Serious work to be done...

... on math ( group theory ). Hard work is required. Work is play. Work hard, play hard.

( MORE LATER... )

Glimpses of Algebra and Geometry

I have read somewhere that at a deep level algebra, geometry and number theory are representations of the same mathematical entities. This book presents topics in math from the perspective of different mathematical disciplines. It is also a beautiful and fun to read book.

A 6****** star math book

I don't rate something 5***** stars easily. I mean what's beyond 5? Today I found a book for which a 5 star rating is simply too low. The book is extremely:
- different
- relevant
- interactive ( even more so than some math 'websites' )
- challenging
- fun.
If there is a book which I ever rated as a 5***** it must be Concrete Mathematics from Graham, Knuth and Patashnik. Polynomials, that's how it's called, is like that but much more coherent. It is a * * * * * * rating, to me anyway. Must have, must read, can't wait, buy now.

Oh, eh, it is out of print, sorry. Not for sale. ;-)

Group Explorer 2.0

"... Group Explorer is mathematical visualization software for the abstract algebra classroom. Users can explore dozens of finite groups (and morphisms among them) visually and interactively. ..."
GE 2.0 developer Nathan Carter.

Where GAP is targeted to professional algebra researchers and Mathematica Abstract Algebra to students who already have completed one or two abstract algebra courses and know the ins- and outs of Mathematica, Group Explorer is meant for beginners. A beautiful tool to demonstrate properties of a limited number of small groups. Version 2.0 is primarily a "look and feel" release. The program is free and downloadable as C++ source or executable.

Lie Algebras

e^ A, e to the power matrix A, e to the power {{2,0},{0,1}}.
Matrices as power coefficients.
Is that cool, or what?

Beauty

Or freak out yourself [ here ].

TeXnicCenter

As far as mathematics is concerned I am more or less illiterate. I can read a bit but when it comes to writing I freeze entirely. What to write? I just can't formulate my thoughts in a mathematical correct manner. What is worse? Well, I can't even reproduce a text from some math book. Look at me, on my age, learning to type. It is depressing. Look at the bright side, I have TeXnicCenter. That's a start. You can't write a letter without a pen either.

Groups of order 18

There are 5 groups of order 18:

gap> grp(18);
Group 1 has structure: D18 and is Non-Abelian
Group 2 has structure: C18 and is Abelian
Group 3 has structure: C3 x S3 and is Non-Abelian
Group 4 has structure: (C3 x C3) : C2 and is Non-Abelian
Group 5 has structure: C6 x C3 and is Abelian

The workhorse here is the function ConstructAllGroups and is part of the GAP package GrpConst.

#
# Prints all groups of order n
# IN: Group
#
grp:=function(n) 
local listGroups;
listGroups:=ConstructAllGroups(n);
i:=1;
while(i<(Length(listGroups)+1)) do
 Print("Group ");
 Print(i);
 Print(" has structure: ");
 Print(StructureDescription(listGroups[i]));
 Print(" and is ");
 if (IsAbelian(listGroups[i])) then
  Print("Abelian");
 else
  Print("Non-Abelian");
 fi;
 Print("\n");
 i:=i+1;
od;
end;

Permutations

Whatever you have to do with a structure-endowed entity S try to determine its group of automorphisms . . . You can expect to gain a deep insight into the constitution of S in this way.
Herman Weyl, Symmetry ( Quote found in this PDF )

Is it possible to translate the above sentence to "Jip en Janneke"-language? Before anything else I should give it a try myself.

Self-study trick

Linear Algebra, extremely important stuff for 3D programming. This book
must be one of the best. It is from Springer, written by the well known Serge Lang and it is a 2nd edition. Must be good. Not? Thing is that I rather spend my money on other things like... bills, other bills and more bills. Solution? Use the table of contents from this book as a sort of plan and get the knowledge from free sources elsewhere. It really works. My Rubik program is the proof of that. Examples? This one to get started: Elements of Abstract and Linear Algebra.

Learning Tex and other preparations

If you write clearly, then your readers may understand your mathematics and conclude that it isn't profound. Worse, a referee may find your errors. Here are some tips for avoiding these awful possibilities. Serious: I learned some new stuff today. Semi-Direct Groups ( at last ) and some first glimpses of Polya Burnside Enumeration.

Hamilton's handwriting

1843...