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Mathematical Signs

published on September 15th, 2007 . by Vanaja

If you look at any mathematics book written before 1500’s, it will be very hard to understand.The Hindu -Arabic numerals familiar to us may have been used. Every thing else was different. The signs and symbols that make up the rest of the language of mathematics as we study it today had not yet been invented.

The sign and sign for subtraction first appeared in 1489 in a German arithmetic handbook. They may have been borrowed from signs used by merchants to mark certain packages . A +was marked on packages with too much of whatever the package contained, while a - meant too little.

The sign for multiplication was invented by an Englishman William Oughtredin 1631.

The sign for division was invented earlier by a German mathematician Johann Heinrich Rahn.

The = for “equals” was invented by the English mathematician Robert Recorde in 1557.


Meaningful learning

published on March 20th, 2007 . by Vanaja

Before we try to understand the concept of meaningful learning, it will be better here to know what learning stands for. according to R.S Wood worth “an activity may be called learning in so far it develops the individual in any way good or bad and makes his environment and experiences different from what it would otherwise have been”.

Learning can produce both good and bad developments in the learner. But the learner, hie parents, his teachers and the society in general want the process of learning to lead to good results and healthy outcomes.
Meaningful learning is therefore that learning which is oriented towards good experiences and outcomes. In it there is no place for meaningless and harmful experiences. It must ensure positive results. It is constructive, productive, purposeful and progressive in nature.

Meaningful learning in mathematics can consist of the mathematical experiences of the following nature;-

  1. Which are helpful in mental, emotional and social development.
  2. which have utilitarian, practical and behavioral values.
  3. Which are useful in learning higher and advanced aspects of the subject.
  4. Which are helpful in the proper learning of other subjects and activities of the curriculum.
  5. Which stimulate and maintain interest in the subject.

Applied Mathematics

published on February 26th, 2007 . by Vanaja

Applied mathematics is the application of pure mathematics in the service of a given purpose. It has some direct or practical application to objects and happenings in the material world. It plays a great role in the development of various subjects. Every discovery in science owes much to applied mathematics. Principles of applied mathematics have been useful in the investigation of such phenomenon as heat , sound, light, optics,navigation and astronomy. applied mathematics is a part of mathematics definitely related to or suggested by some tangible situations, though not always intended for practical use. It is the connecting link between pure mathematics on one side, physical, biological, social sciences and technology on the other.

Pure Mathematics

published on February 20th, 2007 . by Vanaja

Pure mathematics involves systematic and deductive reasoning. It treats only theories and principles without regard to their application to concrete things. It is developed on an abstract, self contained basis without any regard to any possible kind of practical applications that may follow. It consists of all those assertions as that if such and such proposition is true of anything,such and such another proportion is true of that thing.

Basic Concepts of Geometry

published on October 18th, 2006 . by Vanaja

It is very important for a math student to learn the basic concepts in mathematics. It is a common fact that most children find math is very hard and in particular Geometry. The main reason behind this is that they don’t have the basics in maths.
and in Geometry the concepts are more abstract. If the students get some good basic help in math, I am sure most of them do better in maths. So let us learn some basics of Geometry today.
There are three basic concepts of geometry. These are “point“, “line” and “plane“. I am not attempting to define them as it is not possible to define them precisely. We can however, have a good idea of these three by considering examples. A fine dot made by a sharp pencil on a sheet of paper, resembles a geometrical point very closely. The sharper the pencil, the closer is the dot to the concept of a point.

The surface of a sheet of paper or the surface of a smooth table are examples of plane. But these surfaces limited in extent. The geometrical plane extends endlessly in all directions.
A straight line, drawn on a sheet of paper with a sharp pencil, is a close example of a geometrical straight line. A geometrical line is a set of points and extends endlessly in both the directions. To emphasize this we use two arrowheads.
It is impossible to find exact example for point,line and plane in nature. The geometrical point, line and plane are ideal concepts. but for practical purpose it is enough to deal with close examples.
So, a plane is a set of points, line is a subset of plane. Moreover all the other figures in geometry are sets of points. But they are not just set of points. They are special set of points possessing some properties.

Notation
We use capital letters such as A, B, C, P, Q, R, X, Y, Z etc. to denote points.
We use small letters (lower case) such as l,m,n,p,q,r etc. to denote lines.

History of Analytical Geometry

published on October 13th, 2006 . by Vanaja

We know Geometry is one of the most ancient branches of mathematics. The big step forward in geometry after the Greeks, was the development of a new method called Co-ordinate geometry or Analytical geometry. Modern analytical geometry is also called “Cartesian” after the name of Rene Decartes (1596-1665). But the fundamental principles and methods were already discovered by Pierre de Fermat(1601-1665). Unfortunately, Fermats treatise on the subject entitled “Ad locus planos et so lidos Isagoge“(Introduction to plane and solid loci) was published only published posthumously in 1679. So Decartes came to be regarded as the unique inventor of the analytical geometry.
In co-ordinate geometry, we enlist the services of Algebra in aid of Geometry.

History of Trigonometry

published on October 7th, 2006 . by Vanaja

The study of Trigonometry was first started in India. The ancient Indian mathematicians Aryabhatta (A.D 476),Bhaskara I(A.D 600), Bhaskara(A.D 1114)and Brahmagupta(A.D 598) got important results. All this knowledge first went from India to Middle East and from there to Europe. The Greeks had also started the study of trigonometry but their approach was so clumsy that when the Indian approach became known, it was immediately adopted throughout the world.
In India, the predecessor of the modern trigonometric function, known as the sine of an angle, and the introduction of the sine function represents the main contribution of the sidhantas to the history of mathematics.
Baskara I gave formula to find the values of sine function for angles more than 90 degree.
The name of Thales (A.D 600) is associated with height and distances problems. He is credited with the determination of the height of pyramid in Egypt by measuring shadows of the pyramid using similarity property.

Parents can help their children in learning Math effectively.

published on October 2nd, 2006 . by Vanaja

Mathematics is a difficult subject for many students. Children struggle with math because they don’t enjoy it or they don’t see how it is relevant to their future.

As a parent, you should encourage your student to spend time learning mathematics and pointing out how you use math in your everyday life - at home or at work. Even though math is difficult and requires a good deal of study time, parents should maintain a high level of expectations for their children to ensure success. Studies have shown that children perform better in subjects that interest them.

Generally I have seen many people who proudly say “I hate math”. When hearing this young children also think it is some thing great that if they do bad in maths.So unknowingly they began to hate math.So, don’t tell your child “math is hard” because they will believe you.Inspire confidence in them.

Be practical. Find something your child likes and relate it to math.

When doing problems,take it step-by-step. Do not get overwhelmed by the entire problem at once; break it down into small manageable pieces.

Encourage your child to be creative when problem solving. There is always more than one way to skin a cat and math isn’t that different. Let your child explore alternative viewpoints - the teacher’s way is not the only way.

Homework Help from India

published on September 19th, 2006 . by Vanaja

Many and many people from USA and UK are looking India for getting tutoring.You will get a tutor for very low fee. And quality tutoring is guaranteed.Read more

EINSTEIN’S BRAIN

published on July 12th, 2006 . by Vanaja


The secret of Einstein’s immense intellect may finally have been uncovered. One area of his brain was significantly different from most people’s.

Albert Einstein died in 1955, at the age of 76. His brain was then removed and preserved for scientific research. Scientists at McMaster University, Canada compared the size and shape of Einstein’s brain with those of 35 men and 56 women with average intelligence.

In general, Einstein’s brain was the same as all the others except one particular area-the region responsible for mathematical thought and the ability to think in terms of space and movement.

Extensive development of this region meant that his brain was 15% wider than the other brains studied.

Uniquely Einstein’s brain also lacked a groove that normally runs through this area. The researchers suggest that its absence may have allowed the neurons to communicate much more easily.

This unusual brain anatomy may explain why Einstein thought the way he did. Einstein allowed his brain to be studied after his death.

Ref: Mathematics today

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