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My Introduction
#1
Hello all,

I am a second semester graduate student in math at the University of Louisiana at Lafayette - but basically second year because I was taking graduate courses in my final semester of undergrad, so this is my 3rd semester of graduate courses now.

I know most of you are probably more well-versed in tetration than I am, but tetration and zeration have been sort of "back burner" things for me I've liked to learn for awhile, and I hope to eventually do my dissertation in something related to this if possible. I passed 2 comprehensive exams (in Topology and Abstract Algebra) a few weeks ago, and next year around the same time I will take (and probably pass) 2 more (in Complex Analysis and ODE). I have already had some undergrad experience in those areas of course - and also in Real Analysis, for which I will be taking the course in 2012-2013, meaning I might take the comprehensive exam about 2 years from now.

I'm unsure yet if my focus on tetration and zeration will be more algebraic or analytical... probably it will be a mixture of both. I had planned to read through all these forums posts this past summer, but I got busy (and perhaps lazy too), so I've only glanced at a few posts so far. Part of the reason I'm finally making an Introduction post is so that I'm more likely to actually get around to looking through it all this semester. The core of whatever research I do won't start until next year around this time, but I'd really like to familiarize myself this year with the understanding in the area so far.

So yeah... that's my introduction. And speaking of Complex Analysis, I have to run there now. Smile
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#2
Welcome and I bid you good luck in seething through these threads trying to better your understanding of tetration.

Been there, I know it's intimidating, can't say I understood all of it, but it still made for a rigorous reading and it got me thinking.
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#3
Yes, welcome as well from me. I appreciate it to have analytically experienced people around because that's one of my own weaknesses. Because the matrix-based expression of tetration using the carleman-matrices for exponentiation has come to its limit in the case of tetration my posting- and discussion-intensity here in the forum has much decreased but I'm still interested in fresh attempts to the huge problem of continuous iteration of the exponentiatial.

Let's see -

Gottfried
Gottfried Helms, Kassel
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#4
(08/24/2011, 06:44 PM)Dreamwalker Wrote: Hello all,

I am a second semester graduate student in math at the University of Louisiana at Lafayette - but basically second year because I was taking graduate courses in my final semester of undergrad, so this is my 3rd semester of graduate courses now.

I know most of you are probably more well-versed in tetration than I am, but tetration and zeration have been sort of "back burner" things for me I've liked to learn for awhile, and I hope to eventually do my dissertation in something related to this if possible. I passed 2 comprehensive exams (in Topology and Abstract Algebra) a few weeks ago, and next year around the same time I will take (and probably pass) 2 more (in Complex Analysis and ODE). I have already had some undergrad experience in those areas of course - and also in Real Analysis, for which I will be taking the course in 2012-2013, meaning I might take the comprehensive exam about 2 years from now.

I'm unsure yet if my focus on tetration and zeration will be more algebraic or analytical... probably it will be a mixture of both. I had planned to read through all these forums posts this past summer, but I got busy (and perhaps lazy too), so I've only glanced at a few posts so far. Part of the reason I'm finally making an Introduction post is so that I'm more likely to actually get around to looking through it all this semester. The core of whatever research I do won't start until next year around this time, but I'd really like to familiarize myself this year with the understanding in the area so far.

So yeah... that's my introduction. And speaking of Complex Analysis, I have to run there now. Smile

Do they cover Complex Dynamics in your Complex Analysis class? I'm slowly working my way through Milnor's book, "Dynamics in One Complex variable", and I just purchased "Complex Dynamics" by Lennart Carlson. which I should receive soon. I could probably improve my background in complex analysis as well.

Good luck in your studies, and I look forward to any questions or posts you might have.
- Sheldon
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#5
(08/26/2011, 04:36 PM)sheldonison Wrote: Do they cover Complex Dynamics in your Complex Analysis class? I'm slowly working my way through Milnor's book, "Dynamics in One Complex variable", and I just purchased "Complex Dynamics" by Lennart Carlson. which I should receive soon. I could probably improve my background in complex analysis as well.

Unfortunately, I do not know the answer to your question right now. The professor lectures from his own notes and does not use any particular book for the course.

Thanks, everyone, for the welcomes.
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#6
Progress Report:

I devoted some time this weekend reading the Tetration Wiki pages and glancing over the less-used subforums here (Resources & Wiki, About the Forum, Community) before getting into the nitty-gritty of everything. During this time, I bookmarked various FAQ and reference attachments (and a couple off-site things) which will be the next things I'll look at. After I finish a good reading of those things I bookmarked (not sure when that will be), I'll actually start reading the posts in the forums that have the bulk of the mathematical material (Mathematical and General Discussion and Computation). Maybe I'll take notes of what interests me and what ideas I have as I go through. Once I'm done, hopefully I'll have retained enough of an understanding that I can actually be a contributing member of this forum and attempt some research in the topic.

Actually, I probably could contribute right now, but I just don't want to be the guy who brings something up that has been established or refuted a hundred times before. I'd rather get an idea of what all has been discussed first.
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