I’m looking for the world’s easiest self-study text on group theory, something along the lines of “Group Theory for Dummies.” I don’t care how comprehensive it is all I care about is Easy Easy Easy-lots of diagrams and drawings preferred
The easiest linear algebra text I have found is “Elementary Linear Algebra” by Anton-Rorres, and I’m hoping there’s something equivalent for group theory. I’ve found that if I can get an intuitive feel for simple aspects of a subject I can usually understand the more complex stuff. Your help would be appreciated.
I think it may be out of print, but Budden’s Fascination of Groups is a very leisurely introduction. For example, the associative law, identity elements and inverses get a chapter each, and subgroups are covered in chapter 14.
Thanks everyone, but I probably should have been more specific. I don’t seem able to follow math for math’s sake type stuff, my mind just kinds of wanders away. But if I can see a problem that needs a method of solution then I can follow just about anything. So I guess some kind of group theory for physics type problems would be what I’m looking for i.e. pragmatic and easy.
QED your second link was pretty good thanks.
You need a more authoritative answer, but I don’t know of any applications of group theory in physics outside of fairly advanced quantum theory. You may have to suck it up and do the math for math’s sake approach.
Group theory (particularly study of various symettry groups) applies to crystallography as well, which is still probably too advanced a subject for the OP to consider a motivating example.
Here’s a thought which might be helpful. Counting problems are one of the most elementary, concrete applications of group theory.
Two of the most “simple” types of groups (and I’m not talking about simple groups in the mathematical sense) are the cyclic groups and the dihedral groups.
Picture a regular polygon with n sides. Now picture all the “symmetric rotations” of the polygon (so that the polygon “looks” the same after the rotation). For example, a square can be rotated 0, 90, 180, or 270 degrees without changing its appearance. This is a way of visualizing a cyclic group–the collection of symmetric rotations of an n-gon forms the cyclic group of order n.
You can also symmetrically flip a polygon–for example, you can flip a square along one of its diagonals without changing its appearance, or flip it along the line bisecting two of the square’s opposite sides. Take all of the “symmetric flips” and the “symmetric rotations” of an n-gon, and you’ve got the dihedral group of order n.
So where am I going with all of this? You can use these groups (and others) to solve nice counting problems. For example, take a cube, and say you’re going to paint each face of the cube with one of three colors. How many different ways can you paint the cube?
Here’s an elementary illustration of how to do it, involving painting a 4 x 4 chessboard:
(This is not really intended as a way of learning group theory “from scratch”, way too much has been omitted (it doesn’t even define what, in general, a group is), but it should give you a better feel for the subject and the types of things encountered in it).