Definition

1. Noun:
   • A branch of mathematics: "Algebra" is a branch of mathematics that uses symbols, typically letters, to represent numbers and quantities in formulas and equations. It generalizes arithmetic operations.
   • A system of algebra: The word can also refer to a specific system or structure within this branch of mathematics, such as Boolean algebra or linear algebra.

Usage Examples

• Noun:
  • Students must study algebra before they can take calculus.
  • The problem was solved using basic algebra.
  • He is writing a thesis on abstract algebra.

Advanced Usage

• "to do algebra": to perform algebraic calculations or solve algebraic problems.

  • She sat at her desk to do her algebra homework.

• "algebra of sets": a specific system within algebra dealing with set operations.

  • Understanding the algebra of sets is fundamental to probability theory.

Variants and Related Words

• Algebraic (adj): relating to or using algebra.

  • The solution required an algebraic proof.

• Algebraist (n): a specialist in algebra.

  • The famous algebraist published a groundbreaking paper.

Synonyms

• Symbolic logic (in specific, formal contexts).
• Generalized arithmetic (descriptive synonym).

Related Phrases

• Linear algebra: A branch of algebra concerning vector spaces and linear mappings.

  • Linear algebra is essential for computer graphics.

• Boolean algebra: A branch of algebra where variables represent true/false values.

  • Boolean algebra is the foundation of digital circuit design.

Idioms

(No common idioms are directly based on the word "algebra".)

Noun

1. the mathematics of generalized arithmetical operations