Author: paulpatenaude

Paul Patenaude a une expérience de plus de 35 années dans l'enseignement et l'animation pédagogique en mathématiques au primaire et au secondaire, au Québec et à l'étranger. Il est auteur ou co-auteur de nombreux ouvrages dédiés à l'enseignement des mathématiques dont ce lexique des termes utilisés avec les jeunes de 5 à 17 ans. Il peaufine ce lexique depuis plus de 30 ans. Prix d'excellence du GRMS (prix Claude Janvier) en 1997, prix du meilleur article de la revue l'Envol du GRMS (prix Euler) en 1992. Il adore voyager et a déjà exploré de nombreux pays sur les cinq continents, curieux à la fois des cultures et de l'histoire. Il apprécie recevoir vos commentaires et vos questions auxquelles il s'empressera de répondre.

Carl Friedrich Gauss (1777-1855)

German mathematician, astronomer and physicist, referred to by some, such as the king of Hanover, as the "Prince of Mathematics". Carl Friedrich Gauss (1777- 1855) Gauss's range of accomplishments is so remarkable that legends, often unverified, have grown around his youth and work. The story of how he was able to find the sum of [...]

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Sophie Germain (1776-1831)

French mathematician, physicist and philosopher. Sophie Germain (1776-1831) Germain corresponded with other mathematicians of her time such as Gauss and Fourrier, after having familiarized herself with the works of Euler, Newton and Fermat. To be accepted by the scientific community of her time, she had to hide her identity, working under the pseudonym of Antoine [...]

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Hypatia of Alexandria (~355-415)

Greek mathematician and philosopher from Alexandria. Hypatia of Alexandria (~355-415) Daughter of Theon of Alexandria, commentator on Euclid’s Elements and last director of the Library of Alexandria, Hypatia was the first woman mathematician known in the history of mathematics recognized in her era, in addition to excelling in medicine and philosophy. She wrote a commentary [...]

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Eratosthenes (C. 276 BCE – C.194 BCE)

Greek astronomer, geographer, philosopher and mathematician who, at 30 years of age, was appointed chief librarian of the Library of Alexandria by the pharaoh Ptolemy III. Eratosthenes (c. 276 BCE – c. 194 BCE) He is credited with having calculated the circumference of the Earth with an error of less than 1%, which is quite [...]

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Eulerian Graph

Synonym for Eulerian cycle.

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Graph Theory

Mathematics and computer science discipline that studies representations of situations concerning relations between objects using graphs. These representations are abstract models of networks connecting these objects. These models are made up of the elements of "points", called vertices, and "connections" between these points, called arcs or edges depending on whether the graph is directed or not. The [...]

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Leonhard Euler (1707-1783)

Swiss mathematician and physicist mainly known for his contributions to the fields of infinitesimal calculus and graph theory. He is credited with having developed much of the terminology and notations used in modern mathematics, particularly in the field of functions. Leonhard Euler (1707-1783) A gifted student, Euler published his first memoir at the age of [...]

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John Venn (1834-1923)

English theologian, mathematician and logician. John Venn (1834-1923) In his logic and mathematics courses at the University of Cambridge, Venn used Euler and Carroll's representation of sets and syllogisms and replaced Euler's circles with less rigid curves, which made it possible for all attributes to be illustrated using a single, simple model. He introduced shading [...]

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Euclid (~300 B.C.)

Founder of the school of mathematics in Alexandria, Euclid likely received previous mathematical training from the Platonic Academy in Athens. He is known for having written the Elements, a fundamental work on geometry, numbers, elementary algebra, optics, etc., and one of the oldest known treatises on plane and solid geometry. This treatise, which contains thirteen [...]

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Claudius Ptolemy (C. 85 – C. 165)

Mathematician and member of the University of Alexandria from 125 to 160 and author of the Almageste (name of Arabic origin meaning "the greatest"). This work on astronomy acquired the same reputation as Euclid's Elements in geometry. Claudius Ptolemy (C. 85 – C. 165) Ptolemy's Almageste has stood the test of time. In his works [...]

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Lewis Carroll (1832-1898)

Today, Charles Lutwidge Dodgson is primarily known by his pseudonym, Lewis Carroll, author of the stories The Adventures of Alice in Wonderland and Through the Looking Glass. Dodgson was a novelist, essayist, photographer, and professor of mathematics. He was born on January 27, 1832 in Daresbury, in Cheshire, England, and he died on January 14, [...]

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Johannes Widmann (1460-1498)

Fifteenth century German mathematician who at a very young age published a book on commercial arithmetic titled Behende und hüpsche Rechenung auff allen Kauffmansschafft. This work is said to be the first printed book in which the now familiar symbols of addition, "+", and subtraction, "-" first appeared, although they were used to indicate surpluses [...]

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Georg Cantor (1845-1918)

German mathematician to whom we owe set theory. He based his theory on the principle of bijection between sets. He proved that the set of real numbers has a greater cardinality than the set of whole numbers. In other words, there are more real numbers than integers. Georg Cantor (1845-1918)

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Robert Recorde (1512-1558)

Sixteenth century Welsh mathematician who was educated at the University of Cambridge and the University of Oxford. Robert Recorde (1512-1558) In his work published in 1557, Recorde provided an introduction to algebra, used his new symbol for equality "=", and introduced the symbol for addition, "+", which was developed by the mathematician Johann Widmann.

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Incompatible Relations

Algebraic relations are said to be incompatible if they do not have any ordered pairs in common. Examples Two equations are incompatible if their solution sets are disjoints. The equations y = 2x + 1 and y = 2x + 5 correspond to two parallel lines on a Cartesian plane. These lines do not have any points [...]

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Inverse Proposition

In propositional calculation, an inverse proposition of a logical implication is an implication in which the premise and the conclusion are inverted. The inverse proposition of the inverse of an implication is the initial proposition. Example If P and Q are two propositions, then the inverse proposition of P → Q is the proposition Q → [...]

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Reciprocal

Term used to represent a reality that mirrors another one, or a reverse reality. In mathematical language, the term reciprocal has different meanings depending on the context, like in these expressions: Reciprocal pairs Reciprocal operation or reciprocal of an operation Reciprocal proposition Reciprocal of a function Reciprocal relationship

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Relationship of Congruence

Examples Two figures congruent by a rotation: Two figures congruent by a translation: Two figures congruent by a reflection:

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Interest Rate

An interest rate is the percentage of a borrowed or invested amount that is paid to the lender or the investor as repayment. Properties The nominal interest rate is the rate determined at the conclusion of a loan or investment. The periodic interest rate corresponds to the real rate divided by the number of periods of calculation (monthly: [...]

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Eccentricity of a Vertex in a Graph

Maximum distance from one vertex to all other vertices in the graph. Synonym for distance of a vertex in a graph. Example In the graph below, the eccentricity of vertex A is 3, because the maximum distance between vertex A and any other vertices on the graph is 3.

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Polar Coordinate System

In a geometric plane, the coordinate system in which a point P is identified using the coordinates of an ordered pair (r, θ), where r is the distance from the origin to the point P and θ is the angle of rotation. In a polar coordinate system, the coordinates (r, θ) of a point P are [...]

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Trigonometric Circle

Unit circle centered on the origin of a Cartesian plane.

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Zero of a Polynomial

Numerical value that causes the polynomial to vanish. Example Consider the polynomial x² – 7x + 12. The polynomial vanishes when its variable x takes on the value of 3 or 4. Therefore, the numbers 3 and 4 are the zeros of the polynomial.

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Divisibility Criterion

Synonym of divisibility rule.

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Residue

Synonym of remainder or the difference in the case of an arithmetic operation. We say that a ≡ b (mod n) if a − b is divisible by n. If r is the remainder of the division of a by n, r is called the residue a modulo n.

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Eleven

Ten plus one: 10 + 1. Polygon with eleven sides: see hendecagon.

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Seven

Polygon with seven sides: see heptagon.

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Signed Number

A number with a mathematical operation sign. Examples Integers are usually written in signed form: +2, –5. The operators or common difference of an arithmetic or geometric sequence are usually given in the form of signed numbers: +10, ×5, ÷2, etc.

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Spherical Coordinates

Triplet (ρ, θ, φ) of numbers associated with the position of a point P in a three‑dimensional space in a spherical locating system. The numbers ρ, θ and φ are the distance from P to the centre of the sphere and the angles of rotation with the x‑axis and the z‑axis. In this system, ρ represents the distance from the [...]

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Distribution Function of a Random Variable

Probability that the values \(x_i\) taken by the random variable X will be strictly less than a given value. F(\(x_i\)) = P(X ≤ \(x_i\)) A distribution function is a step function that is zero for all values \(x_i\) less than or equal to the least value of X, and equal to one for all values \(x_i\) strictly greater than the greatest [...]

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Distribution Function of a Statistical Variable

Arithmetic function in which the domain is the set of the modalities or the values of a statistical attribute. Example Consider a set of ordered pairs corresponding to the data in the table below, which illustrates the evolution of the price of a computer over the years since personal computers first appeared: Years 1982 1988 [...]

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Glide Reflection Symmetry

Transformation resulting from the composition of an orthogonal symmetry about the axis d and a translation t in the same direction as the axis d.

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Column

A vertical alignment in a grid, table, or matrix. A horizontal alignment in a grid, table or matrix is called a line or a row. Example

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Coefficient of Variation of a Population (Statistics)

Measure of dispersion of the data of a population, equal to \(\dfrac{\textrm{σ}}{\overline{\textrm{x}}}\) where σ represents the standard deviation and \(\overline{\textrm{x}}\) represents the mean of the data series. Example Distribution of people based on their mass Mass (in kg) Frequency [55, 65[ 10 [65, 75[ 12 [75, 85[ 8 [85, 95[ 4 [95, 105[ 2 Total 36 In this [...]

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Standard Deviation

Square root of the variance of a statistical variable. Symbols In the case of an entire population the standard deviation is noted as "σ". In the case of a sample population, the standard deviation is generally noted as "s". Formula In the case of an entire population, the standard deviation is found by applying this [...]

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Mean Deviation

Arithmetic mean of the deviations from the mean of the data in a distribution of a statistical variable. Notation The mean deviation of a statistical distribution is generally noted as: MD. Formules In a statistical distribution of n data (sample) with a mean of \(\overline{x}\), the mean deviation MD is given by: MD \(\dfrac{\Sigma |x_i − \overline{x} [...]

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Partition of a Set

Set \(\mathcal{P}\) of disjoint subsets of a set E with these two properties: Each subset of \(\mathcal{P}\) is not empty; The union of all the subsets of E in \(\mathcal{P}\) is equal to E. A partition of a set is a kind of classification of the elements in a set by an equivalence relationship. The concepts of [...]

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Roman Numeral

Symbols used from the time of the Roman Empire until the end of the Middle Ages in Europe. Today, Roman numerals are mainly used to write the century (XIX century, XX century… ) or to number the chapters or lessons of a book (chapters I, II, III, etc.). The names of kings and queens use [...]

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Sample

Subset of the total population of a phenomenon that we want to study. Sampling is the application of criteria and techniques to choose the sample that will be the subject of a statistical study.

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Vertex of a Polygon

Point where two sides of a polygon meet. Example The vertices of this polygon are points A, B, C and D. A polygon is usually named according to the letters that identify its vertices, which are read in a clockwise order. For example, this polygon is named polygon ABCD.

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Method of Least Squares

Process that makes it possible to define the parameters of a line of regression by calculating, for each element in the scatter plot, the distance between a given point and line and then simplifying the sum of these distances.

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Mayer Method

Process of linear regression that makes it possible to find the parameters of a line of regression by using the mean. This method is sometimes called the double mean method. It is easier to use, but not very reliable if the distribution has any outliers. The method consists of dividing a distribution of data into [...]

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Median-Median Method

Graphic linear regression process that makes it possible to find the parameters of a line of regression by using the median of the data in a distribution. The median-median method is most often used when the distribution has a large quantity of data and is particularly effective when this distribution includes inconsistent data. This method [...]

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Set of Departure of a Relation

The set of values or objects that can be used as the first components of the ordered pairs of a relation. This is not to be confused with the domain of a relation, which is the set of the first components of the ordered pairs of a relation. Therefore, given a relation ℜ from E to [...]

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Euclidean Division

Operation under which, from two whole numbers a and b called the dividend and the divisor, we find two whole numbers q and r called the quotient and the remainder of the Euclidean division, so that we find this numerical relationship: a = b × q + r, with r < b. When the remainder of the Euclidean division is zero, the dividend is a multiple of [...]

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Fractional Notation

Representation of a number or an operation on numbers, or an algebraic expression in the form of a division or a quotient of two numbers, numerical expressions, or algebraic expressions. Notation Fractional notation uses the horizontal bar to separate the two arguments of the expression. Examples These expressions are all written in fractional notation: \(\dfrac{9}{7}\), [...]

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Dividing Fractions

 

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Proper Divisor

Integral divisor of a whole number that is different from itself. Property The set of proper divisors of a prime number is the singleton {1}. Notation The set of proper divisors of a number n is noted as divp(n). Example The set of proper divisors of 60 is: divp(60) = {1, 2, 3, 4, 5, [...]

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Prime Divisor

A prime number that exactly divides a given number. Integral divisor of a whole number that is a prime number. Examples The prime divisors of 15 are: {3, 5} The prime divisors of 18 are: {2, 3} The prime divisors of 42 are: {2, 3, 7} The set of prime divisors of 60 is {2, 3, [...]

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Integral Divisor

If the terms a and b of a division are non-zero whole numbers, with a ≥ b, then b is a whole divisor of a if and only if the remainder of the division is zero. Similarly, if the terms a and b of a division are non-zero integers, with a ≥ b, then b [...]

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Radius of a Graph

Distance from the centre of a graph. Example In this graph, because any vertex can be connected to any other by a chain of two edges, they are all centres of the graph and their distance is 2. Therefore, the radius of this graph is 2.

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Centre of a Graph

In a given graph, the centre is the vertex in which the distance is minimal. A graph can have several centres. The distance to the centre of a graph is called the radius of the graph. Example In this graph, because all of the vertices can be connected to any of the other ones by [...]

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Distance of a Vertex in a Graph

Maximum distance between a given vertex and the other vertices in a graph. Synonym for eccentricity of a vertex in a graph. The distance of the vertex in a graph is the length of the longest chain between this vertex and any other vertex in the graph. If the graph is not connected, the distance [...]

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Position Parameter

Value in a distribution of a quantitative statistical attribute chosen for its representativeness of a tendency in this distribution, whether it is its centre, dominant frequency, or median position in the set of values. See also: Arithmetic mean Measure of central tendency Median of a distribution Mode

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Dispersion Parameter

Number that reflects the range of the values of a quantitative statistical attribute around a given position parameter generally the mean. See also: Measure of dispersion

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Empty Set

Set that does not contain any elements. In a Venn diagram, an empty subset is represented by a cross-hatched region. Symbol An empty set is represented by either of the symbols "Ø" or "{ }". Example In this representation, the set G \ (E ∪ F) is empty.  G \ (E ∪ F)= Ø. This empty region is cross-hatched.

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Intersection of Sets

Consider two sets A and B in a universal set U. The intersection of sets A and B is the set of elements in U that simultaneously belong to A and B. The intersection of A and B refers to both the operation and the result of this operation, which is the set of elements [...]

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Discontinuity

Property of a function that is not continuous in a given interval of its domain. If we consider an interval [m, n] of the domain of a function f of the real variable x and a value a of this interval, we say that the function f is discontinuous in this interval if f(a) is [...]

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Dimensions of a Matrix

Two numbers that represent the number of rows and the number of columns in a matrix. The term "dimensions" of a matrix is a synonym for the size of the matrix. If a matrix has 3 rows and 5 columns, then its dimensions are 3 by 5. Example The dimensions of this matrix are 3 [...]

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Dimension of a Table

Number of directions according to which the data are organized and identifiable in a space with equivalent dimensions. The elements in a table are located based on an index composed of the number of elements corresponding to the dimension of the table. The elements on a one-dimensional data table will be identified by an index [...]

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Symmetric Difference of Sets

In the universal set U, the symmetric difference of sets A and B is the set of elements belonging to either A or B but not both sets at the same time. Symbol The symbol of symmetric difference is "Δ" which is read as "delta" or "symmetric difference". Therefore, "A Δ B" is read as "A [...]

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Difference of Sets

In a universal set U, the difference between sets A and B is the set of elements of A that do not belong to B. Symbol The symbol for the difference of sets is “\” which is read as “less” or “difference.” Therefore, A \ B is read as “set A less set B” or [...]

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Difference Between Two Numbers

Result of the subtraction of two numbers. Example 15 – 7 = 8 ↓ ↓ ↓ ↓ ↓ minuend symbol for subtraction subtrahend symbol for the relationship of equality difference

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Median of a Distribution

In a distribution of the ordered values of a quantitative statistical attribute, the median is a value for which the number of values that are less than it is equal to the number of values that are greater than it. The median of a distribution is not always a datum in the distribution, especially when there [...]

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Simple Cycle

Cycle that does not use the same edge twice. Example In the undirected graph below, the cycle constituted in order by the edges a, b, c, d, h and n is a simple cycle that starts and ends at vertex A.

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Hamiltonian Cycle

Cycle that passes only once through each vertex in an undirected graph. Example In the undirected graph below, the cycle constituted in order by the edges a, b, c, d, h and n is a Hamiltonian cycle that starts and ends at vertex A.  

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Eulerian Cycle

Simple cycle that passes through all of the edges in an undirected graph. Example In this graph, the cycle that is constituted in order by the edges a, b, c, d, e, g, m, f, h and n is a Eulerian cycle that starts and ends at vertex A. It is not possible to define [...]

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Elementary Cycle

Cycle that does not pass through the same vertex twice. Example In the graph below, the cycle constituted in order by the edges a, b, e, h and n is an elementary cycle that starts and ends at vertex A.

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Linear Rule

Expression that defines a relationship of direct variation. A relationship of direct variation is defined by a rule in the form y = kx where k is a constant. Example This graph illustrates the function f defined by f(x) = –2x. In this case, the constant k is –2. We can also represent a linear relationship using a table of values: x [...]

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Decimal Part of a Real Number

Component of a real number expressed in decimal notation and located to the right of the decimal point. Example Consider the real number 907.56. The whole part of this number is 907. Its decimal part is 0.56. Consider the real number \(\sqrt{5}\). The whole part of this real number is 2. Its decimal part is 0.236 [...]

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Decimal Notation

Representation of a real number with a whole part and a decimal part (also called the fractional part) separated from one another by a decimal point. Examples The decimal notation of the number 12\(\frac{3}{4}\) is: 12.75. The whole part is 12 and the decimal part (also called the fractional part) is 0.75. The decimal notation of [...]

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Whole Part of a Real Number

Component of a real number expressed in decimal notation and located to the left of the decimal point. Example Consider the real number 907.56. The whole part of this number is 907. Its decimal part is 0.56

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Period of a Periodic Function

In a periodic function f, the least positive value of the parameter p for which we have f(x+p) = f(x). The period is a synonym for the wavelength. Example Here is the graph of the function defined by f(x) = 3sin (x) + cos (2x + 3) : In this case, the period is: p = 2π.

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Order Relation

Relation of inequality between two quantities with different values. Binary relation in a set that allows us to compare its elements to one another in a coherent way. Properties A set equipped with an order relation is an ordered set. It is also said that the relation defines an order structure or simply an order [...]

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Algebraic Structure

Cartesian product of two sets in which internal or external laws of composition and the properties of these laws are defined. Once we have defined one or more laws of composition in a set of pairs, we say that this set has an algebraic structure. Example The set \(\mathbb{Z}\) of integers equipped with the operation [...]

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Propositional Variable

Symbol that refers to a proposition in propositional calculation. Generally, we use capital letters like P, Q, R, S, …, to indicate a propositional variable. Example In the proposition composed (P ∧ Q) → R, the letters P, Q and R represent propositional variables.

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Propositional Calculation

Branch of mathematical logic in which we apply the rules and methods of calculation on propositions or propositional forms. In propositional calculation, we use the propositional variables P, Q, R, S, etc., connectors between these variables, and parentheses with which we define statements or propositions, and we choose some of them as true statements that [...]

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Statistical Calculations

Branch of applied mathematics based on experimental observations from which we establish plausible hypotheses that allow for predictions about analogous circumstances. Examples Consider the following observations of precipitation recorded during one week, in millimetres of rain: E = {1, 4, 12, 8, 0, 7, 3} The mean of this precipitation is: \(\overline{x}=\frac{1\space +\space 4\space +\space [...]

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Numerical Calculation

Calculating with real numbers according to certain rules and algorithms unique to each class of real numbers. Examples 509 + 42 = 551 1715 ÷ 35 = 49

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Literal Calculations

Calculations on literal expressions in which we apply certain rules and algorithms. See also : Probability calculations Propositional calculation Vector calculations

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Modular Arithmetic

The application of basic arithmetic to finite systems of whole numbers. In the system modulo n or a restricted system of whole numbers less than n, we use the numbers 0, 1, 2, 3, 4, …, (n – 1). The arithmetic operations defined in this system are the same as those in basic arithmetic, except [...]

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Dividing Whole Numbers

Operation under which every pair (a, b) of whole numbers, is made to correspond to a number q, called the whole quotient of a by b, and a number r, called the remainder of the division. The process of dividing whole numbers is often called Euclidean division: a = b × q + r. In this [...]

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Universal Set

In the context of a theory or a problem, the set of all elements considered. If a mathematical statement contains one or more variables, the universal set of these variables is the set of values that we can substitute for them. The universal set is often simply called the universal. Notation The symbol generally used [...]

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Probability Calculations

Methods of enumeration used in probability theory. To calculate probabilities, we apply the rules and principles that govern probability theory. Example When rolling a six-sided fair die, the possible outcomes are: Ω = {1, 2, 3, 4, 5, 6}. In this situation, the probability of getting a 3 is given by: P(3) \(=\frac{1}{6}\).

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Modal Class

Class in which the frequency is the highest in a distribution of a continuous quantitative statistical variable in which the values are grouped into classes with the same dimensions. The mode is rarely used as a measure of central tendency for continuous quantitative variables. The mode is more useful for qualitative variables because the mean [...]

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Statistical Class

Each of the successive intervals in which is divided the total interval of variation of a quantitative statistical variable. The size of these intervals is called the amplitude of the statistical class. Example Mass of 190 students at school Mass (in kg) Numbers of students [36, 38) [38, 40) [40, 42) [42, 44) [44, 46) [...]

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Median Class

Class that contains the median in a distribution of a continuous quantitative statistical variable in which the values are grouped into classes with the same dimensions. Example The median class of the distribution represented below is the class L determined by the bounds A and B, which contain the median, Med, of the distribution.

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Residue Class Modulo N

Set of numbers that have the same remainder from division by n. These numbers are called congruent modulo n. Example If we group the elements of the set H = {2, 3, 4, 6, 7, 8, 10, 11, 12} based on the relation R: … has the same remainder as… when divided by 4, we [...]

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Equivalence Class

Each subset induced in a set by a relation of equivalence defined in this set. Examples The relation of congruence modulo n in the set of integers is a relation of equivalence. If we group together the elements of E ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} based on the relation R: [...]

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Hamiltonian Circuit

Circuit that passes only once through each vertex in a directed graph. Example In this directed graph, the circuit that passes, in order, through the vertices A, B, C, D, E and A is a Hamiltonian circuit:

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Eulerian Circuit

Simple circuit that passes through all of the arcs in a directed graph. Example In this directed graph, the circuit constituted, in order, by the arcs a, b, c, d, g, e and f is a Eulerian circuit.

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Elementary Circuit

Circuit that does not pass through the same vertex twice. Example In this graph, the circuit constituted, in order, by the arcs a, b, c, d, e and n is an elementary circuit.

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Simple circuit

Circuit that does not use the same arc twice. Example In this directed graph, the circuit that passes, in order, through the arcs a, b, c, d, e and n is a simple circuit. In this directed graph, the circuit that passes, in order, through the arcs a, b, c, d, g, b, f and n is a non-simple circuit.

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Diameter of a Graph

The longest of the shortest distances between two vertices in a connected graph. When considering the shortest paths between two vertices (distance), the diameter of the graph is the number of edges in the longest of those distances. Therefore, to find the diameter of a graph, you need to start by finding the shortest path [...]

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Distance in a Graph

In a connected graph or a connected component of a disconnected graph, we call the distance between two vertices the minimum number of edges of a chain going from one to the other. Similarly, in a directed connected graph or a connected component of a directed disconnected graph, we call the distance between two vertices the [...]

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Hamiltonian Path

Path that passes only once through each of the vertices in a directed graph. Example In this directed graph, the path connecting the vertices A, B, C, D and E in order is a Hamiltonian path of length 5. It is formed by the arcs a, b, c, d and e. Note that it is not necessary for the path [...]

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Simple Path

Path that does not use the same arc twice. Examples In the directed graph below, the path, made up in order of the arcs a, c, f, d, e and h is a simple path of length 6. However, the path made up in order of the arcs a, c, f, d, c and f [...]

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Eulerian Path

Simple path that passes through all of the arcs in a directed graph. Example In the graph below, the path formed by the arcs a - b - c - d - e - f - g  is a Eulerian path of length 7.

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Elementary Path

Path that does not pass through the same vertex twice. Example In the directed graph below, the path constituted in order by the arcs a, c, f, g and h is an elementary path of length 5.

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Critical Path

In a valued and directed graph representing different operations to carry out to accomplish a task, a path in which the value is optimal (maximum or minimum depending on the context) between two vertices called the start and the end of the task. Examples In the valued and directed graph below, the critical path with [...]

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