Mathematics

Welcome to the mathematics page. Some special mathematical environments that will be used in this section are listed and explained below.

Definitions : a precise and unambiguous description of the meaning of a mathematical term. It char- acterizes the meaning of a word by giving all the properties and only those properties that must be true.
Theorems : a mathematical statement that is proved to be true using rigorous mathematical reasoning. In a mathematical text, the term theorem is often reserved for the most important results.
Propositions : an often interesting result, but generally less important than a theorem.
Lemmas : a minor result whose purpose is to help in proving a theorem. It is a stepping stone on the path to proving a theorem.
Corollaries : a result in which the (usually short) proof relies heavily on a given theorem (we often say that this is a corollary to Theorem A).
Proofs : a convincing argument that a certain mathematical statement is necessarily true. A proof generally uses deductive reasoning and logic but also contains some amount of ordinary language.
Examples : examples help to understand the meaning of a definition, or the impact of a result.
Algorithms : recipes to do calculations.