Thursday, May 29, 2008
When you are not being able to study math
I am in England for a BPEL course. Haven't done much math for the last three days. It makes me feel empty. Math is like playing an instrument. You must practice every day. It is bearable because just before I left I had this idea which I can freely think about anytime, anywhere.
Sunday, May 25, 2008
Transforming ideas to results...
Cayley table of the group ( C3 X C3 ) : C2
Tuesday, May 20, 2008
Sunday, May 11, 2008
Theorem about normal subgroups
Normal subgroups are very important objects in Group Theory. One of the 'mustneverforget'theorems is the following.
Let N be a normal subgroup of a group G and H be any subgroup of G. Then the intersection of H and N is a normal subgroup of H.
For the proof we use the following theorem.
A subgroup H is a normal subgroup in G if gH=Hg for all elements g in G.
In easy to remember math: "The intersection of a normal subgroup with another subgroup is normal in that subgroup." ( H&N is N(ormal)in H )
If this seems difficult: this theorem becomes trivial real fast.
Let N be a normal subgroup of a group G and H be any subgroup of G. Then the intersection of H and N is a normal subgroup of H.
For the proof we use the following theorem.
A subgroup H is a normal subgroup in G if gH=Hg for all elements g in G.
In easy to remember math: "The intersection of a normal subgroup with another subgroup is normal in that subgroup." ( H&N is N(ormal)in H )
If this seems difficult: this theorem becomes trivial real fast.
Sunday, May 4, 2008
Morphisms
Let G,H be groups and x,y elements of G.
A homomorphism is a mapping
f: G> H
such that
f(1) = 1, and
f(xy) = f(x)f(y).
A homomorphism is a mapping
f: G> H
such that
f(1) = 1, and
f(xy) = f(x)f(y).
morphism  when f is 
Mono  injective 
Epi  surjective 
Iso  bijective 
Endo  any and when H=G 
Auto  bijective and when H=G 
Saturday, May 3, 2008
Math Video
Blogger has been notified, according to the terms of the Digital
Millennium Copyright Act (DMCA), that content in your blog mathematicsdiary.blogspot.com allegedly infringes upon the copyrights of others.
( This post contained a link to a torrent of the video Joy of Mathematics. )
Thursday, May 1, 2008
Math Speak
There are circles where this is common speak, really:
"How many consecutive digits of pi (3.1415 . . . ) can you display with a deck of cards?"
But it is the sort of question Charlie Eppes might have asked when he was eight years old or so.
"How many consecutive digits of pi (3.1415 . . . ) can you display with a deck of cards?"
But it is the sort of question Charlie Eppes might have asked when he was eight years old or so.
Groups of Finite Order By Robert D. Carmichael
I have found a beautiful book on Group Theory which was first published in 1937. I am not at all surprised that it was reprinted in 2000.
Link to Google Books
It is over 440 pages and contains many interesting exercises. I am going to try to solve the following question entirely with the Mathematica Abstract Algebra addon package.
( But more on this interesting question later. )
Link to Google Books
It is over 440 pages and contains many interesting exercises. I am going to try to solve the following question entirely with the Mathematica Abstract Algebra addon package.
( But more on this interesting question later. )
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Mathematics: is it the fabric of MEST?
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To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)