Mathematics Study Guides

This topic involves the methods and principles used to simplify algebraic expressions, including the subtraction of…

Algebraic expressions are mathematical phrases that can contain numbers, variables, and operators.

Arithmetic operations are the basic mathematical processes of addition, subtraction, multiplication, and division,…

Arithmetic operations refer to the basic mathematical operations of addition, subtraction, multiplication, and…

Basic addition is a fundamental arithmetic operation that combines two or more numbers to obtain a sum, serving as a…

The fundamental mathematical operations used in programming, including addition, subtraction, multiplication, and…

Exponent rules involve the application of specific principles to simplify expressions containing exponents, such as…

Fundamental operations in algebra refer to the basic mathematical processes, such as addition, subtraction,…

The fundamental properties of real numbers include the associative, commutative, and distributive properties, which…

This topic covers the basics of algebraic expressions, including the use of square brackets and round brackets.

The mathematical principles governing the manipulation of powers and indices, including the rules for multiplication…

The mathematical rules and principles governing the manipulation of algebraic expressions with integral indices,…

Linear functions are mathematical expressions in which a variable is raised to the first power, and their graphs…

Multiplying fraction parts involves multiplying the numerators together to get the new numerator and multiplying the…

Operations with negative numbers involve the arithmetic processes of addition and subtraction applied to integers that…

Properties of exponents govern how operations involving powers are performed, including multiplication, division, and…

The properties of real numbers describe the rules and relationships governing arithmetic operations such as addition,…

A concept in mathematics that describes the relationships between sets, including the definition of a relation, the…

Removing negative powers involves negating the denominator and simplifying the resulting expression.

The rules for multiplication in algebra involve various properties that govern how numbers and variables interact under…

The rules of algebra are a set of mathematical principles that govern the manipulation of algebraic expressions and…

The various operations that can be performed on sets, including union, intersection, difference, and complement, as…

The fundamental concepts and principles of set theory, including the definition of a set, types of sets such as null,…

Simplifying expressions with indices involves applying the rules of exponents to reduce complex expressions into…

Simplifying fractions involves reducing them to their simplest form by canceling out common factors between the…

Simplifying negative exponents involves removing the negative sign by taking the reciprocal of the base and changing…

Working with fraction denominators involves understanding how to manipulate and simplify fractions by negating or…

Algebraic structures are mathematical systems defined by a set of elements and operations that satisfy specific…

Complex numbers are mathematical objects that extend the real number system to include imaginary numbers, which are…

Determinants are scalar values that provide important information about a matrix, such as whether it is invertible,…

Determinants are scalar values computed from a square matrix that provide important information about the properties of…

A matrix is said to be in echelon form if it satisfies certain conditions: each leading entry of a row is to the right…

Effective graphing techniques are crucial for accurately representing economic concepts such as supply, demand, and…

Elementary matrices are matrices that represent elementary row operations on other matrices, and they play a crucial…

Elementary matrices are matrices that represent elementary row operations, which can be used to perform Gaussian…

Exponential growth refers to a pattern of population increase where the number of individuals grows at a constant rate…

Fraction subtraction methods involve procedures to subtract one fraction from another, including finding common…

The Fundamental Theorem of Algebra states that every non-constant polynomial has at least one complex root, and matrix…

A mathematical algorithm used to transform a matrix into row echelon form (REF) or reduced row echelon form (RREF)…

The study of graphs, which are non-linear data structures consisting of nodes or vertices connected by edges, with…

The greatest common divisor (GCD) of two or more polynomials is the highest degree polynomial that divides each of the…

The Greatest Common Divisor (GCD) of two integers is the largest positive integer that divides both numbers without…

The study of integer factorization and polynomial operations involves understanding the properties of integers, the…

Inverse permutations refer to the operation of reversing the order of elements in a permutation, while the concept of…

Linear algebra studies vector spaces and linear mappings between these spaces, focusing on systems of linear equations,…

Linear algebra is a branch of mathematics concerning linear equations, linear functions, and their representations…

Linear algebra encompasses the study of vectors, vector spaces, and linear transformations, focusing on systems of…

Linear algebra is a branch of mathematics that deals with arrays of numbers, particularly in the form of matrices.

Linear combinations involve creating a new vector by multiplying existing vectors by scalars and adding the results,…

Linear systems consist of equations that can be expressed in matrix form, where the solutions can be determined through…

Linear transformations are functions that map vectors to vectors while preserving the operations of vector addition and…

The log-sum-exp function is a convex and differentiable approximation to the max function, commonly used in…

Linear algebra is a branch of mathematics concerning linear equations, linear functions, and their representations…

Matrix inversion is the process of finding a matrix that, when multiplied with the original matrix, yields the identity…

Matrix inversion is the process of finding a matrix that, when multiplied with the original matrix, results in the…

Matrix multiplication involves combining two matrices to produce a third matrix, where each element is derived from the…

Matrix multiplication involves combining two matrices to produce a third matrix, where the entry in each position of…

Matrix multiplication is a binary operation that produces a matrix from two matrices, where the entries of the…

Matrix multiplication is the mathematical operation that produces a new matrix from two matrices by multiplying their…

Matrix operations refer to mathematical procedures that can be performed on matrices, including addition, subtraction,…

Matrix theory is a branch of mathematics that deals with the study of matrices, which are rectangular arrays of…

A permutation is a one-to-one function that rearranges the elements of a set.

Permutations are arrangements of elements in a specific order, and in linear algebra, they play a crucial role in…

Polynomial division involves determining how many times one polynomial can be divided by another, while row reduction…

Polynomial factorization is the process of expressing a polynomial as a product of its factors, which can include…

Polynomial operations involve the addition, subtraction, multiplication, and scalar multiplication of polynomials,…

The properties of exponents and polynomials govern the manipulation of algebraic expressions involving powers and…

Rational expression simplification involves reducing complex fractions to their simplest form by eliminating common…

The study of various operations that can be performed on sets, including union, intersection, difference, and symmetric…

A statistical technique used to fit a curve to a set of data points by adjusting the level of flexibility, allowing for…

Transformations of functions involve shifting, stretching, or reflecting the graph of a function to create new…

The trigonometric form of complex numbers represents a complex number in terms of its magnitude (or modulus) and…

Unique factorization of polynomials refers to the property that every polynomial can be represented uniquely as a…

This topic covers the methods and principles for simplifying expressions involving negative powers, including the rules…