Branch: 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 socalled 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?
Table of Contents
 Part: Algebraic Structures  Overview
 Part: Group Theory
 Part: Algebraic Number Theory and Ring Theory
 Part: Finite Fields
 Part: Galois Theory
 Part: Linear Algebra
 Part: Constructions with Ruler and Compass
 Part: Ordered Fields and Their Topology
 Part: Solving Strategies and Sample Solutions to Problems in Algebra
Mentioned in:
Branches: 1
Parts: 2
Topics: 3
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