oh yeah and I vote for LaTeX also.

Test this week. Next week we start on n-space

I'm just trying to learn the difference between a donut and a coffee cup.

I sat next to my professor in Seminar yesterday, and asked him about one of the short answer parts that had confused me. He said that I got it right, and that when he wrote the test, he didn't expect that to be a difficult question. Apparently a lot of people had trouble with it, and even he had gotten part of it wrong on his answer key at first!

It's just an introductory course. We've done point-set so far.

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