What is Group Theory?

Srinidhi wrote:

What is the group theory you have invented peddappa?

Dear Srinidhi,

 I have not invented Group theory! I am only a student of  group theory. This subject is atleast two hundred years old.

But its main content-symmetry in nature- is a topic of human interest all through human life.

You might have seen very nice, old buildings with a great deal of symmetry.

In a sense, music is very pleasing because of the symmetry in the sound (raga, tala, as they say). You agree that music can be very pleasant and relaxing and noice is neither pleasant nor relaxing!

Group theory formally is a subject in Mathematics and it largely deals with symmetry in nature. Its main pillars are  Algebra and Geometry. You understand the word symmetry:

a ball is symmetric,

a square is more symmetric than a rectangle,

a symmetric building is nicer to look and perhaps more useful than a building not symmetric,

Vidhana Soudha is very symmetric

nice flowers have a great deal of symmetry,

you may have seen some crystals which are very symmetric;

diamonds derive their beauty by their shining and symmetry, etc.

  Symmetric objects can be very complicated though they are very pleasing. 

Physicists think that our universe is very  symmetric. That is why physicists also study group theory a lot.

Chemists study symmetry to understand the crystals in nature

To impress on you how complicated a symmetric objects could be, I have include a file containing some nice pictures for you. ENJOY!

 [ http://www.math.umass.edu/~gunnells/cells/cells.html ]

(ignore the beginning stuff, only look at the pictures!!)

-Yours affectionately,

Narasimha