Maths AI terms: N

33 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.

IB Maths AI glossary: N | Augment Education

N

Natural logarithmalso ln, log base e, natural logarithms, logₑ: The logarithm with base e, written $\ln x$ , so that $\ln x = \log_{\mathrm{e}} x$ is the power to which e must be raised to give $x$ .
Introduced in 1.5 Exponents and introduction to logarithms
Natural logarithmic modelHL only · also logarithmic model, a + b ln x, log model, natural log model: A model of the form $f(x) = a + b\ln x$ , where $a$ and $b$ are constants and $x > 0$
Natural numberalso natural numbers, ℕ: One of the counting numbers 0, 1, 2, 3, …; the set of natural numbers is written $\mathbb{N}$ .
Introduced in 1.1 Scientific notation
Nature of a stationary pointalso nature, classifying stationary points, classify a stationary point, type of stationary point: Whether a stationary point is a local maximum, a local minimum, or neither.
Introduced in 5.6 Stationary points
Nearest neighbour algorithmHL only · also nearest-neighbour algorithm, nearest neighbour: A method that builds a Hamiltonian cycle by starting at a given vertex, repeatedly travelling to the nearest vertex not yet visited, and finally returning to the start; the weight of this cycle is an upper bound for the travelling salesman problem.
Introduced in 3.16 Tree and cycle algorithms
Nearest neighbour interpolationalso nearest-neighbour interpolation, nearest neighbor interpolation, Thiessen polygon method: Estimating the value of a quantity at a point by the value measured at the nearest site, so that every point in a Voronoi cell is given the value of that cell's site.
Introduced in 3.6 Voronoi diagrams
Negative correlationalso negatively correlated, inverse correlation: A relationship in which larger values of one variable tend to go with smaller values of the other, so the points of a scatter diagram fall from left to right.
Introduced in 4.4 Correlation and regression
Negative exponentalso negative power, negative index, negative indices: An exponent less than zero, defined by $a^{-n} = \frac{1}{a^n}$ for $a \ne 0$
Negative gradientalso f′(x) < 0, negative gradients, negative slope, negative derivative: A curve has a negative gradient at a point if its derivative there is less than zero, $f'(x) < 0$ , so that the tangent slopes downwards from left to right and the function is decreasing.
Introduced in 5.2 Increasing and decreasing functions
Negative integer poweralso x^-n, x⁻ⁿ, negative integer powers, negative integer exponent: A power $x^{n}$ in which $n$ is a negative integer, so that $x^{-k} = \frac{1}{x^k}$
Negative reciprocalalso negative reciprocals, perpendicular gradient, −1/m: For a non-zero number $m$ , the number $-\frac{1}{m}$ , found by turning $m$ upside down and changing its sign; it is the gradient of any line perpendicular to a line of gradient $m$
Negative vectorHL only · also −v, -v, opposite vector, negative of a vector: The vector $-\boldsymbol{v}$ with the same magnitude as $\boldsymbol{v}$ and the opposite direction; its components are the components of $\boldsymbol{v}$ with their signs changed.
Introduced in 3.10 Vectors
Netalso net of a solid, nets: A two-dimensional shape that can be folded along its edges to form the surface of a three-dimensional solid.
Introduced in 3.1 Volume and surface area in three dimensions
Newton's law of coolingHL only · also law of cooling: The law that the rate of change of the temperature $T$ of an object is proportional to the difference between its temperature and the constant temperature $T_s$ of its surroundings, $\frac{\mathrm{d}T}{\mathrm{d}t} = -k(T - T_s)$
NodeHL only · also stable node, unstable node, nodes, improper node: An equilibrium point of a linear system whose eigenvalues are real, distinct and of the same sign; trajectories approach it (stable node, both negative) or leave it (unstable node, both positive) without circling it, tangent to an eigenvector.
Introduced in 5.17 Phase portraits
Nominal annual interest ratealso nominal interest rate, nominal rate, annual interest rate, I%, nominal annual rate: The yearly interest rate $r\%$ as quoted, before it is divided by the number of times interest is added in a year.
Introduced in 1.4 Financial applications of geometric sequences
Non-commutativityHL only · also non-commutative, AB ≠ BA, matrix multiplication is not commutative: The property that the order of the factors in a matrix product matters, so that in general $AB \ne BA$ .
Introduced in 1.14 Matrices
Non-linear regressionHL only · also nonlinear regression, curve fitting, non linear regression: The process of fitting a curve that is not a straight line, such as a quadratic, cubic, exponential, power or sine function, to bivariate data by choosing the values of its parameters that give the closest fit.
Introduced in 4.13 Non-linear regression
Non-right-angled trianglealso oblique triangle, non-right triangle, non right-angled triangle: A triangle in which none of the three angles is 90°.
Introduced in 3.2 Trigonometry in triangles
Non-singular matrixHL only · also invertible matrix, non-singular, invertible, non-singular matrices: A square matrix whose determinant is not 0, so that it has an inverse.
Introduced in 1.14 Matrices
Non-stationary point of inflexionHL only · also non-horizontal point of inflexion, oblique point of inflexion, non-stationary inflexion: A point of inflexion at which the gradient is not zero, so that $f'(a) \ne 0$ while $f''$
Normal curvealso bell curve, bell-shaped curve, normal distribution curve, Gaussian curve: The symmetric bell-shaped graph of a normal distribution, in which the area under the curve between two values equals the probability that the variable lies between them.
Introduced in 4.9 The normal distribution
Normal distributionalso normal distributions, Gaussian distribution, normally distributed, N(μ, σ²): A continuous probability distribution that is symmetric and bell-shaped about its mean $\mu$ , with spread given by its standard deviation $\sigma$ ; it is written $X \sim \mathrm{N}(\mu, \sigma^2)$ .
Introduced in 4.9 The normal distribution
Normal probabilityalso normal probabilities, area under the normal curve, normal cdf, normalcdf: The probability that a normally distributed variable lies in a given interval, equal to the area under the normal curve over that interval.
Introduced in 4.9 The normal distribution
Normal to a curvealso normal line, normals, normal to the curve: The straight line through a point on a curve that is perpendicular to the tangent at that point; at $(a, f(a))$ on $y = f(x)$ its gradient is $-\frac{1}{f'(a)}$
Normal vectorHL only · also normal, unit normal vector, vector normal to a plane, normal to a plane, normal vectors: A non-zero vector perpendicular to a plane, or to every vector lying in that plane; $\boldsymbol{v} \times \boldsymbol{w}$ is a normal to the plane containing $\boldsymbol{v}$ and $\boldsymbol{w}$ , and dividing it by its magnitude gives a unit normal vector $\boldsymbol{n}$
NormalizingHL only · also normalising, normalize, normalise, normalized vector, normalised vector: Dividing a non-zero vector by its magnitude to give the unit vector in the same direction, $\frac{\boldsymbol{v}}{|\boldsymbol{v}|}$ .
Introduced in 3.10 Vectors
NP-hardHL only · also NP-hard problem: Describes a problem that is at least as hard as every problem in a large class of problems whose solutions can be checked quickly; no known algorithm solves every instance of an NP-hard problem in a time that grows only as a power of the problem's size.
Introduced in 3.16 Tree and cycle algorithms
Nth rootHL only · also n-th root, cube root, fourth root, radical, nth roots: For a positive integer $n$ , the $n$ th root of a number $a$ , written $\sqrt[n]{a}$
Null hypothesisalso H0, H₀, null hypotheses: The statement of no difference, no association or no change from a model, written $\mathrm{H}_0$ , that is assumed true while a hypothesis test is carried out.
Introduced in 4.11 Hypothesis testing
NullclineHL only · also zero-gradient curve, curve where dy/dx = 0, nullclines, zero isocline: The isocline on which $\frac{\mathrm{d}y}{\mathrm{d}x} = 0$ , with equation $f(x, y) = 0$
Numerical integrationalso numerical integration methods, numerical method for integrals, approximate integration: The estimation of a definite integral, or of the area it represents, from values of the function at a finite number of points instead of from an anti-derivative.
Introduced in 5.8 The trapezoidal rule
Numerical solutionHL only · also numerical method, numerical solutions, approximate solution: A table of approximate values of the solution of an equation, produced by a step-by-step calculation, instead of an exact formula.
Introduced in 5.16 Euler’s method