Mathematics for Everyday life

                                                                      

         Mathematics is in principle inexpensive. As the old joke says, a mathematician needs only paper, a pencil, an easy chair and a waste basket. Also, the criterion for success in mathematics is by and large universally accepted. This makes mathematics an attractive 'investment'. Moreover, a mathematical result is valid forever. It may fall out of fashion, or fall outside the current area of application, but even the oldest known mathematical formulae - such as that for solving quadratic equations, known 2400 years ago by Babylonians, Chinese and later the Greeks before being crystallized into its present form in 1100 AD by a Hindu mathematician called Baskhara - are the bread and butter of present-day elementary mathematics. Alas, the downside is that the results are usually not immediately applicable – and therein lies the risk. Who wants to 'invest' in something that may not lead to applications for several hundred years? The good news is that the distance between theory and application is becoming shorter and shorter.

          Mathematics can be compared to a pyramid. On the top of the pyramid are applications of mathematics to health, weather, movies and mobile phones. However the top of this pyramid would not be so high if its base were not so wide. Only by extending the width of the base can we eventually build the top higher. This special feature of mathematics derives from its internal structure. A good modern application of mathematics can typically draw from differential equations, numerical analysis and linear algebra. These may very well draw from graph theory, group theory and complex analysis. These in turn rest on the firm basis of number theory, topology and geometry. Going deeper and deeper into the roots of the mathematics, one ends up with such cornerstones of logic as model theory and set theory.It is clear that mathematics is heavily used in large industrial projects and in the ever-growing electronic infrastructure that surrounds us. However, mathematics is also increasingly infiltrating smaller scale circles, such as doctors' reception rooms, sailboat design and of course all kinds of portable devices. 

        There has also been a change in the way mathematics penetrates our society. The oldest applications of mathematics were probably in various aspects of measurement, such as measuring area, price, length or time. This has led to tremendously successful mathematical theories of equations, dynamical systems and so on. In today's world, we already know pretty accurately for example the make-up of the human genome, yet we are just taking the first steps in understanding the mathematics behind this incredibly complex structure of three billion DNA base pairs. Our understanding of the mathematics of the whole universe of heavenly bodies, even going back in time to the first second of its existence, is better than our understanding of the mathematics of our own genes and bodies.

         What is the difference between the hereditary information encoded in DNA and the information we have about the movements of the heavenly bodies? Is it that we have been able to encapsulate the latter into simple equations, but not the former? Or is it perhaps that the latter has a completely different nature than the former, one that makes it susceptible to study in terms of equations, while the former comes from a world governed by chance, and algorithms, a world of digital data, where the methods of the continuous world do not apply?

          Another well-known instance of mathematics in society is cryptography in its various guises. There exist numerous situations in which data must be encrypted such that it can be publicly transmitted without revealing the content. On the other hand, sometimes a party may find it vitally important to break a code that another party has devised for its protection. Some companies want to examine the data of our credit card purchases in order to have access to our shopping patterns. Some governments want to do the same with regard to what they deem less innocuous patterns of behaviour.

      Cryptography is a typical example of the mathematics of the digital world. Digital data has become important in almost all fields of learning, a natural consequence of advances in computer technology. This has undoubtedly influenced the way people look at fields of mathematics such as number theory, that were previously thought to be very pure and virtually devoid of applications, good or bad. Now suddenly everybody in the possession of big primes has someone looking over their shoulder.

            This infiltration is quite remarkable and elevates mathematics to a different position from that which it previously occupied. Mathematics is no longer a strange otherworldly subject, practised by a few curious geniuses but for most people best left alone. The spread of microprocessors into every conceivable aspect of our everyday life has brought heavy-duty computing into our homes, into our classrooms and into scientific laboratories of all kinds. Naturally it is unnecessary for everyone to understand all this computing, which can take place in microseconds without our noticing. But it means that anyone who refuses to acknowledge the role of mathematics will see the changing technosphere as something strange and in the worst case as something irrational or even frightening. A very good way to understand and come to terms with an important aspect of modern life – our ever-growing dependence on interpreting digital data – is to have a basic knowledge of mathematics.

           Basic knowledge: what does this mean and how is it attained? Clearly, this takes us into the realm of mathematics education. Strictly speaking, education is not an application of mathematics, but it is nevertheless of increasing importance to the mathematical world. Every time the OECD’s PISA (Programme for International Students Assessment) results arrive, some people ask why some countries always seem to score highly in the mathematical skills of 15-year-olds. Without attempting to answer this difficult question, one must admit that it is important and that maths education will face huge challenges in the future, not least because of the infiltration of mathematics into all levels of society. This infiltration clearly has much to do with the revolution triggered by the development of computers over the last fifty years. Has this revolution arrived in schools, and in maths education? Most students now own a computer with an Internet connection. This is used for games, chatting, text processing and surfing, but do they use the computer for mathematics? Are mathematical modeling (ambitious problem solving) or algorithmic thinking (expressing mathematics in such a way that the computer can handle it) taught at school? There is much that can be done here, in curricula, in textbooks and in everyday life at school.

                                                                       

                                                                         Sowbagiavathy

                                                                         Dept. of Mathematics

         

All Psychological Theories By Mr. Diane Joseph

Developmental theories	Memory  and transfer of learning theories	Learning theories	Intelligence theories	Personality  theories
1.      Piaget’s theory  of cognitive development 2.      Bruner’s theory  of language development 3.      Erikson’s Psycho-social stages 4.      Kohlberg’s theory  of moral development	Ebbinghaus’s theory  of forgetting William James’s theory of mental discipline: (faculty theory): Thorndike’s theory of identical elements/components Charles Judd’s theory of generalization W.C. Bagley’stheory of ideals	1.      Behavioristic theories 1. Pavlov ‘s classical conditioning 2.Skinner’s operant conditioning 3.Thorndike’s trial & error learning 2.      Cognitive field theories 1. Tolman’s sign learning theory  2. Kohler’s insight learning 3. Yerkes’s theory of arousal and performance 4. Wertheimer ‘s Gestalt theory 5.Lewin’s field theory of learning 3.Reception learning Ausubel 4. Modeling and observational learning Bandura 5. Conditions of learning Gagne 6. Humanistic emphasis Maslow 7. Drive reduction Hull	Thorndike ‘s anarchic  factor theory Spearman’s two factor theory Thurstone’s multi factor theory Vernon’s hierarchical theory Guilford’s Model Of Intellect	1.Jung ‘s type theory 2.Allport’s trait theory 3.Freud’s psycho- analytical theory 4. Adler’s type theory 5. Roger’s client centered theory 6. Ellis’s ABC model of personality 7. Maslow ‘s humanistic theory

A Tribute to Tagore

A tribute to Tagore

            Rabindranath Tagore, a man of versatile genius and achievement, was the first Indian poet and writer who gained for modern India a permanent place on the world literary map.  Tagore was a poet, composer, novelist, short story writer, play-writer, philosopher, lecturer, educator and painter.  Tagore was awarded Nobel Prize for his English Gitanjaliin 1913.  He began his literary career by writing in Bengali.  He had written more than seven thousand verses before he was seventeen.  He wrote over one thousand poems, eight volumes of short stories, almost two dozen plays and plays lets, eight novel, and many books and essays on philosophy, religion, education and social topics.  He wrote only one poem in English The Child.  All the other poems he wrote in Bengali.  He translates his Bengali works in English.  The first English translation of Gitanjaliwas a phenomenal success.

            Gitanjaliis a sequence of 103 lyrics translated from selected lyrics in his own Bengali works – NaivedyaKheya and Gitanjali and a few lyrics published only in periodicals.  The term Gitanjali, rendered as “Song Offerings”.  The lyrics in Gitanjali have a total unity.  The sequence of thematic unities runs through love of god, love of nature and love of humanity.  It is the story of “Soul’s liberation, a tale of soul’s wait to meet her eternal bridegroom, the Divine Lord, a narration of soul’s pilgrimage and voyage to Heaven of Heavens”.  The poem shows the charm of humbleness: it is a prayer to help the poet open his heart to the Divine Beloved without extraneous words or gestures.

            The theme in Tagore’s poetry is varied and treats them in an original manner.  In Gitanjali, he wrote on God, devotion, love, nature, childhood, motherland, beauty and truth, humanity, spiritualism, etc.  Gitanjali is an immortal work of art.  In it many themes are woven together like flowers in a beautiful wreath.  Broadly speaking, the theme of Gitanjali is the realization of God through self-purification, love, constant prayer and devotion, dedication and surrender to God through service to humanity.

            The main theme of Gitanjali is devotional and mystical or the relationship between the human soul and god.  The Gitanjali songs are mainly poems of bhakti in the great Indian tradition.  It is pure poetry and pure poetry aspires to a condition of prayer.  Such poetry is half a prayer from below, half a whisper from above: the prayer evoking the response, or the whisper provoking the prayer, and always prayer and whisper chiming into song.  Gitanjali is full of such poetry.  The poet sings of the immanence and glory of God.  In the opening lyrics the poet pays his obeisance to God in a spirit of humbleness and says that according to the will of God the soul is eternal and immortal.  He sings “Thou hast made me endless, such is thy pleasure.  This frail vessel thou emptiest again and again, fillest it ever with fresh life” (Lyric 1).

            Tagore, in his poetry stresses cordiality of human relations.  Human relationships are the mainspring of spiritual life.  God is not a Sultan in the sky but is an all, through and all over all.  We worship Him in all the true objects of our worship; love him whenever our love is true.  In woman who is good, we feel Him, in the man who is true we know Him.  Tagore has intense love for the oppressed and the persecuted, for the misfits, for the non-conformists, for the homeless and the rejected.  Man is the image of God.  Alone with the relationship of the individual soul and God, the relationship of the individual soul with other man, is also explored.  We should love every creature, the naked and the hungry, the sick and the stranger: God loves the humble and lives among them.  He sings “Here is thy footstool and there rest thy feet where live the poorest, and lowliest, and lost.  When I try to bow to thee, my obeisance cannot reach down to the depth where thy feet rest among the poorest, and lowliest, and lost” (Lyric 10).

            Tagore’s love of God consciously or unconsciously merges with the love of man and nature.  Tagore emphasizes the value of simplicity and intimate contact with Nature.  Man can elevate himself morally and spiritually, if he lives a life of primal simplicity in constant communion with Nature.  Divorced from Nature man is a poor creature; the farther we travel away from Nature, the more degraded we become.  In Gitanjali, Tagore passionately loves various objects of Nature and sensuously and picturesquely describes them.  Gitanjali is a rich treasure house of fresh, original and meaningful images which have a typical Indian favor.  The appeal of Gitanjali is as universal as it was in 1913 when it was first published in English.  It reveals emotions and feelings which are true to all ages and climates.  Tagore stands for pure beauty, for the universal.  In a very real sense, he was a world poet.  It is clear that his ultimate place will be not simple among Indian’s poet, but among those of the world.

                                                                                                  P. Ravisankar 

                                                                                                  Dept. of English

                                         Problems in Teaching English in Schools

            English as a subject in the school curriculum is given great prominence by the authorities. Its study is compulsory for every one.  Naturally there are good many teachers of this subject in the schools.  But it is rather sad to note that there is something wrong with the teaching of English in Indian schools.  The Standards of English are fast deteriorating.  What makes us feel like that?  If we compare the graduate of today with the graduate of a few years back, we notice the marked difference.  That graduate was much better.  Shall we say that there is something wrong with the learning of English?  The fact is that the standards are rather disappearing.  The conditions under which English is being taught in the schools are far from satisfactory.  The following points highlight the fact:

i) Lack of Purpose

The teachers in the schools teach English and the learners learn English but none of them is fully clear about the real purpose of teaching-learning English.  They are not clear about the aims of teaching English. The teacher is like a sailor who does not know his destination and the pupil is like a rudderless vessel which may be drifted along any ashore.

ii) Incompetent Teachers

Many teachers of English who are teaching the subject are not competent.  Very few of them are really competent for teaching this subject.  They have defective pronunciation.  They have hardly a satisfactory command over English.  With the lapse of time, we find that now better qualified teachers are available.  But in basic qualification they are lacking all the more.Their knowledge of English is inadequate.

iii) Faulty Methods of Teaching

The method of teaching English adopted in the schools are quite defective.  The translation method is used almost in all the schools.  The teachers do not show any interest in acquiring knowledge about the latest methods of teaching the subject.  Then they encourage the students for cramming the material.  In short, the composition is dictated by the teacher, the textbooks translated into mother tongue and the entire emphasis is on passing the examination through the magic wand of cramming.

iv) Faulty Examination system

 The students as well as the teachers have become examination minded.  They do every thing for the sake of examination.  The paper setter, the examiner, the teacher etc., don't bother about real teaching-learning of language. The paper setter sets the question paper and only tests the crammed knowledge of the learner.  So everybody ignores this important aspect of learning the language.  The fear of the examination remains taxing for the teachers and the students.  There is hardly any learning in the real sense of word.

v) Faulty Textbooks

The prescribed textbooks of English suffer in many ways.  A number of students find themselves in troubles while reading these books.  The subject teachers also finds many shortcomings in them. The vocabulary, the structures also present difficulties to the learners.  The students hardly feel any attraction for the subject matter contained in the books.

vi) Faulty Syllabus 

The prescribed syllabus of English for different school classes are not satisfactory.  They are not related to the surroundings of the learners. The students are able to pass the examinations but in their real life situations, they can hardly make use of anything learn by them.  In their schools, they learn many essays, stories, letters but in real life situations, they find it hard to write a simple application.

vii) Neglect of Correction Work

In the teaching of a language, correction work is of great importance.  For teaching a foreign language like English, correction work becomes all the more important.  But we find that very little attention is paid to it. The school authorities don't care for it.  In their over-busy schedule of work, the teachers are not able to do justice to their duty of correction work.  All this results into deterioration in the learning of English by the students.

viii) Lack of Research

Teaching-learning process needs continuous overhauling.  The drawbacks in the teaching-learning of English may be many, but their solutions need be thought of.  Who should do this? The teachers of English, the research minded scholars can do it.  A good teacher does not teach the same thing in the same way year after year.  He is always on the look out for introducing new things in new ways.  In this fast changing age of science and technology, research on the part of the teachers is very essential.  But we find that the teachers are not able to carry on any research.  The lack of research deteriorates the situations.

           Thus we find that the conditions under which English is being taught in the Schools are not satisfactory.  The different factors should be checked properly.  All efforts should be made to remedy the drawbacks.  Only then the deteriorating situations will improve. 

                                                                                               P. RAVISANKAR

                                                                                               DEPT. OF ENGLISH