: The Secretary, Central Board of Secondary Education, Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi - 110092 : Multi Graphics, 5745/81, Reghar Pura, Karol Bagh, New Delhi - 110005. Phone : 25783846 :

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Foreword
A major part of the formative years of a child’s life is spent in a school and hence the importance of making it a place of joyous learning has been engaging the attention of educationists. The National Curriculum Framework 2005 has elaborated on the insights of Learning without Burden to ensure that a child is not taken away from the joy of being young by de-linking school knowledge from every day experience. One of the most important areas in this respect is regarding mathematics learning in schools. Mathematical phobia has been a common jargon in school parlance that has created an elite class of good students of mathematics leaving behind a large number of students who fear the subject. In an endeavour to impress upon the schools that this misconception about the subject is mainly due to wrong teaching practices which do not link the subject with real life, the Board had introduced the concept of Mathematics Laboratory in schools up to Secondary level. It is essential to know that mathematics is very much related with real life. It is a vehicle of communication just as every language is. Through mathematics we can describe, understand and work with physical phenomena with utmost precision. The subject has application in almost all walks of life. The symbols and operations are only mechanical tools but the concepts themselves are much more than these and are very much real and related to...

...Why study Mathematics?
The main reason for studying mathematics to an advanced level is that it is interesting and enjoyable. People like its challenge, its clarity, and the fact that you know when you are right. The solution of a problem has an excitement and a satisfaction. You will find all these aspects in a university degree course.
You should also be aware of the wide importance of Mathematics, and the way in which it is advancing at a spectacular rate. Mathematics is about pattern and structure; it is about logical analysis, deduction, calculation within these patterns and structures. When patterns are found, often in widely different areas of science and technology, the mathematics of these patterns can be used to explain and control natural happenings and situations. Mathematics has a pervasive influence on our everyday lives, and contributes to the wealth of the country.
The importance of mathematics
The everyday use of arithmetic and the display of information by means of graphs, are an everyday commonplace. These are the elementary aspects of mathematics. Advanced mathematics is widely used, but often in an unseen and unadvertised way.
• The mathematics of error-correcting codes is applied to CD players and to computers.
• The stunning pictures of far away planets sent by Voyager II could not have had their...

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Set (mathematics)
From Wikipedia, the free encyclopedia
This article is about what mathematicians call "intuitive" or "naive" set theory. For a more detailed account, see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory.
An example of a Venn diagram
The intersection of two sets is made up with the objects contained in both sets
In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.
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Definition[edit]
A set is a well defined collection of objects. The objects that make up a set (also known as the elements or members of a set) can be anything: numbers, people, letters of the alphabet, other sets, and so on. Georg Cantor, the...

...Zero in Mathematics
Zero as a number is incredibly tricky to deal with. Though zero provides us with some useful mathematical tools, such as calculus, it presents some problems that if approached incorrectly, lead to a breakdown of mathematics as we know it.
Adding, subtracting and multiplying by zero are straightforward.
If c is a real number,
c+0=c
c-0=c
c x 0=0
These facts are widely known and regarded to hold true in every situation.
However, division by zero is a far more complicated matter. With most divisions, for example,
10/5=2
We can infer that
2 x 5=10
But if we try to do this with zero,
10/0=a
0 x a=10
Can you think of a number that, when multiplied by 0, equals 10? There is no such number that we have ever encountered that will satisfy this equation.
Another example will emphasise the mysteriousness of dividing by zero.
One may assume that
(c x 0)∕0=c
The zeroes should cancel, as would be done with any other number. But since we know that
c x 0=0
it follows that
(c x 0)/0=0/0=c
This does not seem to make sense. This also means that
1=0/0=2
1=2
since 1 and 2 are both real numbers. Actually, this means that 0/0 is equal to every real number!
In effect, there is no real answer to a division by zero. It cannot be done.
In fact, if we could divide by zero, it would be possible to prove anything that we could dream of. For example, imagine a student trying to prove to his teacher that he...

...Introduction
Mathematics is an indispensable subject of study. It plays an important role in forming the basis of all other sciences which deal with the material substance of space and time.
What is Mathematics?
Mathematics may be described as the fundamental science. It may be broadly described as the science of space, time and number. The universe exists in space and time, and is constituted of units of matter. To calculate the extension or composition of matter in space and time and to compute the units that make up the total mass of the material universe is the object of Mathematics. For the space-time quantum is everywhere full of matter and we have to know matter mathematically in the first instance.
Importance of Mathematics
Knowledge of Mathematics is absolutely necessary for the study of the physical sciences.
Computation and calculation are the bases of all studies that deal with matter in any form.
Even the physician who has to study biological cells and bacilli need to have a knowledge of Mathematics, if he means to reduce the margin of error which alone can make his diagnosis dependable.
To the mechanic and the engineer it is a constant guide and help, and without exact knowledge of Mathematics, they cannot proceed one step in coming to grips with any complicated problem.
Be it the airplane or the atom bomb,...

...π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in the Euclidean plane; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.14159265 in the usual decimal notation. Many formulae from mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants.
π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.
Probably because of the simplicity of its definition, the concept of π has become entrenched in popular culture to a degree far greater than almost any other mathematical construct. It is, perhaps, the most common ground between mathematicians and non-mathematicians. Reports on the latest, most-precise...

...THE FEAR OF MATHEMATICSMathematics is often called the "queen of the sciences. It is a crucially important tool in the study of other scientific disciplines, in addition to being a science in its own right. Its value to scientific accomplishment is as innumerable as it is invaluable. Regarded as the nucleus of the science world itself, most celebrated scientific achievements could hardly have had a jumpstart without the guiding precepts of the basic modules of arithmetic. Most careers in Universities and colleges of education in the country increasingly require mathematics as a prerequisite.
Mathematics is being used in the study of problems in an increasing number of areas like biotechnology, data communications, environmental toxicology, medical imaging, transportation scheduling, and financial risk management.
The phobia for the disciple in high school has been recurring through time. It has endured an unhealthy acuity mainly in the mind of the lower level academic. Most students do not know how much the use of mathematics affects them, both now and in the future. Irrespective of gender, the scare of poor performance plagues parents as their wards grapple this non-avoidable subject. Most times the child that starts abhor mathematics would find no point of attraction with the class or the teacher. The result? Truancy sets in.
This psyche can be corrected.
This piece focuses on...

...Theory of Knowledge
Éanna OBoyle
ToK Mathematics
“... what the ordinary person in the street regards as mathematics is usually nothing more than the operations of counting with perhaps a little geometry thrown in for good measure. This is why banking or accountancy or architecture is regarded as a suitable profession for someone who is ‘good at figures’. Indeed, this popular view of what mathematics is, and what is required to be good at it, is extremely prevalent; yet it would be laughed at by most professional mathematicians, some of whom rather like to boast of their ineptitude when it comes to totalling a column of numbers....Yet ... it is not the mathematics of the accountant that is of most interest. Rather, it is ... abstract structures and everyday intuition and experience” (p.173, Barrow).
2.1 Mathematical Propositions
2.1.1 Mathematics consist of A Priori Propositions (theorems)
We know mathematical propositions (or theorems) to be true independently of any particular experiences. No one ever checks empirically that, for example, 364.112 + 112.364 = 476.476 by counting objects of those numbers separately, adding them together, and then counting the result. The techical term to describe this independence of experiences is to say that the propositions are a priori. Therefore we say that mathematical propositions are a priori propositions.
2.1.2 Universality
When mathematical propositions...

...up the pillar and ran away. The man never saw him again.
Life without mathematics
Do any of us realize the importance of maths in our daily life? This is a subject that is applied to every field and profession. Without the application of maths, no field or profession is complete. To help us realize this why don’t we imagine a world without maths?
Imagine living your days without a watch and a calendar. Both the watch and the calendar use numbers, the most basic and important of mathematic characters. How would you know the time of the day? Wouldn’t you miss your own birthday without a calendar?
Consider this, you go to a shop to buy something but since this is a world without maths, you don’t know what money is, you don’t know measurements. So what do you do?
Whether it is a Zoologist assessing the number of animal species on earth or a doctor checking your heartbeat they have to know how to count. Without mathematics an engineer cannot build a bridge. A quantity checker chemist cannot prepare medicines if he cannot accurately measure the quantity of each chemical.
We wouldn’t have had markets and businesses without math as the world of trade runs on money. And as a country’s development depends heavily on its economic growth, wouldn’t that be a problem?
There wouldn’t be any more advancements of technology as each sector of technology directly or indirectly employs the application of mathematics. We are all...