LEGO Difference Engine

Long before the age of electronic computers, even before Alan Turing invented the theoretical Turing Machine, Charles Babbage invented a mechanical computer which he called the Difference Engine. Andrew Carol rebuilt one using LEGO.


Click to enlarge

Problem ( Group Theory )

Show that, then prove.

Let G be a group in which each proper subgroup is contained in a maximal subgroup of finite index in G. If every two maximal subgroups of G are conjugate in G, then G is a cyclic group.

Group Theory

An introduction to the theory of groups / Joseph Rotman --4th ed.
1995 Springer Verlag ISBN 0-387-94285-8




More is less. While browsing through this book I realized how little I know about the subject. How long will it take before I can conider myself 'current' in the field? And that's only Group Theory. There are a few other topics I would like to know more about... - Every Coin Has Two Sides. The other side of the coin of fascination is fear.

The magic of PI

Download the Pi poster in PDF format below and start zooming in, you'll find the first 350,390 digits of Pi on one single page. The power of what you can do with PDF.

Lie Group E8

From Science Daily:

Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and geometry.

Lang or Artin?

Although I still have decades of stuff to cover before I can really compare Lang and Artin I do have an opinion. Those who studied either or both of them seem to agree on one thing: neither of the books should be used as a text for a course, let alone for self-study: they are works of reference. Now that's strange because at least Artin's book was written from many years of course notes. I think the books should be studied but with many companion books to help you get through. Artin wrote in the preface: "...Sometimes the exercise of deferring material showed that it could be deferred forever - that it was not essential. This happened with dual spaces and multilinear algebra. ..." I tried to start reading Representation theory, by Fulton and Harris with nothing more than an undergraduate abstract algebra introduction as preparation. I couldn't finish the book because it was packed with topics from multilinear algebra. - I have been warned, warned and warned to take it easy but I go for Lang, why not? Mathematics grew into my fascination and passion. What else can I do?

How much is 25 divided by 5 ?

25 divided by 5? That's 14 each. 25/5 = 14.

Cycle Index

Cycle index.

( No Group Theory without Number Theory. )

At last an accessible topology book...

... from Dover Books ( who else?! ).



For 15,80 euro you get a truly beautiful (pocket)book.

After browsing the first pages I am now able to prove Euler's formula on Polyhedra, the beautiful F(aces) - E(dges) + V(ertices) = 2. I can even explain what a polyhedron is in these few, simple and (in fact) beautiful words: A polyhedron is a complex which is topologically equivalent to a sphere.

A bargain

... from Dover Books.



Whenever I am in the city centre I have to go to my favourite bookshop. Since I can download most books that I need I don't buy books that often anymore. But for only 12 euro I couldn't resist this book full of beautiful theorems and exercises.

Flatland

"... Our Women are Straight Lines. ..."

JavaView

JavaView for Mathematica...