The students struggled to solve the algebraic equation before the end of class.

An algebraic number is often easier to study through its minimal polynomial than through its decimal expansion.

She built a strong intuition for vector algebra by visualizing vectors as arrows and practicing geometric operations.

Understanding linear algebra helped me design a more robust recommendation system based on matrix factorization.

An algebraic integer is a number in a number field that is a root of a monic polynomial with integer coefficients.

The researcher published a paper on linear algebraic methods for solving large-scale systems.

After attending the lecture, he became fascinated by algebraic geometry and decided to pursue research in the subject.

An algebraic function can often be expressed using only addition, subtraction, multiplication, division, and raising to rational powers.

Researchers in universal algebra often discover that similar theorems from different branches of algebra can be proved by the same general principles.

In the seminar, we demonstrated that a Boolean algebra is an algebraic structure (Σ, ∨, ∧, ∼, 0, 1) in which the binary operations ∨ and ∧ are idempotent, the unary operator ∼ is an involution called complement, 0 and 1 are constants, (Σ, ∨, 0) and (Σ, ∧, 1) form commutative monoids, ∨ and ∧ distribute over each other, and combining two complementary elements with one binary operation yields the identity of the other.