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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

  • 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


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Bibliography (further reading)

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