## Algebra

*Algebra* is a discipline of mathematics dealing with *sets* (see set theory), which are structured by one or more binary operations. While studying these so-called *algebraic structures* (i.e. *groups*, *rings*, *fields*, *modules*, and *vector spaces*), algebra provides means to find solutions of *equations* and *systems of equations* formulated inside these structures.

### Theoretical minimum (in a nutshell)

You should be acquainted with set theory, especially the set operations and basics about functions.

### Concepts you will learn in this part of **BookofProofs**

- What are
*groups*, which are their properties and applications? - What are
*rings*and which are the different types of rings and their properties? - What are
*fields*and how they improve the solvability of*equations*in comparison to rings? - What are
*vector spaces*,*matrices*,*determinants*and how these and other concepts of*linear algebra*help to solve*systems of linear equations*? - What are
*modules*? - How the
*Galois theory*helps to form new fields out of existing ones and what solvability of equations has to do with geometry?

| | | | created: 2014-02-20 20:27:42 | modified: 2014-04-30 21:29:02 | by: *bookofproofs*

## 1.Algebraic Structures

## 2.Field Extensions

## 3.Galois Theory

## 4.Linear Algebra

## 5.Constructions with Ruler and Compass

## 6.Universal Algebras

## 7.Categories

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