business mathematics

You feel difficult when you are learning this type of maths specially at the age of 11 or 12 years. When i was studying my 6th class, i was first introduced this maths.

Business maths is one of the branches of mathematics just as algebra, geometry, statics. You can also call business maths as arithmetic.

Topics like simple interest, compound interest, percentages, distances will definitely create problems. Even though it is difficult it is useful in real life. When you are buying or selling some goods, you can not calculate your profit or loss if you don't know business mathematics. When it comes to money borrowing from others(generally persons who you don't know), you should know simple interest. otherwise they may cheat you. I too have seen many such cases.

Pure mathematics is more like art. Pure mathematicians work on building a foundation for a theory. One nice feature about pure mathematics is that it is free from argument. When a mathematician makes a discovery there is no opposition, as in science. And his theory stands the test of time, unlike science where one law is shown to be wrong in special cases. But once a foundation is build (like complex analysis) applied mathematicians take its result and use it to solve important problems.

Pure math is much more difficult. Classes in applied math consist of memorizing the steps to solve problems. However, classes in pure math involve proofs, which implies a good understanding of the subject matter is required. In pure math you need to justify everything you do. Which can sometimes make a simple argument long and complicated. It is easier for someone in pure math to learn applied math rather than someone in applied math to learn pure math.

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.

The most difficult mathematics is that which you do not know.

A surprising amount of mathematics is actually easy once you've learned it. Of course, once you learn the easy stuff, then you have to start tacking the deep stuff, and that gets harder.

One teacher I had, was introducing a new concept, and we did an example in class. (and this was a class for good mathematicians -- not your average students) There was a lot of blank stares, and not everybody seemed to follow all the way through.

The very next thing he asked was for us to differentiate the function x² with respect to x. Of course, everybody could do that very easily.

His response? "The reason you can do differentiation, but not the other thing, is that you've differentiated things hundreds of times, but you haven't done this other thing very much yet."

In my experience, main reason is "The Fear Factor".

The first is, because the feelings of inferiority and outright fear that many, probably most, students feel when they confront mathematics, severely inhibit students’ natural intelligence and creativity. It is as though every mathematical subject, and every concept within a subject, is surrounded by a kind of “force field” that radiates, “Not for you!”, “You aren’t smart enough!”. The origin of this force field may be early experiences in a family in which, say, a father had always been good at mathematics, and had made it clear he expected his children to likewise be good at the subject. In the case of women, the origin might be subtle messages sent by teachers through out the primary and secondary school years — perhaps without conscious intention — that technical subjects are too hard for girls. Or, it might be the atmosphere that surrounds mathematics and indeed all technical subjects in the nation’s most schools.

My opinion is that mathematics is indeed a descriptive language. It is somewhat unique in this role though. The reason for this uniqueness is the fact that when people created this abstract system they wanted to use the most basic elements inherent in our reasoning, rather than just describe the observed. The result of this was a system that had very few and very basic axioms that seemed to match precisely the most basic patterns we observe in the Universe. It also meant that this system could evolve and create many patterns that appear to be greatly similar to those that we find in nature and can describe those.

What do I mean by basic elements ?
Well, one basic element of all reasoning systems we had so far is the existence of separate entities. Others are space, time, laws/relations that control the entities and possibly more.

Before beginning to solve any problem you must understand what it is that you are trying to solve. Look at the problem.

There are two parts, what you are given and what you are trying to show. Clearly
identify these parts. What are you given? What are you trying to show?.

Thats it you can understand the problem.

It doesn't matter what part of math you study, there will always be pages in a textbook that take a solid day or two to really understand. i guess it could be slightly easier for someone to study a subject & then study a subject that is relatively close to it.

Like some sort of algebraist might not have as much trouble working on some other kind of algebra because of their background. It would probably be harder for an analyst to start working on graph theory because they don't have a lot to do with each other.

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

We will have equations of one or two unknowns invariably in every problem. Some times we get three equations in three unknowns. In general, we need as many equations as the variables we will have to solve for. So, for solving for the values of two unknowns, we need two equations (or two conditions given in the problem) and for solving for the values of three unknowns, we need three equations.

One equation in one unknown:
An equation like 2x + 6 = 36 is an equation in one variable. We have only one variable x whose value we have to find out.

Two equations in two unknowns:
A set of equations like
2x + 3y = 10 ………… (1)
3x + 5y = 12 ………… (2)
Is called simultaneous equations in two unknowns. Here, we have two variables ( or unknowns) x and y whose values we have to find out.

And also we use three equations in three unknowns.

Factorial is defined for any positive integer. It is denoted by !. Thus “Factorial n” is written as n!. n! is defined as the product of all the integers from 1 to n.

Thus n! = 1.2.3.. ... (n-1),n.

Example 5! = 1*2*3*4*5 = 120

0! is defined to be equal to 1.
Therefore 0! = 1 and 1! = 1

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

Least Common Multiple (L.C.M):


Rules:

The smallest of the common multiples of two natural numbers (a and b) is called the least common multiple(LCM) of the numbers a and b.

The smallest of the common multiples of two or more natural numbers is called the least common multiple(LCM).

If two numbers are c0-prime, then their LCM is equal to their product.

Given two numbers, if the first number is a multiple of the second number, then their LCM is equal to the first number.

Relationship Between GCD and LCM:
If a and b are any two natural numbers and L and G are respectively their LCM and GCD, then a*b=L*G

Example:

LCM of 30,48

2 |30,48
_______
3 |15,24
_____
5,8

LCM of 30,48 = 2*3*5*8= 240

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)

Area of the four walls of a room:

If we look around and observe the walls of a room, we find that generally the walls are in the shape of a rectangle the floor and the ceiling of the room are also of rectangular shape.
Let l, b, h be the lengths of AB,AD and AE as shown in the figure. Here l and b are the length and breadth of the floor and h the height of the room.
For the rectangle ABFE, the lengths of two adjacent sides are l and h. its area = lh
For the rectangle BCGF, the lengths of two adjacent sides are b and h. its area = bh
For the rectangle CDHG, the lengths of two adjacent sides are l and h. its area = lh
For the rectangle DAEH, the lengths of two adjacent sides are b and h. its area = bh
Observe the opposite walls being of the same size and shape have the same area too.

Hence the total area of the four walls = lh+bh+lh+bh
= 2lh+2bh
= 2h(l+b)

mensuration :Areas

The area of simple closed figure is the measure of the region closed by the boundary of the figure.

The area is measured in square units. A square meter is the area of square whose side is one meter.

A square centimeter is the area of square whose side is one centimeter.

If l and b denote the length and breadth of a rectangle and A its area, then A=l*b=lb

If s denotes the side of a square and A its area, then A=s^2.

Greatest Common Divisor or Highest Common Factor :

The greatest of the common factors of two or more numbers is called their Greatest Common Divisor(G.C.D) or Highest Common Factor(H.C.F).

If there is no common factor (other than 1)for two numbers , the numbers are said to be prime to each other or co-prime or relatively prime.

Example:
Consider fallowing numbers:
36,48,60.

36=2×2×3×3
48=2×2×2×2×3
60=2×2×3×5

We see that for the above three numbers
2,3,2×2=4,2×3=6,2×2×3=12 are the common factors. Among these 12 is the greatest.
So 12 is the G.C.D or H.C.F.

Basic Numbers-Number System:

Natural Numbers:
The numbers we use for counting are called natural numbers. The set of all natural numbers is denoted by “N”.
Hence N= {1,2,3,4……..}.

Whole Numbers:
When all the natural numbers and zero are put together, we get a new set of whole numbers. The set of whole numbers is denoted by “W”.
Hence W={0,1,2,3,4………}.

Integers:
The set containing positive numbers(1,2,3….), negative numbers(-1,-2,-3,…..) together with zero is called as set of integers. We denote the set of integers with “Z”.
Hence Z={……-3,-2,-1,0,1,2,3,……..}.

Rational Numbers:
A rational number is a number of the form a/b. Where a and b are integers, b≠0.
Example: {2/3, 4/7,7/9……..}

Prime Numbers:
Numbers which do not have any other factors except 1 and itself are called prime numbers.
Examples: {1,2,3,5,7,11,13,17,19,23,29,31,37,41……….}

Composite Numbers:
All numbers greater than 1 and except prime numbers are called composite numbers.
Examples: {4,6,8,9,10,12…….}.
Even Numbers:
Numbers which are exactly divisible by 2 are called even numbers.
Examples: {2,4,6,8,10…….}

Odd Numbers:
Numbers which are not exactly divisible by 2 are called even numbers.
(or)
Numbers which are not even numbers are called odd numbers.
Examples: {1,3,5,7,9……..}.

Basic Mathematical Symbols:

+ Plus

- Minus

× Multiply

÷ Divide

= Equal

% percent

: Ratio

> Greater than

< Less than

.∙. Therefore

∙.∙ Because

± Plus- minus sign

≠ Not equal to

≤ Less than or equal to

≥ Greater than or equal to

∞ Infinity

≈ Almost equal to