CHARACTERISTICS OF RESEARCH    

By - Vijayarajalakshmi, Asst. Prof.

Introduction

            The term research and scientific method are sometimes used synonymously in educational discussions. Although it is true that the terms have some common elements of meaning, a distinction is helpful. Research is considered to the more formal, systematic and intensive process of carrying on a scientific method of analysis. Scientific method in problem solving may be an informal application of problem identification, hypothesis formulation, observation, analysis, and conclusion. Research is more systematic activity that is directed toward discovery and the development of an organized body of knowledge. Research may be defined as the systematic and objective analysis and recording of controlled observations that may led to the development of generalizations , principles, or theories, resulting in prediction and possibly ultimate control of events.

Characteristics of research

            Research is directed toward the solution of a problem. The ultimate goal is to discover cause and effect relationships between variables, though researches often have to settle for the useful discovery of a systematic relationship  is insufficient.

            Research emphasizes the development of generalisations, principles or theories that will be helpful in predicting future occurrences. Research usually goes beyond the specific objects, groups, or situations investigated and infers characteristics of a target population from the sample observed.

            Research is based upon experiences or empirical evidence. Research rejects revelation and dogma as methods of establishing knowledge and accepts only what can be verified by observation.

            Research demands accurate observation and description. When quantitative measuring devices are not possible, researchers may choose variety of qualitative or no quantitative  descriptions for their research questions. Good research utilizes valid and reliable data gathering procedures.

            Research involves gathering new data from primary or first- hand sources or using existing data a for a new purpose. 

            Although research activity may at times be somewhat random and unsystematic, it is more often characterised by carefully designed procedures that apply rigorous analysis.

            Research requires expertise. The researcher knows what is already known about the problem and how others have investigated it. He or she has searched the related literature carefully and is also thoroughly grounded in the terminology, concepts, and technical skills necessary to understand and analyze the data gathered.

            Research strives to be objective and logical, applying every possible test to validate the procedures employed , the data collected and the conclusions researched.

            Research involves the quest for answers to unsolved problems. Pushing back the frontiers of ignorance is its goal, and originality is frequently the quality of a good research project. Previous important studies are deliberately repeated , using identical or similar procedures, with different subjects, different settings, and at a different time. This process  is replication, a fusion of  the words repetition and duplication. Replication is always desirable to conform or to raise questions about the conclusions of a previous study

Research is characterized by patient and unhurried activity. It is rarely spectacular, and researchers must expect disappointment and discouragement as they pursue the answers to difficult questions.

            Research is carefully recorded and reported. Each important term is defined, limiting factors are recognized, procedures are described in detail, references are carefully documented, results are objectively recorded and conclusions are presented with scholarly caution and restraint.

conclusion

In the field of education, we identify research with a better understanding of the individual and a better understanding of the teaching _ learning process and the conditions under which it is most successfully carried on.

MATHEMATICIANS

                   SRINIVASA RAMANUJAN -A MATHEMATICIAN

INTRODUCTION

Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

EARLY LIFE:

He was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras. When he was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. In December 1889 he contracted smallpox.

When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898. At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series.

CONTRIBUTION:

Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quadratic. The following year, not knowing that the quintic(Polynomial of degree five) could not be solved by radicals, he to solve the quintic.

It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics. The book contained theorems, formulae and short proofs.

By 1904 Ramanujan had begun to undertake deep research. He investigated the series ∑(¹/_n) and calculated Euler's constant to 15 decimal places. He began to study the Bernoulli numbers, although this was entirely his own independent discovery. He worked on hypergeometric series and investigated relations between integrals and series. He was to discover later that he had been studying elliptic functions.

Continuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908.  Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society. He devoloped relations between elliptic modular equations in 1910. After publication of a brilliant research paper on Bernoulli numbers in 1911 in the Journal of the Indian Mathematical Society he gained recognition for his work. Despite his lack of a university education, he was becoming well known in the Madras area as a mathematical genius.

RAMANUJAN-HARDY

In January 1913 Ramanujan wrote to G H Hardy having seen a copy of his 1910 book Orders of infinity.  They had communicated through letters. Hardy, together with Littlewood, studied the long list of unproved theorems which Ramanujan enclosed with his letter.

Indeed the University of Madras did give Ramanujan a scholarship in May 1913 for two years and, in 1914, Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration.

Ramanujan sailed from India on 17 March 1914.   He arrived in London on 14 April 1914.  The outbreak of World War I made obtaining special items of food harder and it was not long before Ramanujan had health problems.

The war soon took Littlewood away on war duty but Hardy remained in Cambridge to work with Ramanujan. Even in his first winter in England, Ramanujan was ill and he wrote in March 1915 that he had been ill due to the winter weather and had not been able to publish anything for five months. What he did publish was the work he did in England, the decision having been made that the results he had obtained while in India, many of which he had communicated to Hardy in his letters, would not be published until the war had ended.

On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (the degree was called a Ph.D. from 1920). Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England.

Ramanujan fell seriously ill in 1917 and his doctors feared that he would die.

HARDY- RAMANUJAN NUMBER:

The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Ramanujan. In Hardy's words

“I remember once going to see him when he was ill at Putney.  I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen.  “No”, he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways”.

The two different ways are 1729 = 1³ + 12³ = 9³+10³

Generalizations of the idea have created the notion of “ taxicab numbers”.  Coincidentally, 1729 is also a Carmichael number.

ACHIEVEMENT:

On 18 February 1918 Ramanujan was elected a fellow of the Cambridge Philosophical Society and then three days later, the greatest honor that he would receive; his name appeared on the list for election as a fellow of the Royal Society of London. His election as a fellow of the Royal Society was confirmed on 2 May 1918, then on 10 October 1918 he was elected a Fellow of Trinity College Cambridge, the fellowship to run for six years.

The honors which were bestowed on Ramanujan seemed to help his health improve a little and he renewed his efforts at producing mathematics. By the end of November 1918 Ramanujan's health had greatly improved. 

BACK TO INDIA:

Ramanujan sailed to India on 27 February 1919 arriving on 13 March. However his health was very poor and, despite medical treatment, he died there the following year.

Ramanujan independently discovered results of Gauss, Kummer and others on hyper geometric series. Ramanujan's own work on partial sums and products of hyper geometric series have led to major development in the topic.  Ramanujan left a number of unpublished notebooks filled with theorems that mathematicians have continued to study. G N Watson, Mason Professor of Pure Mathematics at Birmingham from 1918 to 1951 published 14 papers under the general title Theorems stated by Ramanujan and in all he published nearly 30 papers which were inspired by Ramanujan's work.

RECOGNITION:

1.      Tamil Nadu Celebrates Ramanujan’s Birthday, 22 December, as 'State IT Day'.

2.       A stamp picturing Ramanujan was released by the Government of India in 1962.

3.       The 75th anniversary of Ramanujan's birth – commemorating his achievements in the field of number theory,  and a new design was issued on December 26, 2011, by the India Post.

4.      A prize for young mathematicians from developing countries has been created in the name of Ramanujan by the International Centre for Theoretical Physics (ICTP).

5.       On the 125th anniversary of his birth, India declared the birthday of Ramanujan, December 22, as 'National Mathematics Day.'

6.      The year 2012 declared as the National Mathematics Year in India. 
                                                                                             -C. Sowbagiavathy
                                                                                                Mathematics

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