Complex analysis videos

I am dividing my (study-)time between M381, M373, David Leavitt's novel The Indian Clerk (TIC) and self-study activities related to analytical number theory and complex analysis. ( And when I finished reading The Indian Clerk I'll start a book about the life of Kurt Goedel, or I might reread the book on Alan Turing. ) Reading, always keep reading, is my motto.

Excellent mathematicians work harder, have more luck in chosing their subjects and belong to more influential networks than less excellent mathematicians. Is that true? If we can prove so many theorems couldn't we have created one or two as well? Of course. Unless it was a 'theorem' of Ramanujan. His work, providing one has access to it ( read: understands it ) is of the jaw dropping class.

How did Srinivasa Ramanujan perceive the mest world?

In my self-study project I am struggling with the proof of the Prime Number Theorem as well as with understanding the Riemann hypothesis (RH). - In TIC it is G.H. Hardy's wish to prove the RH. At that point in his life he lectures at Cambridge. People in his surroundings we meet in the book are ( amongst others ) John Littlewood, Betrand Russell, Ludwig Wittgenstein and John Maynard Keynes. One day Hardy receives a letter full of mathematical scribblings. The impact of the magnitude of these scribblings reaches him, but slowly. The letter came from no one less than Srinivasa Ramanujan, an until then unknown Indian mathematician. Hardy discusses the letter with his young collaborator Littlewood and the story unfolds... An excellent companion to this reading adventure is Number Theory in the spirit of Ramanujan.



The main goal I have set for myself this -mathematical- year is understanding the PNT. The best way to reach that point was in my opinion studying Apostol's Analytic Number Theory. I make progress, but slow, although I am not terribly behind on schedule. The single most important effect though is that I now feel naturally motivated and ready to attack complex analysis. Last but not least: another set of video lectures on Complex Analysis by Bernd Schröder from Louisiana Tech University.

Lecture 1: Introduction

A measure I took based on my experiences with M208 last year is implementing a TMA-(latex-)code-freeze-date. I have set that date for next Tuesday when I'll start the check-double-checks. As M381 is a level 3 course I am content with the 65-sure I am at right now. Although there is no such thing as a 'sure' before the result is 'in'.

My URM emulator now automatically concatenates two URM programs. I want to automate substitution as well as primitive recursion. Although I am still struggling a bit with the manual implementation of a primitive recursive function at the deeper URM level. Knowing that this all leads ( and I am sure it does ) to understanding Goedels incompleteness theorems makes this all a worthwile adventure.

Touching complex analysis

Prof. Mattuck is in top form in lecture 6 when he talks about Euler and the beauty of complex numbers. Although it is a lecture in the DE series it can be watched as a stand-alone lecture. So if you are doing MST121, MS221 or M208 it is great fun to watch this lecture. He even touches the field of Complex Analysis when he explains differentiating $e^{i\theta}$. He notes ( jokes ) that time is always a real variable but he isn't so sure when the next Einstein comes around: he may very well decide we need complex time! Anyway, how would you integrate $\int{e^{x}}\cos{x}\ dx$ ? Prof. Mattuck says these integrals are easy if you switch to the complex domain. Finally he solves the beautiful equation $x^n+1=0$ ( as we have seen in MS221, M208 ).



Hopefully, after or during MST209, I will be able to analyze the synchronization of metronomes problem using differential equations some day.

Learning mathematics the fast way.

The video course I found has been streamed on EDGE. Some sort of system for distance learners. It is a 10 week course split over two subjects: vector analysis ( 4 weeks ) and complex analysis ( 6 weeks ). For the moment I am primarily interested in the complex analysis lectures. If everything goes well I do M337 next year. It is still very, very early but I am thinking of MST209 ( Mathematical modelling ) + M381 ( Logic and elementary number theory ) + M337 ( Complex analysis ) for next year. To the point. I am rather surprised by the sheer speed they go through a topic like complex analysis. They cover basicly what's in the book A First Course in Complex Analysis which has 500 pages. Well, you would say that's roughly 85 pages a week. Or 20 pages per lecture. Or three minutes per page. Now suppose a page is a theorem + proof + example that would reduce the time to one minute for a proof. Reasoning like this doesn't work of course but there is this Eternal Truth: "Mathematics is hard and there is no royal way." Some King ( don't remember which one ) supposedly asked one of his mathematicians that there surely must be a faster way -for him- to learn mathematics. The answer he got was "There is no royal way to mathematics." Maybe they discovered one after all, in Seattle.

AMATH 401/501 Video Lectures

Because of my special interest in number theory I read ahead on the topic of complex analysis ( M337 ) which is a prerequisite for analytical number theory. I like to watch video lectures because it gives me an idea about how the topic is presented to students. Until a few days ago I wasn't able to find any lectures on the topic. Although the lectures aren't currently online at the site of the University of Washington they must have been in the past or they are available to enrolled students only. Anyway, some student has been so very kind to upload 38 lectures given in 2009 of +/- 50 min each in a total of 6GB compressed video data to the filesharing site Rapidshare. I do not know if the student violated copyright laws or anything. I don't think so. I think the files are offline because having the files online involves quite a lot of bandwidth for the university which is expensive. Mathematics video lectures have a global appeal and seem to be very popular.