Gute Mathematik Skripten und Bücher

Wednesday, November 11th, 2009 | Author:

Book

Ich mach mal eine Liste von den Grundlagen, und woher ich sie gelernt habe (=was ich als brauchbare Lektüre empfinde, also meine Lieblingsliteratur)
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Category: German, Mathematics | 3 Comments

Walk-through to Morel-Voevodsky A¹-homotopy theory part II (page 48, Lemma 1.1)

Wednesday, November 04th, 2009 | Author:

A^1

Here is the second part of my walk-through to Voevodskys A¹-homotopy theory:

On page 48, the first Lemma is shown. Without proof - so I will try to illuminate things a little bit by giving the proof. This lemma isn't used until section 3, so you can skip it, if you want to. I suggest not to do so, if you are intimidated by the diagram, because it isn't that hard, and it's a nice exercise to get the concepts in your head right.

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Category: English, Walkthrough to A1-Homotopy Theory | 3 Comments

Some nice introductory/expository papers

Thursday, October 29th, 2009 | Author:

Something written

On Math Overflow, someone asked for "A single paper everyone should read?"
and some answers were particularly nice to read for me, so I repeat it for you, ordered by how much math is needed (from none up to little):

  • Paul Lockhart: "A Mathematician's Lament" shares my opinion about the math eduction disaster in schools. I think you should read this if you disliked your math classes in school or if you will ever have children (who will have to take a math class, then).
  • Terry Tao: "What is good mathematics?" which is a short (10 pages) paper about the benefit we have from mathematicians different tastes and approaches. I recommend to every scientist reading the first 3 pages (the other 7 pages are only understandable with some background in mathematics).
  • Freeman Dyson: "Birds and Frogs" which is a must-read for anyone interested in history and/or progress of mathematics.
  • Misha Gromov: "Spaces and Questions" which is readable with almost no background, although might be funnier if you know basic differential geometry. It tells a dense story of geometric ideas and their development in history. And it doesn't take much time to read/skim it.
  • Timothy Chow: A beginner's guide to forcing is a really gentle introduction to forcing.

Math Overflow is a new community website where mathematicians can discuss research problems. It is based on Stack Exchange, the software powering Stack Overflow, which does the same for computer science.

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Classifying Riemann surfaces

Wednesday, October 21st, 2009 | Author:

Geometry

In this post, I will sketch a classification of Riemann surfaces.

For those who haven't heard about the subject before, there is an introduction. For the impatient, look at the bottom of the post, where I have written a very short summary.

Table of contents:

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Walk-through to Morel-Voevodsky: A¹-homotopy theory of schemes (1999)

Tuesday, October 20th, 2009 | Author:

A^1

As I'm currently reading Morel&Voevodskys paper on A¹-homotopy theory of schemes, I will by and by write a little "walk-through" with hints & comments on how to find additional information to better (or even start to) understand the paper. Maybe for a newcomer to the subject (like me) it's difficult at first to stick together all these concepts like model theory, simplicial objects, Grothendieck topologies, algebraic geometry and so on. I will try to provide helpful comments to make the paper more accessible to those who are not that familiar with these notions above.

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Category: English, Walkthrough to A1-Homotopy Theory | Leave a Comment

Holomorphe Abbildungen sind manchmal schon Überlagerungen

Wednesday, October 14th, 2009 | Author:

Geometry

Gegeben eine holomorphe Abbildung f : X \rightarrow Y zwischen Riemannschen Flächen X,\ Y, können wir uns fragen: Ist f eine Überlagerung? Unter welchen hinreichenden oder notwendigen Bedingungen?

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Category: German | Comments off