Discrete Algebraic Methods

1 Algebraic structures

Algebra is one of the oldest mathematical disciplines. Language and techniques from modern algebra are used in most areas of mathematics. Algebraic methods have their origins in the elementary theory of numbers and the study of equations. The elementary theory of numbers considers the properties of number systems such as the integers, the rationals, or the reals. The theory of equations, on the other hand, deals with solving equations and systems thereof. Both subjects date back to classical times. The Babylonians already knew how to solve linear and quadratic equations and how to compute square roots several hundred years before the Common Era. Their applications included land surveying and mapping, architecture, tax collection, ...