Study: Glossary of Mathematics Terms

Mar 15, 2020 CE

Mathematical terms and definitions.

Glossary of Mathematics Terms

| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

A⇮
Abstract Algebra the area of modern mathematics that considers algebraic structures to be sets with operations defined on them, and extends algebraic concepts usually associated with the real number system to other more general systems, such as groups, rings, fields, modules and vector spaces
Algebra a branch of mathematics that uses symbols or letters to represent variables, values or numbers, which can then be used to express operations and relationships and to solve equations
Algebraic Expression a combination of numbers and letters equivalent to a phrase in language, for example x² + 3x - 4
Algebraic Equation a combination of numbers and letters equivalent to a sentence in language, for example y = x² + 3x - 4
Algorithm a step by step procedure by which an operation can be carried out
Amicable Numbers pairs of numbers for which the sum of the divisors of one number equals the other number, for example 220 and 284, 1184 and 1210
Analytic Geometry Synonyms: Cartesian Geometry, Cartesian Geometry, Cartesian Geometry, Cartesian Geometry the study of geometry using a coordinate system and the principles of algebra and analysis, thus defining geometrical shapes in a numerical way and extracting numerical information from that representation
Analysis Synonym: Mathematical Analysis grounded in the rigorous formulation of calculus, analysis is the branch of pure mathematics concerned with the notion of a limit (whether of a sequence or of a function)
Arithmetic the part of mathematics that studies quantity, especially as the result of combining numbers (as opposed to variables) using the traditional operations of addition, subtraction, multiplication and division (the more advanced manipulation of numbers is usually known as number theory)
Associative Property property (which applies both to multiplication and addition) by which numbers can be added or multiplied in any order and still yield the same value, for example (a + b) + c = a + (b + c) or (ab)c = a(bc)
Asymptote a line that the curve of a function tends towards as the independent variable of the curve approaches some limit (usually infinity) i.e. the distance between the curve and the line approaches zero
Axiom a proposition that is not actually proved or demonstrated, but is considered to be self-evident and universally accepted as a starting point for deducing and inferring other truths and theorems, without any need of proof
B⇮
Base N the number of unique digits (including zero) that a positional numeral system uses to represent numbers, for example base 10 (decimal) uses 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in each place value position; base 2 (binary) uses just 0 and 1; base 60 (sexagesimal, as used in ancient Mesopotamia) uses all the numbers from 0 to 59; etc.
Bayesian Probability a popular interpretation of probability which evaluates the probability of a hypothesis by specifying some prior probability, and then updating in the light of new relevant data
Bell Curve the shape of the graph that indicates a normal distribution in probability and statistics
Bijection a one-to-one comparison or correspondence of the members of two sets, so that there are no unmapped elements in either set, which are therefore of the same size and cardinality
Binomial a polynomial algebraic expression or equation with just two terms, for example 2x³ - 3y = 7; x² + 4x; etc
Binomial Coefficients the coefficients of the polynomial expansion of a binomial power of the form (x + y)ⁿ, which can be arranged geometrically according to the binomioal theorem as a symmetrical triangle of numbers known as Pascal’s Triangle, for example (x + y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴ the coefficients are 1, 4, 6, 4, 1
Boolean Algebra or Logic a type of algebra which can be applied to the solution of logical problems and mathematical functions, in which the variables are logical rather than numerical, and in which the only operators are AND, OR and NOT
C⇮
Calculus Synonym: Infinitesimal Calculus a branch of mathematics involving derivatives and integrals, used to study motion and changing values
Calculus of Variations an extension of calculus used to search for a function which minimizes a certain functional (a functional is a function of a function)
Cardinal Numbers numbers used to measure the cardinality or size (but not the order) of sets - the cardinality of a finite set is just a natural number indicating the number of elements in the set; the sizes of infinite sets are described by transfinite cardinal numbers, ₀ (aleph-null), ₁ (aleph-one), etc
Cartesian Coordinates a pair of numerical coordinates which specify the position of a point on a plane based on its distance from the two fixed perpendicular axes (which, with their positive and negative values, split the plane into four quadrants)
Coefficients the factors of the terms (i.e. the numbers in front of the letters) in a mathematical expression or equation, for example in the expression 4x + 5y² + 3z, the coefficients for x, y² and z are 4, 5 and 3 respectively
Combinatorics the study of different combinations and groupings of numbers, often used in probability and statistics, as well as in scheduling problems and Sudoku puzzles
Complex Dynamics the study of mathematical models and dynamical systems defined by iteration of functions on complex number spaces
Complex Number "a number expressed as an ordered pair comprising a real number and an imaginary number, written in the form a + bi, where a and b are real numbers, and i is the imaginary unit (equal to the square root of -1)
Composite Number a number with at least one other factor besides itself and one, i.e. not a prime number
Congruence two geometrical figures are congruent to one another if they have the same size and shape, and so one can be transformed into the other by a combination of translation, rotation and reflection
Conic Section the section or curve formed by the intersection of a plane and a cone (or conical surface), depending on the angle of the plane it could be an ellipse, a hyperbola or a parabola
Continued Fraction a fraction whose denominator contains a fraction, whose denominator in turn contains a fraction, etc.
Coordinate the ordered pair that gives the location or position of a point on a coordinate plane, determined by the point’s distance from the x and y axes, for example (2, 3.7) or (-5, 4)
Coordinate Plane a plane with two scaled perpendicular lines that intersect at the origin, usually designated x (horizontal axis) and y (vertical axis)
Correlation a measure of relationship between two variables or sets of data, a positive correlation coefficient indicating that one variable tends to increase or decrease as the other does, and a negative correlation coefficient indicating that one variable tends to increase as the other decreases and vice versa
Cubic Equation a polynomial having a degree of 3 (i.e. the highest power is 3), of the form ax³ + bx² + cx + d = 0, which can be solved by factorization or formula to find its three roots
D⇮
Decimal Number Synonym: Decimal Fraction a fraction in the standard (base 10) numbering system, for example the fraction $\dfrac{37}{100}$ can be written $0.37$ in decimal notation.
Decimal Number System Synonym: Hindu-Arabic Number System the Decimal Number System, also called Hindu-Arabic number system, is a positional numeral system that uses 10 as the base and requires 10 different symbols which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It also uses a dot (the decimal point) to represent fractions. In this system, the numerals used to show a value take different place values depending upon position. In a base-10 system the number 543.21 represents the sum: \begin{array}{} (5 \times 10^2) &+ &(4 \times 10^1) &+ &(3 \times 10^0) &+ &(2 \times 10^{−1}) &+ &(1 \times 10^{−2}) \\ 500 &+ &40 &+ &3 &+ &0.2 &+ &0.001 \end{array}
Decimal Point A point (.) used to separate the whole and fractional parts of a decimal number, for example between the 3 (whole part) and 4 (fractional part) in $3.4$.
Deductive Reasoning or Logic a type of reasoning where the truth of a conclusion necessarily follows from, or is a logical consequence of, the truth of the premises (as opposed to inductive reasoning)
Denominator the number (or experession) below the line in a fraction, such as the $2$ in $\dfrac{1}{2}$, and $(x - 4)$ in $\dfrac{(x + 3)}{(x - 4)}$
Derivative a measure of how a function or curve changes as its input changes, i.e. the best linear approximation of the function at a particular input value, as represented by the slope of the tangent line to the graph of the function at that point, found by the operation of differentiation
Descriptive Geometry a method of representing three-dimensional objects by projections on the two-dimensional plane using a specific set of procedures
Differential Equation an equation that expresses a relationship between a function and its derivative, the solution of which is not a single value but a function (has many applications in engineering, physics economics, etc)
Differential Geometry a field of mathematics that uses the methods of differential and integral calculus (as well as linear and multilinear algebra) to study the geometry of curves and surfaces
Differentiation the operation in calculus (inverse to the operation of integration) of finding the derivative of a function or equation
Diophantine Equation a polynomial equation with integer coefficients that also allows the variables and solutions to be integers only
Distributive Property property whereby summing two numbers and then multiplying by another number yields the same value as multiplying both values by the other value and then adding them together, for example a(b + c) = ab + ac
Dividend the number being divided, for example 12 is the dividend in $12 \div 3 = 4$.
Divisor the quantity by which another quantity, the dividend, is divided, for example 3 is the divisor in $12 \div 3 = 4$.
E⇮
Element a member of, or an object in, a set
Ellipse a plane curve resulting from the intersection of a cone by a plane, that looks like a slightly flattened circle (a circle is a special case of an ellipse)
Elliptic Geometry a non-Euclidean geometry based (at its simplest) on a spherical plane, in which there are no parallel lines and the angles of a triangle sum to more than 180°
Empty (Null) Set a set that has no members, and therefore has zero size, usually represented by {} or ø
Equivalent Fractions two or more fractions having the same value, such as $\dfrac{2}{4}$ and $\dfrac{8}{16}$
Euclidean Geometry “normal” geometry based on a flat plane, in which there are parallel lines and the angles of a triangle sum to 180°
Expected Value the amount predicted to be gained, using the calculation for average expected payoff, which can be calculated as the integral of a random variable with respect to its probability measure (the expected value may not actually be the most probable value and may not even exist, for example 2.5 children)
Exponentiation the mathematical operation where a number (the base) is multiplied by itself a specified number of times (the exponent), usually written as a superscript aⁿ, where a is the base and n is the exponent, for example 4³ = 4 x 4 x 4
F⇮
Factor a number that will divide into another number exactly, for example the factors of 10 are 1, 2 and 5
Factorial the product of all the consecutive integers up to a given number (used to give the number of permutations of a set of objects), denoted by n!, for example 5! = 1 x 2 x 3 x 4 x 5 = 120
Fermat Primes prime numbers that are one more than a power of 2 (and where the exponent is itself a power of 2), for example 3 (2¹ + 1), 5 (2² + 1), 17 (2⁴ + 1), 257 (2⁸ + 1), 65,537 (2¹⁶ + 1), etc
Fibonacci Numbers Synonym: Fibonacci Series a set of numbers formed by adding the last two numbers to get the next in the series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Finite Differences a method of approximating the derivative or slope of a function using approximately equivalent difference quotients (the function difference divided by the point difference) for small differences
Formula a rule or equation describing the relationship of two or more variables or quantities, for example A = πr²
Fourier Series an approximation of more complex periodic functions (such as square or saw-tooth functions) by adding together various simple trigonometric functions (e.g. sine, cosine, tangent, etc)
Fraction a way of writing rational numbers (numbers that are not whole numbers), also used to represent ratios or division, in the form of a numerator over a denominator, for example ³⁄₅ (a unit fraction is a fraction whose numerator is 1)
Fractal a self-similar geometric shape (one that appears similar at all levels of magnification) produced by an equation that undergoes repeated iterative steps or recursion
Function a relation or correspondence between two sets in which one element of the second (codomain or range) set ƒ(x) is assigned to each element of the first (domain) set x, for example ƒ(x) = x² or y = x² assigns a value to ƒ(x) or y based on the square of each value of x
G⇮
Game Theory a branch of mathematics that attempts to mathematically capture behaviour in strategic situations, in which an individual's success in making choices depends on the choices of others, with applications in the areas of economics, politics, biology, engineering, etc
Gaussian Curvature an intrinsic measure of the curvature of a point on a surface, dependent only on how distances are measured on the surface and not on the way it is embedded in space
Geometry the part of mathematics concerned with the size, shape and relative position of figures, or the study of lines, angles, shapes and their properties
Golden Ratio Synonyms: Golden Mean, Divine Proportion the ratio of two quantities (equivalent to approximately 1 : 1.6180339887) where the ratio of the sum of the quantities to the larger quantity equals the ratio of the larger quantity to the smaller one, usually denoted by the Greek letter phi φ (phi)
Graph Theory a branch of mathematics focusing on the properties of a variety of graphs (meaning visual representations of data and their relationships, as opposed to graphs of functions on a Cartesian plane)
Greatest Common Denominator (GCD) The largest number that goes evenly into two or more fractions
Group a mathematical structure consisting of a set together with an operation that combines any two of its elements to form a third element, for example the set of integers and the addition operation form a group
Group Theory the mathematical field that studies the algebraic structures and properties of groups and the mappings between them
H⇮
Hilbert Problems an influential list of 23 open (unsolved) problems in mathematics described by David Hilbert in 1900
Hyperbola a smooth symmetrical curve with two branches produced by the section of a conical surface
Hyperbolic Geometry a non-Euclidean geometry based on a saddle-shaped plane, in which there are no parallel lines and the angles of a triangle sum to less than 180°
I⇮
Identity an equality that remains true regardless of the values of any variables that appear within it, for example for multiplication, the identity is one; for addition, the identity is zero
Imaginary Numbers numbers in the form bi, where b is a real number and i is the “imaginary unit”, equal to √-1 (i.e. i² = -1)
Inductive Reasoning or Logic a type of reasoning that involves moving from a set of specific facts to a general conclusion, indicating some degree of support for the conclusion without actually ensuring its truth
Inequality two or more values or expressions that are NOT equal, for example, "2 is less than (or not equal) to 3", ($2 \lt 3$)
Infinite Series the sum of an infinite sequence of numbers (which are usually produced according to a certain rule, formula or algorithm)
Infinitesimal quantities or objects so small that there is no way to see them or to measure them, so that for all practical purposes they approach zero as a limit (an idea used in the developement of infinitesimal calculus)
Infinity a quantity or set of numbers without bound, limit or end, whether countably infinite like the set of integers, or uncountably infinite like the set of real numbers (represented by the symbol ∞)
Integers whole numbers, both positive (natural numbers) and negative, including zero
Integral the area bounded by a graph or curve of a function and the x axis, between two given values of x (definite integral), found by the operation of integration
Integration the operation in calculus (inverse to the operation of differentiation) of finding the integral of a function or equation
Irrational Numbers numbers that can not be represented as decimals (because they would contain an infinite number of non-repeating digits) or as fractions of one integer over another, for example π, √2, e
J⇮
Julia Set the set of points for a function of the form z² + c (where c is a complex parameter), such that a small perturbation can cause drastic changes in the sequence of iterated function values and iterations will either approach zero, approach infinity or get trapped in a loop
K⇮
Knot Theory an area of topology that studies mathematical knots (a knot is a closed curve in space formed by interlacing a piece of “string” and joining the ends)
L⇮
Least Squares Method a method of regression analysis used in probability theory and statistics to fit a curve-of-best-fit to observed data by minimizing the sum of the squares of the differences between the observed values and the values provided by the model
Limit the point towards which a series or function converges, for example as x becomes closer and closer to zero, ^{(sin x)}⁄_x becomes closer and closer to the limit of 1
Line in geometry, a one-dimensional figure following a continuous straight path joining two or more points, whether infinite in both directions or just a line segment bounded by two distinct end points
Linear Equation an algebraic equation in which each term is either a constant or the product of a constant and the first power of a single variable, and whose graph is therefore a straight line, for example y = 4, y = 5x + 3
Linear Regression a technique in statistics and probability theory for modelling scattered data by assuming an approximate linear relationship between the dependent and independent variables
Least Common Multiple (LCM) the smallest number that is a product of two or more other numbers, for example the LCM of 2 and 5 is 10
Logarithm the inverse operation to exponentiation, the exponent of a power to which a base (usually 10 or e for natural logarithms) must be raised to produce a given number, for example because 1,000 = 10³, the log₁₀ 100 = 3
Logic the study of the formal laws of reasoning (mathematical logic the application of the techniques of formal logic to mathematics and mathematical reasoning, and vice versa)
Logicism the theory that mathematics is just an extension of logic, and that therefore some or all mathematics is reducible to logic
M⇮
Magic Square a square array of numbers where each row, column and diagonal added up to the same total, known as the magic sum or constant (a semi-magic square is a square numbers where just the rows and columns, but not both diagonals, sum to a constant)
Mandelbrot Set a set of points in the complex plane, the boundary of which forms a fractal, based on all the possible c points and Julia sets of a function of the form z² + c (where c is a complex parameter)
Manifold a topological space or surface which, on a small enough scale, resembles the Euclidean space of a specific dimension (called the dimension of the manifold), for example a line and a circle are one-dimensional manifolds; a plane and the surface of a sphere are two-dimensional manifolds; etc
Matrix a rectangular array of numbers, which can be added, subtracted and multiplied, and used to represent linear transformations and vectors, solve equations, etc
Mersenne Number numbers that are one less than 2 to the power of a prime number, for example 3 (2² - 1); 7 (2³ - 1); 31 (2⁵ - 1); 127 (2⁷ - 1); 8,191 (2¹³ - 1); etc
Mersenne Primes prime numbers that are one less than a power of 2, for example 3 (2² - 1); 7 (2³ - 1); 31 (2⁵ - 1); 127 (2⁷ - 1); 8,191 (2¹³ - 1); etc - many, but not all, Mersenne numbers are primes, for example 2,047 = 2¹¹ - 1 = 23 x 89, so 2,047 is a Mersenne number but not a Mersenne prime
Method of Exhaustion a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape (a precursor to the methods of calculus)
Mixed Number a value made of both a whole number and a fraction, such as $12\dfrac{3}{5}$
Modular Arithmetic a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value (the modulus), for example on a 12-hour clock, 15 o’clock is actually 3 o’clock (15 = 3 mod 12)
Modulus a number by which two given numbers can be divided by integer division, and produce the same remainder, for example 38 ÷ 12 = 3 remainder 2, and 26 ÷ 12 = 2 remainder 2, therefore 38 and 26 are congruent modulo 12, or (38 ≡ 26) mod 12
Monomial an algebraic expression consisting of a single term (although that term could be an exponent), for example y = 7x, y = 2x³
Multiplicative Inverse a number that when multiplied by the original gives the product of 1, such as $\dfrac{1}{2} \times \dfrac{2}{1} = 1$
N⇮
Natural Numbers the set of positive integers (regular whole counting numbers), sometimes including zero
Negative Numbers any integer, ration or real number which is less than 0, for example -743, -1.4, -√5 (but not √-1, which is an imaginary or complex number)
Non-Commutative Algebra an algebra in which a x b does not always equal b x a, such as that used by quaternions
Non-Euclidean Geometry geometry based on a curved plane, whether elliptic (spherical) or hyperbolic (saddle-shaped), in which there are no parallel lines and the angles of a triangle do not sum to 180°
Normal (Gaussian) Distribution a continuous probability distribution in probability theory and statistics that describes data which clusters around the mean in a curved “bell curve”, highest in the middle and quickly tapering off to each side
Numerator the number or expression above the line in a fraction, such as the 5 in $\dfrac{5}{25}$
Number Line a line on which all points correspond to real numbers to +/- infinity; includes all: * integers $( ... 3,2,1,0,1,2,3 ... )$, * rational numbers $ ( -\\frac{1}{2}, \\frac{4}{7}, \\frac{23}{6}, \\textit{etc} ) $, and * irrational numbers $ ( \\pi, \\sqrt{2}, \\sqrt{5}, \textit{etc.} ) $
Number Theory the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular
O⇮
Ordinal Numbers an extension of the natural numbers (different from integers and from cardinal numbers) used to describe the order type of sets, i.e. the order of elements within a set or series
P⇮
Parabola a type of conic section curve, any point of which is equally distant from a fixed focus point and a fixed straight line
Paradox a statement that appears to contradict itself, suggesting a solution which is actually impossible
Partial Differential Equation a relation involving an unknown function with several independent variables and its partial derivatives with respect to those variables
Pascal’s Triangle a geometrical arrangement of the coefficients of the polynomial expansion of a binomial power of the form (x + y)ⁿ as a symmetrical triangle of numbers
Perfect Number a number that is the sum of its divisors (excluding the number itself), for example 28 = 1 + 2 + 4 + 7 + 14
Periodic Function a function that repeats its values in regular intervals or periods, such as the trigonometric functions of sine, cosine, tangent, etc
Permutation a particular ordering of a set of objects, for example given the set {1, 2, 3}, there are six permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}
Pi the ratio of a circumference of a circle to its diameter, an irrational (and transcendental) number approximately equal to 3.141593...
Place Value positional notation for numbers, allowing the use of the same symbols for different orders of magnitude, for example the "one's place" ($1$), "ten's place" ($10$), "hundred's place" ($100$), etc.
Platonic Solids the five regular convex polyhedra (symmetrical 3-dimensional shapes): the tetrahedron (made up of 4 regular triangles), the octahedron (made up of 8 triangles), the icosahedron (made up of 20 triangles), the cube (made up of 6 squares) and the dodecahedron (made up of 12 pentagons)
Prime Factors the factors of a number that are prime numbers
Polar Coordinates a two-dimensional coordinate system in which each point on a plane is determined by its distance r from a fixed point (e.g. the origin) and its angle θ (theta) from a fixed direction (e.g the x axis)
Polynomial an algebraic expression or equation with more than one term, constructed from variables and constants using only the operations of addition, subtraction, multiplication and non-negative whole-number exponents, for example 5x² - 4x + 4y + 7
Prime Numbers integers greater than 1 which are only divisible by themselves and 1
Projective Geometry a kind of non-Euclidean geometry which considers what happens to shapes when they are projected on to a non-parallel plane, for example a circle may be projected into an ellipse or a hyperbola
Plane a flat two-dimensional surface (physical or theoretical) with infinite width and length, zero thickness and zero curvature
Probability Theory the branch of mathematics concerned with analysis of random variables and events, and with the interpretation of probabilities (the likelihood of an event happening)
Pythagorean Theorem the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the two sides (a² + b² = c²)
Pythagorean Triples "groups of three positive integers a, b and c such that the a² + b² = c² equation of Pythagoras’ theorem, for example ( 3, 4, 5), ( 5, 12, 13), ( 7, 24, 25), ( 8, 15, 17), etc
Q⇮
Quadratic Equation a polynomial equation with a degree of 2 (i.e. the highest power is 2), of the form ax² + bx + c = 0, which can be solved by various methods including factoring, completing the square, graphing, Newton's method and the quadratic formula
Quadrature the act of squaring, or finding a square equal in area to a given figure, or finding the area of a geometrical figure or the area under a curve (such as by a process of numerical integration)
Quartic Equation a polynomial having a degree of 4 (i.e. the highest power is 4), of the form ax⁴ + bx³ + cx² + dx + e = 0, the highest order polynomial equation that can be solved by factorization into radicals by a general formula
Quaternions a number system that extends complex numbers to four dimensions (so that an object is described by a real number and three complex numbers, all mutually perpendicular to each other), which can be used to represent a three-dimensional rotation by just an angle and a vector
Quintic Equation a polynomial having a degree of 5 (i.e. the highest power is 5), of the form ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0, not solvable by factorization into radicals for all rational numbers
Quotient the solution to a division problem, for example 4 is the quotient in $12 \div 3 = 4$.
R⇮
Rational Numbers numbers that can be expressed as a fraction (or ratio) ^a⁄_b of two integers (the integers are therefore a subset of the rationals), or alternatively a decimal which terminates after a finite number of digits or begins to repeat a sequence
Real Numbers all numbers (including natural numbers, integers, decimals, rational numbers and irrational numbers) which do not involve imaginary numbers (multiples of the imaginary unit i, or the square root of -1), may be thought of as all points on an infinitely long number line
Reciprocal a number which, when multiplied by x yields the multiplicative identity 1, and can therefore be thought of as the inverse of multiplication, for example the reciprocal of x is ¹⁄_x, the reciprocal of ³⁄₅ is ⁵⁄₃
Repeating Decimal a decimal number with a digit, or group of digits to the right of the decimal point that repeat infinitely, such as $4.605605605...$; the repeating digits cannot all be zero; 1.000000 is not considered a repeating decimal even though we can add an infinite number of 0s after the decimal point.
Riemannian Geometry a non-Euclidean geometry that studies curved surfaces and differentiable manifolds in higher dimensional spaces
Right Triangle a triangle (three sided polygon) containing an angle of 90°
S⇮
Self-Similarity object is exactly or approximately similar to a part of itself (in fractals, the shapes of lines at different iterations look like smaller versions of earlier shapes)
Sequence an ordered set whose elements are usually determined based on some function of the counting numbers, for example a geometric sequence is a set where each element is a multiple of the previous element; an arithmetic sequence is a set where each element is the previous element plus or minus a number
Set a collection of distinct objects or numbers, without regard to their order, considered as an object in its own right
Significant Digits the number of digits to consider when using measuring numbers, those digits that carry meaning contributing to its precision (i.e. ignoring leading and trailing zeros)
Simultaneous Equations a set or system of equations containing multiple variables which has a solution that simultaneously satisfies all of the equations (e.g. the set of simultaneous linear equations 2x + y = 8 and x + y = 6, has a solution x = 2 and y = 4)
Slope the steepness or incline of a line, determined by reference to two points on the line, for example the slope of the line y = mx + b is m, and represents the rate at which y is changing per unit of change in x
Spherical Geometry a type of non-Euclidean (elliptic) geometry using the two-dimensional surface of a sphere, where a curved geodesic (not a straight line) is the shortest path between points
Spherical Trigonometry a branch of spherical geometry which deals with polygons (especially triangles) on the sphere, and the relationships between their sides and angles
Subset a subsidiary collection of objects that all belong to, or is contained in, an original given set, for example subsets of $\{ a \}$ and $\{ b \}$ could include $\{ a \}$, $\{ b \}$, $\{a, b \}$ and $\{ \}$
Surd the n-th root a number, such as √5, the cube root of 7, etc
Symmetry the correspondence in size, form or arrangement of parts on a plane or line (line symmetry is where each point on one side of a line has a corresponding point on the opposite side, for example a picture a butterfly with wings that are identical on either side; plane symmetry refers to similar figures being repeated at different but regular locations on the plane)
T⇮
Tensor a collection of numbers at every point in space which describe how much the space is curved, for example in four spatial dimensions, a collection of ten numbers is needed at each point to describe the properties of the mathematical space or manifold, no matter how distorted it may be
Term in an algebraic expression or equation, either a single number or variable, or the product of several numbers and variables separated from another term by a + or - sign, for example in the expression 3 + 4x + 5yzw, the 3, the 4x and the 5yzw are all separate terms
Terminating Decimal a decimal number that has a finite number of digits. All terminating decimals can be writtn in the form of a fraction. Terminating decimal: $\dfrac{1}{4} = 0.25$ Non-terminating decimal:$\dfrac{1}{3} = 0.3333333...$ Repeating decimal:$\dfrac{1}{11} = 0.09090909...$
Theorem a mathematical statement or hypothesis which has been proved on the basis of previously established theorems and previously accepted axioms, effectively the proof of the truth of a statement or expression
Topology the field of mathematics concerned with spatial properties that are preserved under continuous deformations of objects (such as stretching, bending and morphing, but not tearing or gluing)
Transcendental Number an irrational number that is “not algebraic”, i.e. no finite sequence of algebraic operations on integers (such as powers, roots, sums, etc.) can be equal to its value, examples being π and e. For example, √2 is irrational but not transcendental because it is the solution to the polynomial x² = 2.
Transfinite Numbers cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite
Triangular Number a number which can be represented as an equilateral triangle of dots, and is the sum of all the consecutive numbers up to its largest prime factor - it can also be calculated as ^{n(n + 1)}⁄₂, for example 15 = 1 + 2 + 3 + 4 + 5 = ^{5(5 + 1)}⁄₂
Trigonometry the branch of mathematics that studies the relationships between the sides and the angles of right triangles, and deals with and with the trigonometric functions (sine, cosine, tangent and their reciprocals)
Trinomial an algebraic equation with 3 terms, for example 3x + 5y + 8z; 3x³ + 2x² + x; etc
Type Theory an alternative to naive set theory in which all mathematical entities are assigned to a type within a hierarchy of types, so that objects of a given type are built exclusively from objects of preceding types lower in the hierarchy, thus preventing loops and paradoxes
U⇮
Unit equlalent to the value of 1.
V⇮
Vector a physical quantity having magnitude and direction, represented by a directed arrow indicating its orientation in space
Vector Space a three-dimensional area where vectors can be plotted, or a mathematical structure formed by a collection of vectors
Venn Diagram a diagram where sets are represented as simple geometric figures (often circles), and overlapping and similar sets are represented by intersections and unions of the figures
Z⇮
Zermelo-Fraenkel Set Theory the standard form of set theory and the most common foundation of modern mathematics, based on a list of nine axioms (usually modified by a tenth, the axiom of choice) about what kinds of sets exist, commonly abbreviated together as ZFC
Zeta Function A function based on an infinite series of reciprocals of exponents (Riemann’s zeta function is the extension of Euler’s simple zeta function into the domain of complex numbers) See also Cut The Knot

Source: https://class.ronliskey.com/resources/glossary/

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Page Contents

Glossary of Mathematics Terms

A⇮

Abstract Algebra

Algebra

Algebraic Expression

Algebraic Equation

Algorithm

Amicable Numbers

Analytic Geometry

Synonyms: Cartesian Geometry, Cartesian Geometry, Cartesian Geometry, Cartesian Geometry

Analysis

Synonym: Mathematical Analysis

Arithmetic

Associative Property

Asymptote

Axiom

B⇮

Base N

Bayesian Probability

Bell Curve

Bijection

Binomial

Binomial Coefficients

Boolean Algebra or Logic

C⇮

Calculus

Synonym: Infinitesimal Calculus

Calculus of Variations

Cardinal Numbers

Cartesian Coordinates

Coefficients

Combinatorics

Complex Dynamics

Complex Number

Composite Number

Congruence

Conic Section

Continued Fraction

Coordinate

Coordinate Plane

Correlation

Cubic Equation

D⇮

Decimal Number

Synonym: Decimal Fraction

Decimal Number System

Synonym: Hindu-Arabic Number System

Decimal Point

Deductive Reasoning or Logic

Denominator

Derivative

Descriptive Geometry

Differential Equation

Differential Geometry

Differentiation

Diophantine Equation

Distributive Property

Dividend

Divisor

E⇮

Element

Ellipse

Elliptic Geometry

Empty (Null) Set

Equivalent Fractions

Euclidean Geometry

Expected Value

Exponentiation

F⇮

Factor

Factorial

Fermat Primes

Fibonacci Numbers

Synonym: Fibonacci Series

Finite Differences

Formula

Fourier Series

Fraction