MyMaths MyLife

Mathematical concept means just about anything with a mathematical name. For example, some of the mathematical concepts we learn in high school are: constant, variable, polynomial, factor, factoring, equation, solving an equation, logarithm, sine, cosine, tangent, etc., point, line, triangle, square, and other geometric figures, area, perimeter of a geometric figure, etc., and many others. Among the mathematical concepts we learn in our first years of college mathematics are: set, operation, limit, function, and, specifically, continuous function, derivative, integral, theorem, proof, countable infinity, uncountable infinity, algebra, linear algebra, vector space, group, ring, field, and many others.

Now one thing that makes the understanding of these concepts difficult is that they are defined in terms of other concepts.

Thus, e.g., a vector space is defined in terms of the concepts of vector, set, function, abelian group, field, and others. How does the typical mathematics textbook, and mathematics course, deal with this fact? It attempts to teach the concepts in logical order, i.e., it assumes that, e.g., when you begin your study of vector spaces, you will already know — through having remembered what you learned in previous courses — the meaning of each of the concepts in terms of which a vector space is defined. And, indeed, one of the things that makes mathematics such a frightening subject to many students, is the grandiose manner with which these assumptions are set forth in the list of prerequisites for the course.

Combinations:
Each of different groups or selections which can be formed by
taking some or all of a number of objects,is called a combination.
eg:- Suppose we want to select two out of three boys A,B,C .
then ,possible selection are AB,BC & CA.
Note that AB and BA represent the same selection.

Number of Combination:
The number of all combination of n things taken r at a time is:
nCr = n! / (r!)(n-r)!
= n(n-1)(n-2). . . . . . . tor factors / r!
Note: nCn = 1 and nC0 =1

An Important Result:
nCr = nC(n-r)

For problems click Here.

An equation which has the unknown quantity raised only to powers which are whole numbers and the highest power being the square of the unknown quantity, is called a quadratic equation.
The most general form of a quadratic equation is ax^2 + bx + c = 0.
There are two values of x that satisfy such a quadratic equation. These values are called the roots of the quadratic equation.

The roots of the above quadratic equation are given by (-b±√(b^2-4ac))/2a

For ax^2 + bx + c = 0, sum of the roots = -b/a; Product of the roots = c/a

cube and cuboid:

Consider the fallowing objects: a brick, a box of matches, a die, a text book, a room in the house. They have a common shape, though their sizes are different. The geometrical name that we give to each of these objects is the cuboid.
It has six rectangular faces. There are in all 12 edges of the cuboid. A cuboid has 8 corners called vertices.
The total area of all the six faces of a cuboid is called the total surface area of the cuboid.
Let l,b, and h, be the length, the breadth and the height of a cuboid,
then the lateral surface area= 2h(l+b)

The total surface area
=(the lateral surface area)+(area of ABCD)+(area of EFGH)
=2h(l+b)+lb+lb
=2lh+2bh+2lb
=2(lb+bh+hl)

The Relation Between G.C.D and L.C.M:

For GCD concept click here:http://business-maths.blogspot.com/2009/02/greatest-common-divisor.html
For LCM concept click here:http://business-maths.blogspot.com/2009/02/least-common-multiple-lcm.html
Find the G.C.D and L.C.M of 30 and 48 and it shows that the product of GCD and LCM is equal to the product of the two given numbers.
GCD of 30,48 is 6.
And LCM of 30,40 is 240.
LCM*GCD=240*6=1440
Product of 30 and 48= 30*48=1440.
Hence the product of the two numbers is equal to the product of their G.C.D and L.C.M.
If a and b are any two natural numbers and L and G are respectively their L.C.M and G.C.D., then a*b=L*G

->(a+b)²=a²+b²+2ab
->(a-b)²=a²+b²-2ab
->(a+b)²-(a-b)²=4ab
->(a+b)²+(a-b)²=2(a²+b²)
->a²-b²=(a+b)(a-b)
->(a-+b+c)²=a²+b²+c²+2(ab+b c+ca)
->a³+b³=(a+b)(a²+b²-ab)
->a³-b³=(a-b)(a²+b²+ab)
->a³+b³+c³-3a b c=(a+b+c)(a²+b²+c²-ab-b c-ca)
->If a+b+c=0 then a³+b³+c³=3a b c

Addition and Multiplication are said to be commutative, because
A+B = B+A
A*B = B*A

Addition and Multiplication are said to be Associative, because
(A+B)+C = A+(B+C)
(A*B)*C = A*(B*C)

Multiplication is Distributive over Addition, because
A*(B+C) = (A*B)+(A*C)

here A, B, C represent any Real Number