Generally, I’m a tech optimist. I truly believe that we are living in the most exciting times and that life in general for most people is only going to get better. 575 more words

## Tags » Group Theory

#### In her own words: honouring Hanna Neumann

Image: Wikimedia Commons

Hanna Neumann (1914-1971, born Johanna von Caemmerer) was a German-born UK and Australian group theorist. She was the first woman Chair of Pure Mathematics in Australia. 104 more words

#### First Isomorphism Theorem of Groups

Let us first define quotient group, an important group constructed from our original group, then state and prove the *First Isomorphism Theorem*, a fundamental theorem that relates quotient group to the original group. 947 more words

#### Nice Explanation of Irreducible Representation

http://math.stackexchange.com/questions/38958/what-is-the-meaning-of-an-irreducible-representation

A nice explanation of irreducible representation from someone at Math SE:

A *representation of the group G* means a homomorphism from G into the group of automorphisms of a vector space V. 645 more words

#### Real world applications of representation theory

### (Subtitle: Representation theorists *will* rule the world one day just you wait)

This post describes some applications of representation theory of non-abelian groups to various fields and gives some references. 964 more words

#### Elementary school math, again

Remember when you were five years old and you learned that one plus one is two? Remember when you were just about to enter middle school or sometime around there and you learned about finding x? 1,050 more words

#### Correspondence Theorem of Groups

In our previous post, we have demonstrated that the normality of subgroups is preserved under surjective homomorphism (surjectivity is not necessarily needed for the inverse mapping). 336 more words