Introduction to group theory

An Introduction to Focus Group Research

A focus group refers to a group of people who share some common characteristics. A researcher gathers these people in the group in order that they share their points of view and interact with each other over a specific issue. Focus group and Interview group are used interchangeably in the scientific literature and both refer to a method of collecting data in qualitative studies. Given the impor...

An Introduction to Computational Group Theory

C an one rotate only one corner piece in Rubik’s cube? What are the energy levels of the buckyball molecule? Are the graphs on Figure 1 isomorphic? What is the Galois group of the polynomial x8 + 2x7 + 28x6 + 1728x + 3456? What are the possible symmetry groups of crystals? These are all questions which, directly or in a not so obvious way, lead to problems in computational group theory. Algebra...

A Friendly Introduction to Group Theory

You do, prefrosh. If you’re a math major, then you probably want to pass Math 5. If you’re a chemistry major, then you probably want to take that one chem class I heard involves representation theory. If you’re a physics major, then at some point you might want to know what the Standard Model is. And I’ll bet at least a few of you CS majors care at least a little bit about cryptography. Anyway,...

An Introduction to Wedderburn Theory & Group Representations

Matrix Groups : An Introduction to Lie Group Theory

The elementary theory of Lie groups has something in common with precalculus: One wants to get past it in order to get on with the beautiful and powerful theory that follows, as well as the applications. With precalculus the theory that follows is built around calculus and its fundamental theorem, extending into calculus of several variables and having profound applications through the subject ...