J
Jacobian
The term Jacobian is used to denote the jacobian matrix in vector calculus. In vector calculus, the jacobian matrix is the matrix of the first order partial derivatives of a vector valued function. Conceptually, the jacobian of a function represents the orientation or inclination of a tangent plane to the function at a given point.
Joint variation
When a quantity varies directly with the other quantity then it is called as the joint variation. For example when we say x is directly proportional to the square of y, it means that x = ky2, where k = proportionality constant.
Jacobian
The term Jacobian is used to denote the jacobian matrix in vector calculus. In vector calculus, the jacobian matrix is the matrix of the first order partial derivatives of a vector valued function. Conceptually, the jacobian of a function represents the orientation or inclination of a tangent plane to the function at a given point.
Joint variation
When a quantity varies directly with the other quantity then it is called as the joint variation. For example when we say x is directly proportional to the square of y, it means that x = ky2, where k = proportionality constant.
K
Kite
A kite is nothing but a quadrilateral, with each pair of its adjacent sides congruent to each other and diagonals perpendicular to each other.
Kite
A kite is nothing but a quadrilateral, with each pair of its adjacent sides congruent to each other and diagonals perpendicular to each other.
L
L'Hospital's Rule
This is a technique that is used to find out the limit of the functions that evaluate to indeterminate forms, like 0/0 or infinity/infinity. The solution is found out by individually calculating the limits of the numerator and the denominator.
Lateral Surface Area
Lateral Surface Area is nothing but the surface area of the lateral surfaces of a solid. It does not include the area of the base(s) of the solid.
Latus Rectum
It is the line segment that passes through the focus of a conic section and is perpendicular to the major axis, with both its end points on the curve.
Law of Cosines
An equation that relates the cosine of an interior angle of a triangle to the length of its sides is called the law of cosines.
If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle between a and c and C the angle between a and b, then the law of cosines states that c2 = a2 + b2 - 2abcosC, b2 = a2 + b2 - 2accosB and a2 = b2 + c2 - 2bccosA
Law of Sine
An equation that relates the sine of an interior angle of a triangle to the length of its sides is called the law of sines.
If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle between a and c and C the angle between a and b, then the law of cosines states that
sin A/a = sin B/b = sin C/c
Least Common Multiple (LCM)
The smallest common multiple to which two or more numbers can be divided evenly. For example, the LCM of 2, 3 and 6 is 12.
Leading Coefficient
The coefficient of a polynomials leading term or the term with the variable having the highest degree.
For example, the leading coefficient of 7x4 + 5x3 + 92 + 2x +21 is 7.
Leading Term
The term of a polynomial which contains the highest value of the variable is called the leading term.
For example, the leading coefficient of 7x4 + 5x3 + 92 + 2x +21 is 7x4.
Least Common Denominator
The least common denominator is the smallest whole number that can be used as a denominator for two or more fractions. The Least Common Denominator is nothing but the Least Common Multiple of the denominators of the fractions.
For example, the least common denominator of 3/4 and 4/3 is 12. Since 3/4=6/8=9/12 and 4/3=8/6=12/9=16/12. Hence we see that the least common denominator is 12.
Least Integer Function
The least integer function of x is a step function of x, which is the least integer greater than or equal to x. This function is sometimes written with reversed boldface brackets ]x[ or reversed plain brackets ]x[.
Least Squares Regression Line
The Linear Squares Regression Line is the linear fit that matches the pattern of a set of paired data, as closely as possible. Out of all possible linear fits, the least-squares regression line is the one that has the smallest possible value for the sum of the squares of the residuals.
It is also known as Least Squares Fit and Least Squares Line.
Least-Squares Regression Equation
An equation of any form (linear, quadratic, exponential, etc) that helps in fitting a set of paired data as closely as possible is called the least squares regression equation.
Least Upper Bound of a Set
The smallest of all upper bounds of a set of number is called the Least Upper Bound.
Leg of an Isosceles Triangle
Any of the two equal sides of an isosceles triangle can be referred to as the leg of the isosceles triangle.
Leg of a Right Angle Triangle
Either of the sides of a right angle triangle, between which the right angle is formed can be referred to as the leg of the right angle triangle.
Leg of a Trapezoid
Either of the two non parallel sides of a trapezoid that join its bases can be referred to as the leg of the trapezoid.
Lemma
More accurately referred to as a helping theorem, a lemma helps in proving a theorem. But it is not important enought to be a theorem.
Lemniscate
A curve that takes form on the numerical number 8, in any orientation can be referred to as the lemniscate. Its equations are generally given in the polar coordinates. r2 = a2cos2θ.
Like Terms
Terms that have the same variables and with the same power are called like terms. The coefficients of the like terms can be directly added and subtracted. For example 5x3y2 and 135x3y2 are like terms and hence can be added directly to give the number 140x3y2.
Limacon
A limacon is a family of related curves usually expressed in polar coordinates.
Limit
The limit of a function is the value of the function as its variable tends to reach a particular value.
For example for f(x)=limx-><5>1/x2= 1/25. As x->5, the function f(x) tends to reach to 1/25.
Limit Comparison Test
The limit comparison test is performed to determine if a series is as good as a good series or as bad as a bad series. The test is used specially in cases when the terms of a series are rational functions.
Limit from Above
The limit from the above is usually taken in cases when the values of the variable is taken greater than that to which the limit approaches. For example limx->0+1/x=infinity, is taken such that the value of x>0. Limit from above is often referred to as limit from the right. This is a one sided limit.
Limit from Below
The limit from the below is usually taken in cases when the values of the variable is taken less than that to which the limit approaches. For example limx->0-1/x=-infinity, is taken such that the value of x>0. Limit from below is often referred to as limit from the left. This is a one sided limit.
Limit Involving Infinity
A limit involving infinity or an infinite limit is one whose result approaches infinity or the value of the variable approaches infinity.
Limit Test for DivergenceA limit test for divergence is a convergence test which is based upon the fact that the terms of a convergent series must have a limit of zero.
Line
A line is a geometric figure that connects two points and extends beyond both of them in both directions.
Line Segment
A line segment is nothing but the set of points between any two points including those two points.
Linear
The world linear means like a line. It is nothing but a graph or data that can be molded by a linear polynomial.
Linear Combination
A linear combination is the sum of multiples of the variables in a set. For example, for the set {x, y, z}, one possible linear combination is 7x + 3y - 4z.
Linear Equation
An equation that can be written in the form "linear polynomial" = "linear polynomial" or "linear polynomial"=constant is known as a linear equation.
For example 3x + 26y = 34 is a linear polynomial.
Linear Factorization
If a polynomial can be factorized such that the factors formed after the factorization are linear polynomials, then this factorization is known as a linear factorization. For example x2-9 can be factorized as (x+3) and (x-3).
Linear Fit Regression Line
Any line that can be used as a fit in the process to model the pattern in a set of paired data.
Linear Inequality
An inequality that can be written such that the value of a polynomial is greater than, less than, greater than equal to or less than equal to a particular number is called linear inequality. For example 3x + 7y >9.
Linear Pair of Angles
When two lines intersect each other, then the adjacent angles formed due to intersection of the two lines are called linear pair angles. The linear pair angles formed are supplementary.
Linear Polynomial
A linear polynomial is a polynomial with degree 1. The highest power of the variables involved in the polynomial should be one. For example 9x + 7 is a linear polynomial.
Linear Programming
The linear programming is an algorithm that is used for solving problems. The method of using linear programming is by asking the largest or smallest possible value of a linear polynomial. If there are any restrictions, then the system of inequalities is used to present any restriction to the equations.
Linear Regression
The process of finding a linear fit is referred to as the linear regression.
Linear System of Equations
If there are more than one equations such that each equation is a linear equation, then the system of equations will be known as linear system of equations.
For example, 2x + 3y - 5z
9x + 7y + 12x = 19
15x - 6y + 11z = 9 is a linear system of equations, that can be used to determine the values of x, y and z.
Local Behavior
The behavior of a function in the immediate neighborhood of any point is called the local behavior. The local behavior of geometric figures can also be studied with respect to a particular point.
For example, for the graph of the equation y=2x + 3, if studied closely can be said to have the local behavior of a straight line parallel to the x-axis and at a distance of 3 units from the origin.
Local Maximum
The local maximum is the highest point in a particular section of the graph. It is also often referred as the local max or relative maximum or relative max.
Local Maximum
The local minimum is the lowest point in a particular section of the graph. It is also often referred as the local min or relative minimum or relative min.
Locus
A locus is nothing but the set of points that form a particular geometric figure. For example, a circle with radius 2 cm is the locus of all points which are at a distance of 2 cms from a particular point.
Logarithm
The logarithm of x with respect to the base c is the power to which the base c must be raised in order to be equal to x. For example, logcx=z then cz=x.
Logarthmic Rules
The logarithmic rules are the algebra rules that need to be used when working with logarithms. Some of them can be listed as under:
If log x = y then 10y=x. It means that if the base of the logarithm is not mentioned then consider the base as 10.
If ln x = y then ey=x. It means that when log is replaced by ln then take the logartihm as natural logartihm and has the base e.
log 1 = 0, since whatever be the base, if raised to the power 0 then the result is always 1.
log ab = log a + log b
lob (a/b) = log a - log b
log b3 = 3log b
logax = logbx/logba
Logarithmic Differentiation
It is the type of differentiation that is used in special circumstances. For example the equation y = xtan x can be differentiated, more easily if the logarithm of both the sides are taken.
On taking the logarithm of both the sides the equation can be reduced to log y = tan x. log x (using logarithmic formula). Hence the process of differentiation becomes simple.
Logistic Growth
A logistic growth is shown by using an equation. It is used to determine the demand of products in situations where the demand increases initially, then the demand goes down and finally reaches a particular upper limit.
Long Division of Polynomials
The process of dividing polynomials is known as polynomial long division. The polynomial long division is used to divide improper rational numbers into proper rational numbers or sum of polynomials. The process of polynomial long division is same as that of long division of numbers.
Lower Bound
The lower bound of a set is any number that is less than or equal to all the numbers in a set. For example 1, 2 and 3 are all lower bounds of the interval [4, 5].
Low Quartile
The low quartile is the number for which 25% of the number is less than the number.
Least Upper Bound of a Set
The smallest of all the upper bounds of a set of numbers is called the least upper bound of the set. For example the least upper bound of the interval [9, 10] is 10.
L'Hospital's Rule
This is a technique that is used to find out the limit of the functions that evaluate to indeterminate forms, like 0/0 or infinity/infinity. The solution is found out by individually calculating the limits of the numerator and the denominator.
Lateral Surface Area
Lateral Surface Area is nothing but the surface area of the lateral surfaces of a solid. It does not include the area of the base(s) of the solid.
Latus Rectum
It is the line segment that passes through the focus of a conic section and is perpendicular to the major axis, with both its end points on the curve.
Law of Cosines
An equation that relates the cosine of an interior angle of a triangle to the length of its sides is called the law of cosines.
If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle between a and c and C the angle between a and b, then the law of cosines states that c2 = a2 + b2 - 2abcosC, b2 = a2 + b2 - 2accosB and a2 = b2 + c2 - 2bccosA
Law of Sine
An equation that relates the sine of an interior angle of a triangle to the length of its sides is called the law of sines.
If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle between a and c and C the angle between a and b, then the law of cosines states that
sin A/a = sin B/b = sin C/c
Least Common Multiple (LCM)
The smallest common multiple to which two or more numbers can be divided evenly. For example, the LCM of 2, 3 and 6 is 12.
Leading Coefficient
The coefficient of a polynomials leading term or the term with the variable having the highest degree.
For example, the leading coefficient of 7x4 + 5x3 + 92 + 2x +21 is 7.
Leading Term
The term of a polynomial which contains the highest value of the variable is called the leading term.
For example, the leading coefficient of 7x4 + 5x3 + 92 + 2x +21 is 7x4.
Least Common Denominator
The least common denominator is the smallest whole number that can be used as a denominator for two or more fractions. The Least Common Denominator is nothing but the Least Common Multiple of the denominators of the fractions.
For example, the least common denominator of 3/4 and 4/3 is 12. Since 3/4=6/8=9/12 and 4/3=8/6=12/9=16/12. Hence we see that the least common denominator is 12.
Least Integer Function
The least integer function of x is a step function of x, which is the least integer greater than or equal to x. This function is sometimes written with reversed boldface brackets ]x[ or reversed plain brackets ]x[.
Least Squares Regression Line
The Linear Squares Regression Line is the linear fit that matches the pattern of a set of paired data, as closely as possible. Out of all possible linear fits, the least-squares regression line is the one that has the smallest possible value for the sum of the squares of the residuals.
It is also known as Least Squares Fit and Least Squares Line.
Least-Squares Regression Equation
An equation of any form (linear, quadratic, exponential, etc) that helps in fitting a set of paired data as closely as possible is called the least squares regression equation.
Least Upper Bound of a Set
The smallest of all upper bounds of a set of number is called the Least Upper Bound.
Leg of an Isosceles Triangle
Any of the two equal sides of an isosceles triangle can be referred to as the leg of the isosceles triangle.
Leg of a Right Angle Triangle
Either of the sides of a right angle triangle, between which the right angle is formed can be referred to as the leg of the right angle triangle.
Leg of a Trapezoid
Either of the two non parallel sides of a trapezoid that join its bases can be referred to as the leg of the trapezoid.
Lemma
More accurately referred to as a helping theorem, a lemma helps in proving a theorem. But it is not important enought to be a theorem.
Lemniscate
A curve that takes form on the numerical number 8, in any orientation can be referred to as the lemniscate. Its equations are generally given in the polar coordinates. r2 = a2cos2θ.
Like Terms
Terms that have the same variables and with the same power are called like terms. The coefficients of the like terms can be directly added and subtracted. For example 5x3y2 and 135x3y2 are like terms and hence can be added directly to give the number 140x3y2.
Limacon
A limacon is a family of related curves usually expressed in polar coordinates.
Limit
The limit of a function is the value of the function as its variable tends to reach a particular value.
For example for f(x)=limx-><5>1/x2= 1/25. As x->5, the function f(x) tends to reach to 1/25.
Limit Comparison Test
The limit comparison test is performed to determine if a series is as good as a good series or as bad as a bad series. The test is used specially in cases when the terms of a series are rational functions.
Limit from Above
The limit from the above is usually taken in cases when the values of the variable is taken greater than that to which the limit approaches. For example limx->0+1/x=infinity, is taken such that the value of x>0. Limit from above is often referred to as limit from the right. This is a one sided limit.
Limit from Below
The limit from the below is usually taken in cases when the values of the variable is taken less than that to which the limit approaches. For example limx->0-1/x=-infinity, is taken such that the value of x>0. Limit from below is often referred to as limit from the left. This is a one sided limit.
Limit Involving Infinity
A limit involving infinity or an infinite limit is one whose result approaches infinity or the value of the variable approaches infinity.
Limit Test for DivergenceA limit test for divergence is a convergence test which is based upon the fact that the terms of a convergent series must have a limit of zero.
Line
A line is a geometric figure that connects two points and extends beyond both of them in both directions.
Line Segment
A line segment is nothing but the set of points between any two points including those two points.
Linear
The world linear means like a line. It is nothing but a graph or data that can be molded by a linear polynomial.
Linear Combination
A linear combination is the sum of multiples of the variables in a set. For example, for the set {x, y, z}, one possible linear combination is 7x + 3y - 4z.
Linear Equation
An equation that can be written in the form "linear polynomial" = "linear polynomial" or "linear polynomial"=constant is known as a linear equation.
For example 3x + 26y = 34 is a linear polynomial.
Linear Factorization
If a polynomial can be factorized such that the factors formed after the factorization are linear polynomials, then this factorization is known as a linear factorization. For example x2-9 can be factorized as (x+3) and (x-3).
Linear Fit Regression Line
Any line that can be used as a fit in the process to model the pattern in a set of paired data.
Linear Inequality
An inequality that can be written such that the value of a polynomial is greater than, less than, greater than equal to or less than equal to a particular number is called linear inequality. For example 3x + 7y >9.
Linear Pair of Angles
When two lines intersect each other, then the adjacent angles formed due to intersection of the two lines are called linear pair angles. The linear pair angles formed are supplementary.
Linear Polynomial
A linear polynomial is a polynomial with degree 1. The highest power of the variables involved in the polynomial should be one. For example 9x + 7 is a linear polynomial.
Linear Programming
The linear programming is an algorithm that is used for solving problems. The method of using linear programming is by asking the largest or smallest possible value of a linear polynomial. If there are any restrictions, then the system of inequalities is used to present any restriction to the equations.
Linear Regression
The process of finding a linear fit is referred to as the linear regression.
Linear System of Equations
If there are more than one equations such that each equation is a linear equation, then the system of equations will be known as linear system of equations.
For example, 2x + 3y - 5z
9x + 7y + 12x = 19
15x - 6y + 11z = 9 is a linear system of equations, that can be used to determine the values of x, y and z.
Local Behavior
The behavior of a function in the immediate neighborhood of any point is called the local behavior. The local behavior of geometric figures can also be studied with respect to a particular point.
For example, for the graph of the equation y=2x + 3, if studied closely can be said to have the local behavior of a straight line parallel to the x-axis and at a distance of 3 units from the origin.
Local Maximum
The local maximum is the highest point in a particular section of the graph. It is also often referred as the local max or relative maximum or relative max.
Local Maximum
The local minimum is the lowest point in a particular section of the graph. It is also often referred as the local min or relative minimum or relative min.
Locus
A locus is nothing but the set of points that form a particular geometric figure. For example, a circle with radius 2 cm is the locus of all points which are at a distance of 2 cms from a particular point.
Logarithm
The logarithm of x with respect to the base c is the power to which the base c must be raised in order to be equal to x. For example, logcx=z then cz=x.
Logarthmic Rules
The logarithmic rules are the algebra rules that need to be used when working with logarithms. Some of them can be listed as under:
If log x = y then 10y=x. It means that if the base of the logarithm is not mentioned then consider the base as 10.
If ln x = y then ey=x. It means that when log is replaced by ln then take the logartihm as natural logartihm and has the base e.
log 1 = 0, since whatever be the base, if raised to the power 0 then the result is always 1.
log ab = log a + log b
lob (a/b) = log a - log b
log b3 = 3log b
logax = logbx/logba
Logarithmic Differentiation
It is the type of differentiation that is used in special circumstances. For example the equation y = xtan x can be differentiated, more easily if the logarithm of both the sides are taken.
On taking the logarithm of both the sides the equation can be reduced to log y = tan x. log x (using logarithmic formula). Hence the process of differentiation becomes simple.
Logistic Growth
A logistic growth is shown by using an equation. It is used to determine the demand of products in situations where the demand increases initially, then the demand goes down and finally reaches a particular upper limit.
Long Division of Polynomials
The process of dividing polynomials is known as polynomial long division. The polynomial long division is used to divide improper rational numbers into proper rational numbers or sum of polynomials. The process of polynomial long division is same as that of long division of numbers.
Lower Bound
The lower bound of a set is any number that is less than or equal to all the numbers in a set. For example 1, 2 and 3 are all lower bounds of the interval [4, 5].
Low Quartile
The low quartile is the number for which 25% of the number is less than the number.
Least Upper Bound of a Set
The smallest of all the upper bounds of a set of numbers is called the least upper bound of the set. For example the least upper bound of the interval [9, 10] is 10.
M
Maclaurin Series
The power series in x for a function f(x) is known as Maclaurin series.
Magnitude
The magnitude is the absolute value of a quantity. Magnitude is a value and it can never be a negative number.
Magnitude of a vector
The magnitude of a vector is the length of the vector.
Main Diagonal of a Matrix: It is the numbers of a matrix taken diagonally starting from the number at the upper left corner and ending at the lower right corner.
Major Arc
The longer of the two arcs between the two arcs of a circle is called the major arc of the circle.
Major Axis of an Ellipse
The line passing through the two foci, the two vertex and the center of the eclipse is called the major axis of the ellipse.
Major Axis of a Hyperbola
The line passing through the two foci, the two vertex and the center of the hyperbola is called the major axis of the hyperbola.
Major Diameter of an Ellipse
The line segment joining the two vertex of ellipse and passing through its center and two foci is known as the major diameter of the ellipse.
Mathematical Model
Mathematical Model or model is nothing but a system of equations that is used for representing a graphs, some data or even some real world phenomenon.
Matrix
A matrix is a rectangular or square array of numbers. All the rows of the matrix is equal lengths and all the columns are also of equal lengths.
Matrix Addition
Two matrices with the same dimensions can be added using the process of matrix addition. The process of matrix addition is such that the element in the position Row 1, Column 1 must be added to the element at the location Row 1, Column 1 of the other matrix.
Matrix Element
Any number in a matrix is known as the matrix element. The position of the number in the matrix is defined by the row number and column number.
Matrix Inverse
The matrix inverse of a matrix is the one, which on being multiplied with the matrix gives the identity matrix. If the matrix is denoted by A, then its inverse is denoted by A-1.
Matrix Multiplication
Two matrices can be multiplied only if the number of columns in the first matrix is equal to the number of rows in the second matrix.
Maximum of a Function
The highest point in the graph of the function is often referred to as the maximum of the function.
Mean
It is nothing but another word for average. When the word mean is used, it is generally referred to the arithmetic mean of a function.
For example, the arithmetic mean of the numbers 1, 4, 6, 7, 8 is (1+4+6+7+8)/5.
Mean of a Random Variable
This is often referred to in the case of probability where a number of trials are performed to see the most expected result. The average of all the outcomes of all these trials is considered the mean of a random variable.
Mean Value Theorem
This is a theorem used in Calculus. It states that for every secant for the graph of a 'nice' function, there is a tangent parallel to the secant.
Mean Value Theorem for Integrals
The mean value theorem for integrals states that for every function there is at least one point where the value of the function equals the average value of the function.
Measure of an Angle
The value of an angle in radians or degrees is referred to as the measure of an angle.
Measurement
The process of assigning a value for any physical quantity (eg. Length, breadth, height, area, volume, etc.) is called measurement.
Median of a Set of Numbers
The median of a set of numbers is the number which is greater than half the numbers in the set and smaller than the remaining half. In case of two medians, simply find out the arithmetic mean of the two numbers.
Median of a Trapezoid
The line joining the two non parallel lines of the trapezoid and parallel to the base of the trapezoids is called the median of the trapezoid.
Median of a Triangle
The line segment joining the vertex of a triangle to the mid point of the opposite side is called the median of the triangle. It is very clear from the definition that every triangle has three medians.
Members of an Equation For any equation, the polynomials on the two sides of the equation are referred to as the members of the equation. For example; for the equation, 3x2+5=26x, the members of the equation are 3x2+5 and 26x.
Menelaus' Theorem
The Menelaus' theorem is an equation that shows how the two cevians of a triangle divide the two sides of the triangle and each other.
For example, if A, B and C are the three vertex of the triangles and BF is the line segment from B to the side AC intersecting AC at F, CD is the line segment from C intersecting at B and BF and CD intersect at the point P then, (AD/DB)(BP/PF)(FC/CA)=1.
Mensuration
The process of finding out the measurement of the physical quantities in geometry is refered as mensuration.
Mesh of a Partition
In any partition, the width of the largest sub interval is called the mesh of the partition.
Midpoint
The point at exactly half of the distance from the two points on the line segment joining the two points.
Midpoint Formula
The midpoint formula states the for any two points (x1, y1) and (x2, y2) the mid point is given by ((x1+x2)/2 ,(y1+y2)/2).
Max/Min Theorem
The max/min theorem states that for any continuous function f(x) in the interval [a,b] there exist two numbers in the interval (say c and d) such that, for f(c) and f(d) the function has its absolute maximum and minimum.
Minimum
The process of finding out the smallest possible value of the variable in a function is referred to as the minimum of the function.
Minimum of a function
The minimum value of the function within a limited region or entire region of the function is referred to as the minimum of the function.
Minor arc
If the circumference of the circle is divided into two arcs, then the smaller arc is referred to as the minor arc of the circle.
Minor Axis of an Ellipse
The minor axis of an ellipse is the line passing through the center of the ellipse and perpendicular to the major axis.
Minor Axis of a Hyperbola
The minor axis of a hyperbola is the line passing through the center of the hyperbola and perpendicular to the major axis.
Minor Diameter of an Ellipse
The minor diameter of an ellipse is the line passing through the center of the ellipse and perpendicular to the major diameter
Minute
A minute is a measurement equal to 1/60th of a degree. It is represented by the symbol '. Thus 12°36' is called 12 degree and 36 minutes.
Mixed Number
Mixed number is also called mixed fraction. This is a way of representing improper fraction as the sum of a number and a proper fraction. For example 31/4 can be written as the mixed number 7 ¾, since 7+3/4 is 31/4.
Mobius strip
A mobius strip is a figure that can be represented as a strip of paper fixed at both the ends and with a half turn in the middle.
Mode The number that occurs the maximum times in a list is referred as the mode of the number. For example, in the series 1, 3, 3, 3, 5, 6. 6 the mode is 3 since, it occurs the maximum number of times.
Modular Arithmetic
When normal arithmetic operations are performed and the result is given in modular form then the process is known as modular arithmetic.
For example 15 – 3 = 12, but in mod(7) form the result is 15 – 3 = 5(mod 7).
Modular equivalence Two or more integers are considered to be in modular equivalence if they leave the same integer on being divided by the same number. For example 10 and 16 are both mod 3 equivalent numbers, because they leave the remainder 1 on being divided by 3.
Modular Equivalence Rules
The modular equivalence rules can be listed as under:
Suppose a and b are two mod n equivalent numbers.
Maclaurin Series
The power series in x for a function f(x) is known as Maclaurin series.
Magnitude
The magnitude is the absolute value of a quantity. Magnitude is a value and it can never be a negative number.
Magnitude of a vector
The magnitude of a vector is the length of the vector.
Main Diagonal of a Matrix: It is the numbers of a matrix taken diagonally starting from the number at the upper left corner and ending at the lower right corner.
Major Arc
The longer of the two arcs between the two arcs of a circle is called the major arc of the circle.
Major Axis of an Ellipse
The line passing through the two foci, the two vertex and the center of the eclipse is called the major axis of the ellipse.
Major Axis of a Hyperbola
The line passing through the two foci, the two vertex and the center of the hyperbola is called the major axis of the hyperbola.
Major Diameter of an Ellipse
The line segment joining the two vertex of ellipse and passing through its center and two foci is known as the major diameter of the ellipse.
Mathematical Model
Mathematical Model or model is nothing but a system of equations that is used for representing a graphs, some data or even some real world phenomenon.
Matrix
A matrix is a rectangular or square array of numbers. All the rows of the matrix is equal lengths and all the columns are also of equal lengths.
Matrix Addition
Two matrices with the same dimensions can be added using the process of matrix addition. The process of matrix addition is such that the element in the position Row 1, Column 1 must be added to the element at the location Row 1, Column 1 of the other matrix.
Matrix Element
Any number in a matrix is known as the matrix element. The position of the number in the matrix is defined by the row number and column number.
Matrix Inverse
The matrix inverse of a matrix is the one, which on being multiplied with the matrix gives the identity matrix. If the matrix is denoted by A, then its inverse is denoted by A-1.
Matrix Multiplication
Two matrices can be multiplied only if the number of columns in the first matrix is equal to the number of rows in the second matrix.
Maximum of a Function
The highest point in the graph of the function is often referred to as the maximum of the function.
Mean
It is nothing but another word for average. When the word mean is used, it is generally referred to the arithmetic mean of a function.
For example, the arithmetic mean of the numbers 1, 4, 6, 7, 8 is (1+4+6+7+8)/5.
Mean of a Random Variable
This is often referred to in the case of probability where a number of trials are performed to see the most expected result. The average of all the outcomes of all these trials is considered the mean of a random variable.
Mean Value Theorem
This is a theorem used in Calculus. It states that for every secant for the graph of a 'nice' function, there is a tangent parallel to the secant.
Mean Value Theorem for Integrals
The mean value theorem for integrals states that for every function there is at least one point where the value of the function equals the average value of the function.
Measure of an Angle
The value of an angle in radians or degrees is referred to as the measure of an angle.
Measurement
The process of assigning a value for any physical quantity (eg. Length, breadth, height, area, volume, etc.) is called measurement.
Median of a Set of Numbers
The median of a set of numbers is the number which is greater than half the numbers in the set and smaller than the remaining half. In case of two medians, simply find out the arithmetic mean of the two numbers.
Median of a Trapezoid
The line joining the two non parallel lines of the trapezoid and parallel to the base of the trapezoids is called the median of the trapezoid.
Median of a Triangle
The line segment joining the vertex of a triangle to the mid point of the opposite side is called the median of the triangle. It is very clear from the definition that every triangle has three medians.
Members of an Equation For any equation, the polynomials on the two sides of the equation are referred to as the members of the equation. For example; for the equation, 3x2+5=26x, the members of the equation are 3x2+5 and 26x.
Menelaus' Theorem
The Menelaus' theorem is an equation that shows how the two cevians of a triangle divide the two sides of the triangle and each other.
For example, if A, B and C are the three vertex of the triangles and BF is the line segment from B to the side AC intersecting AC at F, CD is the line segment from C intersecting at B and BF and CD intersect at the point P then, (AD/DB)(BP/PF)(FC/CA)=1.
Mensuration
The process of finding out the measurement of the physical quantities in geometry is refered as mensuration.
Mesh of a Partition
In any partition, the width of the largest sub interval is called the mesh of the partition.
Midpoint
The point at exactly half of the distance from the two points on the line segment joining the two points.
Midpoint Formula
The midpoint formula states the for any two points (x1, y1) and (x2, y2) the mid point is given by ((x1+x2)/2 ,(y1+y2)/2).
Max/Min Theorem
The max/min theorem states that for any continuous function f(x) in the interval [a,b] there exist two numbers in the interval (say c and d) such that, for f(c) and f(d) the function has its absolute maximum and minimum.
Minimum
The process of finding out the smallest possible value of the variable in a function is referred to as the minimum of the function.
Minimum of a function
The minimum value of the function within a limited region or entire region of the function is referred to as the minimum of the function.
Minor arc
If the circumference of the circle is divided into two arcs, then the smaller arc is referred to as the minor arc of the circle.
Minor Axis of an Ellipse
The minor axis of an ellipse is the line passing through the center of the ellipse and perpendicular to the major axis.
Minor Axis of a Hyperbola
The minor axis of a hyperbola is the line passing through the center of the hyperbola and perpendicular to the major axis.
Minor Diameter of an Ellipse
The minor diameter of an ellipse is the line passing through the center of the ellipse and perpendicular to the major diameter
Minute
A minute is a measurement equal to 1/60th of a degree. It is represented by the symbol '. Thus 12°36' is called 12 degree and 36 minutes.
Mixed Number
Mixed number is also called mixed fraction. This is a way of representing improper fraction as the sum of a number and a proper fraction. For example 31/4 can be written as the mixed number 7 ¾, since 7+3/4 is 31/4.
Mobius strip
A mobius strip is a figure that can be represented as a strip of paper fixed at both the ends and with a half turn in the middle.
Mode The number that occurs the maximum times in a list is referred as the mode of the number. For example, in the series 1, 3, 3, 3, 5, 6. 6 the mode is 3 since, it occurs the maximum number of times.
Modular Arithmetic
When normal arithmetic operations are performed and the result is given in modular form then the process is known as modular arithmetic.
For example 15 – 3 = 12, but in mod(7) form the result is 15 – 3 = 5(mod 7).
Modular equivalence Two or more integers are considered to be in modular equivalence if they leave the same integer on being divided by the same number. For example 10 and 16 are both mod 3 equivalent numbers, because they leave the remainder 1 on being divided by 3.
Modular Equivalence Rules
The modular equivalence rules can be listed as under:
Suppose a and b are two mod n equivalent numbers.
- a+c and b+c are modular equivalent.
- Similarly a-c and b-c are modular equivalent.
- a.c and b.c are modular equivalent. If ac and bc are modular equivalent numbers then a and b are modular equivalent.
These were the modular equivalent rules for normal modular arithmetic operations.
Modulo n
Modulo n or mod n of a number is the remainder of the number when divided by n. For example the number 7 when written in mod 3 form can be written as 7 ≡ 1 (mod 3).
Modulus of a Complex Number
The modulus of a complex number is the distance of the number from the origin on the complex plane. For example, for the number a+bi, the modulus of the number is given by (a2 + b2)½. If the number is given in polar coordinates and the number is rcos θ + irsin θ, then the modulus is given by r.
Modus Ponens
Modus Ponens is a form of logical argument. For example if the pen is working the pencil is working. Now, if the argument is that the pen is working then we can conclude that the pencil is working.
Modus Tolens
Modus Tolens is a form of logical argument that employs the proof of contradiction. For example, if the pen is working then the pencil is working. The pen is not working, hence the pencil is not working.
Monomial
A polynomial with one term is called monomial.
Multiplication Rule
The multiplication rule is used in probability to find out if two events have occured. For example, if there are two events A and B then, P(A and B) = P(A)P(B) or P(A and B)=P(A).P(B|A).
Multiplicative Inverse of a Number
The multiplicative inverse of a number is nothing but the reciprocal of the number. In other words, it is 1 divided by the number. For example, the multiplicative inverse of the number 3/5 is 1/(3/5)=5/3.
Multiplicative Property of Equality
The multiplicative property of equality states that if a and b are two numbers such that a = b, then a.c = b.c.
Multiples
Multiples are the numbers that can be evenly divided by the number whose multiple we are considering. For example, 16 is a multiple of 4 because 16 can be evenly divided by 4.
Multiplicity
The multiplicity of a polynomial is the number of times the number is zero for the given polynomial. For example in the function f(x) = (x + 3)2(x-2)4(x – 7)3, the number -3 has multiplicity 2, 2 has multiplicity 4 and 7 has multiplicity 3.
Multivariable
Any problem that involves more than one variable is called a multivariable problem.
Multivariable calculus If the problems in calculus involve two or more independent or dependent varialbes then the calculus is called multivariable calculus.
Mutually ExclusiveIf the outcome of two events in probability have no common outcomes then the events are called mutually exclusive.
Modulo n
Modulo n or mod n of a number is the remainder of the number when divided by n. For example the number 7 when written in mod 3 form can be written as 7 ≡ 1 (mod 3).
Modulus of a Complex Number
The modulus of a complex number is the distance of the number from the origin on the complex plane. For example, for the number a+bi, the modulus of the number is given by (a2 + b2)½. If the number is given in polar coordinates and the number is rcos θ + irsin θ, then the modulus is given by r.
Modus Ponens
Modus Ponens is a form of logical argument. For example if the pen is working the pencil is working. Now, if the argument is that the pen is working then we can conclude that the pencil is working.
Modus Tolens
Modus Tolens is a form of logical argument that employs the proof of contradiction. For example, if the pen is working then the pencil is working. The pen is not working, hence the pencil is not working.
Monomial
A polynomial with one term is called monomial.
Multiplication Rule
The multiplication rule is used in probability to find out if two events have occured. For example, if there are two events A and B then, P(A and B) = P(A)P(B) or P(A and B)=P(A).P(B|A).
Multiplicative Inverse of a Number
The multiplicative inverse of a number is nothing but the reciprocal of the number. In other words, it is 1 divided by the number. For example, the multiplicative inverse of the number 3/5 is 1/(3/5)=5/3.
Multiplicative Property of Equality
The multiplicative property of equality states that if a and b are two numbers such that a = b, then a.c = b.c.
Multiples
Multiples are the numbers that can be evenly divided by the number whose multiple we are considering. For example, 16 is a multiple of 4 because 16 can be evenly divided by 4.
Multiplicity
The multiplicity of a polynomial is the number of times the number is zero for the given polynomial. For example in the function f(x) = (x + 3)2(x-2)4(x – 7)3, the number -3 has multiplicity 2, 2 has multiplicity 4 and 7 has multiplicity 3.
Multivariable
Any problem that involves more than one variable is called a multivariable problem.
Multivariable calculus If the problems in calculus involve two or more independent or dependent varialbes then the calculus is called multivariable calculus.
Mutually ExclusiveIf the outcome of two events in probability have no common outcomes then the events are called mutually exclusive.
Mathamatics is very interesting
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