# Articles

## Stubs

Abstract Algebra I (Group theory, Field theory and polynomials, level2)

The main goal in abstract algebra is extending the operations and properties we take for granted on sets we're used to working with (like integers, reals, complex numbers, etc.) to arbitrary sets. This requires precise definitions and requirements on the structure of the set in order to ensure the desired properties are present.

Complex Analysis II (Functions of a complex variable, level4)

Complex analysis…. greater depth…

Group Representations (Topological groups, Lie groups, level5)

Using mathematical formalism, a group *G* may be "represented'' by transformations on a vector space.

Point-Set Topology (General topology, level3)

Point-set topology is the study of the intrinsic properties of surfaces that are independent of distance. The classic example is the donut and the coffee cup, which, from our point of view, will be the same object.

Probability I (Probability theory, level3)

Probability is the study of chance…

The Fundamental Group (Algebraic topology, level4)

The fundamental group is a tool used to study topological spaces. It is a *topological invariant*, which means that it is the same for homeomorphic spaces. Because of this, it is frequently used to determine when two spaces are *not* homeomorphic.

Vectors & Space (mscname, level1)

This guide will discuss vectors and mathematical objects in 3-dimensional space. Vectors provide a significant portion of the language of multivariable calculus, and must be understood before adequately broaching that subject.

# Glossaries

## Stubs

Glossary of Abstract Algebra (General algebraic systems, level4)

This glossary lists common terms in abstract algebra, at a level typical for graduate school qualifying exams.