#algebra
19 concepts
Concepts
Variables
A symbol representing an unknown or changeable value.
Polynomial
An expression consisting of terms with variables and coefficients combined by addition.
Linear Equation
An equation where the highest power of the variable is 1.
Factoring
Expressing a polynomial as a product of two or more polynomials.
Quadratic Equation
An equation where the highest power of the variable is 2.
Inequality
An expression showing the relationship between two values using inequality symbols.
System of Equations
A set of two or more equations that must be satisfied simultaneously.
Exponential Function
A function where the base is a positive constant and the exponent is the variable.
Logarithm
The inverse of exponential function, indicating how many times a base must be multiplied to get a number.
Arithmetic Sequence
A sequence where the difference between consecutive terms is constant.
Geometric Sequence
A sequence where the ratio between consecutive terms is constant.
Series
The sum of terms in a sequence, which can be finite or infinite.
Boolean Algebra
An algebraic system on 0 and 1 (or true and false), fundamental to logic circuits and computer science.
Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra states every polynomial of degree n≥1 has exactly n roots (counting multiplicity) in complex numbers.
Sigma-Algebra (σ-algebra)
Collection of sets closed under complement and countable union. Structure for defining measures
Tensor
A mathematical object defined as a multilinear map. A (p,q)-tensor has p covariant and q contravariant components.
Tensor Product
An operation constructing a new vector space from two vector spaces. Characterized by the universal property of bilinear maps.
Lie Algebra
The tangent space at the identity of a Lie group, equipped with Lie bracket. Encodes infinitesimal structure of the group.
Exact Sequence
A sequence of group homomorphisms where image equals kernel at each step. Short and long exact sequences are important.