# Famous Theorems of Mathematics/Algebra

Algebra is a branch of mathematics concerning the study of structure, relation and quantity. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.

Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.

Proofs are arranged in the following sections:

## Abstract Algebra[edit]

## Linear Algebra[edit]

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Linear algebra is also intimately connected with matrix theory. Proofs in linear algebra are also sub-divided into these portions:

## Category Theory[edit]

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