Mathematics for Business and Economics GEN1201/ECN1201 L, Kalybay Aigerim

Algebra is 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 equation is a combination of numbers and letters equivalent to a sentence in language

Algebraic expression is a combination of numbers and letters equivalent to a phrase in language

Algorithm is a step by step procedure by which an operation can be carried out.

Associative property is 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

Asymptote is 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 is 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. 

Base n is 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; etc. 

Binomial is a polynomial algebraic expression or equation with just two terms

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

Coefficients are the factors of the terms (i.e. The numbers in front of the letters) in a mathematical expression or equation

Coordinate is 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). 

Cubic equation is a polynomial having a degree of 3 (i.e. The highest power is 3), which can be solved by factorization or formula to find its three roots. 

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

Derivative is 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.

Element is a member of, or an object in, a set. 

Factor is a number that will divide into another number exactly, e.g. the factors of 10 are 1, 2 and 5. 

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

Function is 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.

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

Infinity is 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 are whole numbers, both positive (natural numbers) and negative, including zero. 

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

Irrational numbers are 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, e.g. Π, √2, e. 

Limit is the point towards which a series or function converges, e.g. as x becomes closer and closer to zero, (sin x)⁄x becomes closer and closer to the limit of 1. 

Line is 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 is 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, e.g. y = 4, y = 5x + 3. 

Logarithm is 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. 

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

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

Negative numbers is any integer, ration or real number which is less than 0, e.g. -743, -1.4, -√5 (but not √-1, which is an imaginary or complex number). 

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

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

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

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

Polynomial is 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. 

Quadratic equation is a polynomial equation with a degree of 2. 

Quartic equation is a polynomial having a degree of 4. 

Rational numbers are 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 are 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.

Sequence is an ordered set whose elements are usually determined based on some function of the counting numbers, e.g. 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 is a collection of distinct objects or numbers, without regard to their order, considered as an object in its own right. 

Slope is 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.

Subset is a subsidiary collection of objects that all belong to, or is contained in, an original given set, e.g. subsets of {a, b} could include - {a}, {b}, {a, b} and {}. 

Symmetry is 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, e.g. 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). 

Term is 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, e.g. In the expression 3 + 4x + 5yzw, the 3, the 4x and the 5yzw are all separate terms.

Theorem is 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.

Trigonometry is 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).