Definition:Algebra (Mathematical Branch)

This page is about algebra in the context of the branch of mathematics. For other uses, see algebra.

Definition

Algebra is the branch of mathematics which studies the techniques of manipulation of objects and expressions.

Also see

• Results about algebra can be found here.

Historical Note

The study of algebra dates back to Muhammad ibn Musa al-Khwarizmi, who published his Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala (The Compendious Book on Calculation by Completion and Balancing) in around $\text {825}$$\text { CE}$.

François Viète made significant advances in the use of algebraic notation in the $16$th century.

Linguistic Note

The word algebra originates from the Arabic word al-ğabr, meaning balancing, reduction or restoration.

It originates from the name of a book, circa $\text {825}$$\text { CE}$, by Muhammad ibn Musa al-Khwarizmi:

Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala (The Compendious Book on Calculation by Completion and Balancing)

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.1$: Constants and variables (footnote)
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Introduction
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebra: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): algebra
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): algebra: 1.
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $4$: Lure of the Unknown: Algebra
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): algebra
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebra