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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

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

1.Algebraic Structures - Overview

2.Motivation: Common Concepts Of Algebra: Substructures and Morphisms

3.Group Theory

4.Algebraic Number Theory and Ring Theory

5.Finite Fields

6.Galois Theory

7.Linear Algebra

8.Constructions with Ruler and Compass

9.Ordered Fields and Their Topology

10.Solving Strategies and Sample Solutions to Problems in Algebra

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)