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## 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?

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