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Saturday, March 19, 2011

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.

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