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

(a)  

a combination of numbers and letters equivalent to a phrase in language, e.g. x² + 3x - 4

(a)  

a combination of numbers and letters equivalent to a sentence in language, e.g. y = x² + 3x - 4

(a)  

a step by step procedure by which an operation can be carried out

(a)  

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

(a)  

pairs of numbers for which the sum of the divisors of one number equals the other number, e.g. 220 and 284, 1184 and 1210

(a)  

grounded in the rigorous formulation of calculus, (a)   is the branch of pure mathematics concerned with the notion of a limit (whether of a sequence or of a function)

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)

(a)  

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

(a)  

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

(a)  

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

(a)  

the number of unique digits (including zero) that a positional numeral system uses to represent numbers, e.g. 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; et

(a)  

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

(a)  

the shape of the graph that indicates a normal distribution in probability and statistics

(a)  

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

(a)  

a polynomial algebraic expression or equation with just two terms

(a)  

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

(a)  

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

(a)  

the ratio of a circumference of a circle to its diameter, an irrational (and transcendental) number approximately equal to 3.141593...

(a)  

a collection of distinct objects or numbers, without regard to their order, considered as an object in its own right

(a)  

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

(a)  

the n-th root a number, such as √5, the cube root of 7, etc.

(a)  

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

(a)  

a mathematical structure consisting of a set together with an operation that combines any two of its elements to form a third element, e.g. the set of integers and the addition operation form a group

(a)  

the point towards which a series or function converges

(a)  

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)

(a)  

a flat two-dimensional surface (physical or theoretical) with infinite width and length, zero thickness and zero curvature

(a)  

the steepness or incline of a line, determined by reference to two points on the line, e.g. 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

(a)  

a number that will divide into another number exactly

(a)  

a rectangular array of numbers, which can be added, subtracted and multiplied, and used to represent linear transformations and vectors, solve equations, etc.

(a)  

a subsidiary collection of objects that all belong to, or is contained in, an original given set

(a)  

a collection of numbers at every point in space which describe how much the space is curved, e.g. 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

(a)  

a physical quantity having magnitude and direction, represented by a directed arrow indicating its orientation in space

(a)  

a member of, or an object in, a set

(a)  

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)

(a)  

a rule or equation describing the relationship of two or more variables or quantities

(a)  

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

(a)  

a number by which two given numbers can be divided by integer division, and produce the same remainder

(a)  

a statement that appears to contradict itself, suggesting a solution which is actually impossible

(a)  

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

(a)  

a branch of mathematics involving derivatives and integrals, used to study motion and changing values

(a)  

a way of writing rational numbers (numbers that are not whole numbers), also used to represent ratios or division

(a)  

a relation or correspondence between two sets in which one element of the second set is assigned to each element of the first set

(a)  

the part of mathematics concerned with the size, shape and relative position of figures, or the study of lines, angles, shapes and their properties

(a)  

an equality that remains true regardless of the values of any variables that appear within it

(a)  

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

(a)  

whole numbers, both positive (natural numbers) and negative, including zero

(a)  

the area bounded by a graph or curve of a function and the x axis, between two given values of x, found by the operation of integration

(a)  

the theory that mathematics is just an extension of logic, and that therefore some or all mathematics is reducible to logic

(a)  

a topological space or surface which, on a small enough scale, resembles the Euclidean space of a specific dimension

(a)  

an algebraic expression consisting of a single term (although that term could be an exponent)

(a)  

a type of conic section curve, any point of which is equally distant from a fixed focus point and a fixed straight line

(a)  

an ordered set whose elements are usually determined based on some function of the counting numbers

(a)  

the correspondence in size, form or arrangement of parts on a plane or line

(a)  

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)

(a)  

the product of all the consecutive integers up to a given number (used to give the number of permutations of a set of objects),

(a)  

the inverse operation to exponentiation, the exponent of a power to which a base

(a)  

an algebraic equation with 3 terms, e.g. 3x + 5y + 8z; 3x3 + 2x2 + x; etc.

(a)  

two geometrical figures that have the same size and shape, and so one can be transformed into the other by a combination of translation, rotation and reflection

(a)  

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, e.g. (2, 3.7) or (-5, 4)

(a)  

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

(a)  

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, e.g. 5x2 - 4x + 4y + 7

(a)  

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)

(a)  

a number which, when multiplied by x yields the multiplicative identity 1, and can therefore be thought of as the inverse of multiplication

(a)  

a measure of relationship between two variables or sets of data

(a)  

the operation in calculus (inverse to the operation of differentiation) of finding the integral of a function or equation

(a)  

a particular ordering of a set of objects, e.g. given the set {1, 2, 3}, there are six (a)   : {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}

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

(a)  

the factors of the terms in a mathematical expression or equation

(a)  

the branch of mathematics that studies the relationships between the sides and the angles of right triangles, and deals with (sine, cosine, tangent and their reciprocals)

(a)  

the study of different combinations and groupings of numbers, often used in probability and statistics, as well as in scheduling problems and Sudoku puzzles

(a)  

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

(a)  

the mathematical operation where a number (the base) is multiplied by itself a specified number of times

(a)  

the operation in calculus of finding the derivative of a function or equation

(a)  

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 loop

(a)  

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

(a)  

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

(a)  

a triangle containing an angle of 90°

(a)  

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

(a)  

an extension of calculus used to search for a function which minimizes a certain functional (a functional is a function of a function)

(a)  

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

(a)  

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 up into four quadrants)

(a)  

the study of mathematical models and dynamical systems defined by iteration of functions on complex number spaces

(a)  

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)

(a)  

a number with at least one other factor besides itself and one

(a)  

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

(a)  

a fraction whose denominator contains a fraction, whose denominator in turn contains a fraction, etc., etc.

(a)  

a plane with two scaled perpendicular lines that intersect at the origin, usually designated x (horizontal axis) and y (vertical axis)

(a)  

a real number which expresses fractions on the base 10 standard numbering system using place value

(a)  

a type of reasoning where the truth of a conclusion necessarily follows from, or is a logical consequence of, the truth of the premises

(a)  

a method of representing three-dimensional objects by projections on the two dimensional plane using a specific set of procedures

(a)  

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.)

(a)  

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

(a)  

a polynomial equation with integer coefficients that also allows the variables and solutions to be integers only

(a)  

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

(a)  

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°

(a)  

a set that has no members, and therefore has zero size

(a)  

“normal” geometry based on a flat plane, in which there are parallel lines and the angles of a triangle sum to 180°

(a)  

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

(a)  

prime numbers that are one more than a power of 2 (and where the exponent is itself a power of 2)

(a)  

a set of numbers formed by adding the last two numbers to get the next in the series

(a)  

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

(a)  

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.)

(a)  

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.

(a)  

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

(a)  

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)

(a)  

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)

(a)  

the mathematical field that studies the algebraic structures and properties of groups and the mappings between them

(a)  

an influential list of 23 open (unsolved) problems in mathematics described by David Hilbert in 1900

(a)  

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°

(a)  

a smooth symmetrical curve with two branches produced by the section of a conical surface

(a)  

numbers in the form bi, where b is a real number and i is the “imaginary unit"

(a)  

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

(a)  

the sum of an infinite sequence of numbers (which are usually produced according to a certain rule, formula or algorithm)

(a)  

numbers that cannot be represented as decimals (because they would contain an infinite number of non-repeating digits) or as fractions of one integer over another

(a)  

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

(a)  

a technique in statistics and probability theory for modelling scattered data by assuming an approximate linear relationship between the dependent and independent variables

(a)  

a square array of numbers where each row, column and diagonal added up to the same total

(a)  

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)

(a)  

numbers that are one less than 2 to the power of a prime number, e.g. 3 (22 - 1); 7 (23 - 1); 31 (25 - 1); 127 (27 - 1); 8,191 (213 - 1); etc.

(a)  

prime numbers that are one less than a power of 2, e.g. 3 (22 - 1); 7 (23 - 1); 31 (25 - 1); 127 (27 - 1); 8,191 (213 - 1); etc. - many, but not all

(a)  

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)

(a)  

a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value (the modulus)

(a)  

the set of positive integers (regular whole counting numbers), sometimes including zero

(a)  

any integer, ration or real number which is less than 0

(a)  

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

(a)  

a line on which all points correspond to real numbers

(a)  

the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular

(a)  

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

(a)  

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

(a)  

a number that is the sum of its divisors (excluding the number itself), e.g. 28 = 1 + 2 + 4 + 7 + 14

(a)  

a function that repeats its values in regular intervals or periods, such as the trigonometric functions of sine, cosine, tangent, etc.

(a)  

positional notation for numbers, allowing the use of the same symbols for different orders of magnitude.

(a)  

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)

(a)  

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)

(a)  

integers greater than 1 which are only divisible by themselves and 1

(a)  

a kind of non-Euclidean geometry which considers what happens to shapes when they are projected on to a non-parallel plane

(a)  

the branch of mathematics concerned with analysis of random variables and events, and with the interpretation of probabilities

(a)  

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)

(a)  

groups of three positive integers a, b and c such that the a2 + b2 = c2 equation of Pythagoras’ theorem, e.g. ( 3, 4, 5), ( 5, 12, 13), ( 7, 24, 25), ( 8, 15, 17), etc.

(a)  

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

(a)  

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

(a)  

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

(a)  

numbers that can be expressed as a fraction a⁄b of two integers , or alternatively a decimal which terminates after a finite number of digits or begins to repeat a sequence

(a)  

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

(a)  

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)

(a)  

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)

(a)  

a set or system of equations containing multiple variables which has a solution that simultaneously satisfies all of the equations

(a)  

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 paths between points

(a)  

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, e.g. 15 = 1 + 2 + 3 + 4 + 5 = 5(5 + 1)⁄2

(a)  

a three-dimensional area where vectors can be plotted, or a mathematical structure formed by a collection of vectors

(a)  

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

(a)  

A function based on an infinite series of reciprocals of exponents

(a)  

cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite

(a)  

a branch of spherical geometry which deals with polygons (especially triangles) on the sphere, and the relationships between their sides and angles

(a)  

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

(a)  

a non-Euclidean geometry that studies curved surfaces and differentiable manifolds in higher dimensional spaces

(a)  

a non-Euclidean geometry that studies curved surfaces and differentiable manifolds in higher dimensional spaces

(a)  

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

(a)  

an algebra in which a x b does not always equal b x a, such as that used by quaternions

(a)  

geometry based on a curved plane, in which there are no parallel lines and the angles of a triangle do not sum to 180°

(a)  

a relation involving an unknown function with several independent variables and its partial derivatives with respect to those variables

(a)  

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

(a)