A Brief History of Mathematics

Anjana K. 

1345301

Research Scholar

Christ University

History of Mathematics

 

Mathematics is the study of abstract ideas and topics such as quantity, structure, space, and change. Although formally introduced much later Mathematics has been a part of evolution since time immemorial. This can be said with certainty since the cave paintings provide proofs of counting and numbers. The most ancient mathematical texts available are Babylonian Mathematics in 1900 BC, Egyptian mathematics in 2000-1800 BC and the Moscow Mathematical Papyrus. All of these texts concern the Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.

The study of mathematics is attributed to Pythagoras who coined the term 'Mathematics' in 6^th century BC. After the Egyptian Mathematics, came the Chinese Mathematics. There has been a large contribution of the Chinese to the subject including the place value system. The study of the mathematics of these early civilizations were very different from that of the Greeks, who developed the model of abstract mathematics via geometry which was to serve as the model of mathematical achievement until essentially modern times.

 

Mathematical Writings and Mathematical Societies

Although there have been numerous writings in mathematics the first printed arithmetic book was published in Treviso, Italy, in 1478, the first edition of Euclid's Elements appeared in 1482, and the first work on mathematics printed in the New World appeared in 1556.  The great increase in scientific and mathematical activity that began to flourish in the sixteenth century led to the formation of groups of persons who met, sometimes regularly, for discussion and an exchange of ideas. Some of these groups later crystallized into what became academies, the first of which seems to have been established in Naples around 1560. It is difficult to say where and when the first official Mathematical society was founded, but the oldest one still in existence is the Mathematische Gesellschaft  in Hamburg. It was founded in 1690 as the Kunstrechnungsliebende Societ¨at, and has long published a journal. Another early one is the Spitalfields Mathematical Society, which lasted from 1717 to 1846, initially meeting in a pub in east London; it was ultimately absorbed into the Royal Astronomical Society in 1846. The day of the amateurs passed, and the professionals began to take over with the formation of the national mathematical societies. The first such society is the Wiskundig Genootschap, founded in Amsterdam in 1778, but most national societies were founded considerably later : the Moscow Mathematical Society in 1864, the London Mathematical Society in 1865, the Soci´et´e Math´ematique de France in 1872, the Mathematical Society of Japan in 1877, The Edinburgh Mathematical Society in 1883, the Circolo Matematico di Palermo in 1884, the New York Mathematical Society (later the American Mathematical Society) in 1888 and the Deutsche Mathematiker-Vereinigung in 1890. Most of these societies commenced the publication of a mathematical journal soon after their foundation and many of these journals have played, and still play, an important role in mathematical communication.

The Accademia dei Lincei (Academy of the Lynx-like) was founded in 1603and Galileo became a member in 1611. According to Kline in France, Desargues, Descartes, Fermat, and Pascal, among others, met privately under the leadership of Mersenne from 1630, and corresponded widely. This informal group led to the chartering of the Academie Royale des Sciences in 1616 by Louis XIV. Similarly, an English group led by John Wallis began to hold meetings in 1645 in Gresham College, London. This group was given a charter by Charles II in 1662 and adopted the name of the Royal Society of London for the Promotion of Natural Knowledge; Wallis was a charter member. The Berlin Academy of Sciences was founded in 1700 with Leibniz as its first president. In Russia, Peter the Great founded the Academy of Sciences in St. Petersburg in 1724. These academies were very important for the development of science and, in particular, of mathematics; indeed, many of the most important mathematicians of the eighteenth century were supported by these academies and never had a university position. The academies promoted the exchange of ideas both by facilitating the direct contact of the leading scientists and also by the publications that the academies soon started. While there were various reasons for the support of the academies by the rulers, it is clear that one reason was that the monarchs saw the importance of the emerging science and technology for the civil and military needs of their realms, and realized that mathematics was essential for this scientific development.

 

 

Mathematics in India

In India, Mathematics emerged in the 1200 BC. Aryabhata, Brahmagupta, Bhaskara are few pioneers of Indian Mathematics. Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. The development of expansions of trigonometric functions was one of the greatest inventions in Mathematics in India. Vedic Mathematics is credited to India too. It goes without saying that Mathematics would not have reached its present state if not for the Indian decimal system. In recent times India saw a brilliant Mathematician in Srinivasa Ramanujan who changed the way world sees number theory.

Professor Syamdas Mukhopadhyay was the first to earn a Ph.D in Mathematics in India from the University of Calcutta. He got the degree in geometry in the year 1910.

 

Development of Mathematics

The progress of accounting and mathematics were somewhat linked during the renaissance. This is because people felt the need to learn basic arithmetic in order to do trade of any sort.  In   the Renaissance, the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of natural and metaphysical philosophy. This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619. However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661. 

During the twentieth century, mathematics education was established as an independent field of research. Here are some of the main events in this development:

·         In 1893, a Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein/

·         The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix Klein became the first president of the organisation

·         A new interest in mathematics education emerged in the 1960s, and the commission was revitalised

·         In 1968, the Shell center of Mathematical Education was established in Nottingham.

·         The first International Congress on Mathematical Education (ICME) was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that it has been held every four years.

References

1. E.T.Bell. Men of Mathematics.New York: Simon and Schuster, 1937

2. http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html

3. http://fclass.vaniercollege.qc.ca/web/mathematics/about/history.htm

4.http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Indian_mathematics.html

5. http://www.mayyam.com/talk/showthread.php?3295-History-of-Indian-Mathematics

6. https://www.google.co.in/?gfe_rd=cr&ei=xUZKU4z5IJSEuASCuIH4Cg#q=men+of+mathematics

History of Psychology in India

History of Psychology in India

 

 Psychology as an academic discipline made a new beginning in India in the first decade of this century. Calcutta University established the first Department of Psychology in 1915 under the leadership of Dr N.N. Sengupta, who had worked under Professor Hugo Munsterberg, a former student of Wundt. Due to the fact that Calcutta University became the first centre of psychological research and teaching in India, it was able to play a key role in the development of psychology in the country (Kundu & Chakrabati, 1979).

 

Before independence, psychological research in India was greatly influenced by the British universities. Most of the Indian psychologists during this time were trained abroad and they followed the western theories of psychology. This psychology, transplanted to India as part of the total imperialist domination by the West, came as a ready-made intellectual package in the first decade of the century (Nandy, 1974). In doing so it almost entirely challenged and to a greater extent replaced the intellectual traditions and indigenous systems that had existed for thousands of years – systems that contained elaborate theories about human nature, actions, personality and their relationships with the world. For instance, mentally ill patients in India were historically treated using various approaches such as herbal or ayurvedic medicines, yoga and music (Prasadarao & Sudhir, 2001). But with the advent of scientific (Western) psychology all these traditional and effective treatments were replaced with ‘scientific’ techniques.

 

Following the independence of India in 1947, there were many efforts from the part of government to integrate social science into science and technology research as part of the nation building programme. India’s first Prime Minister Jawaharlal Nehru was a great promoter of psychology, encouraging students to go abroad to obtain their degrees under eminent psychology professors. He also invited and encouraged psychologists to research on certain issues in India.

 

Dr Girindra Shekar Bose, who succeeded Dr N.N. Sengupta at Calcutta University, was a medical practitioner who became a pioneer in psychoanalysis in India. In 1922 he established the Indian Psychoanalytical Society, affiliated to the international Psychoanalytic Association. The Indian Psychological Association appeared in 1925.The Indian Association of Clinical Psychologists (IACP) was started in 1968 (Prabhu, 1983). The Indian Psychological Association appeared in 1925.The Indian Association of Clinical Psychologists (IACP) was started in 1968 (Prabhu, 1983).

 

In the early days psychology was mainly applied in clinical settings, and courses focused on training clinical psychologists. With the growth in the discipline, counseling psychology became popular and was extensively used in different areas of counseling. The growth in the economy and industrial sector resulted in the use of psychology in industrial and organizational settings. Psychology has also been applied in military settings since independence. After independence the defense ministry emphasized the need to include psychologists on research and selection boards of armed forces to provide help and assistance and then they started doing it. Also in the fields of sports and health, psychology is widely used today and disciplines have emerged in all these areas.

 

Until the mid-1980s the public viewed psychology primarily as a remedy for abnormal behavior. But the popularity of psychology has increased a lot with its application in different and diverse areas such as education, organizations, defense, health, sports etc. According to the Association of Indian Universities, 51 of the 101 recognised universities were offering psychology by the end of 1975. By 1995 the number of universities had risen to 219 and those offering psychology at various levels had risen to 70 (Prasadarao & Sudhir, 2001). The period after the mid-1990s has seen an even sharper growth in the popularity of psychology. Psychology has been introduced in the curriculum of senior secondary schools.

 

Indian psychology has come a long way in the hundred years of its existence. Research in psychology is conducted in many universities and research establishments. It is not known how many colleges and universities offer psychology courses and how many psychologists are professionally active.  The National Institute of Mental Health and Neurociences, Bangalore is an institution of international repute for research in clinical psychology and training clinical psychologists. The Central Institute of Psychiatry, Ranchi is another highly reputed institution carrying out research in clinical psychology.

 

Indian psychology in the twenty-first century shows that the initial emphasis on the replication of Western studies has given way to socially relevant research, and that there is a shift from experimental work (micro) toward understanding the psychological, social and cultural contexts (macro) using qualitative approaches. Academicians and researchers have started looking at problems in a more holistic manner and an eclectic approach is preferred today.

 

References

Kundu, R. & Chakrabati, P.H. (1979).From Leipzig to Calcutta. Calcutta:Department of    

Psychology,Calcutta University.

 

Nandy,A. (1974).The non-paradigmatic crisis in Indian psychology:Reflections on a recipient

culture science. Indian Journal of Psychology, 49, 1–20.

 

Prabhu, G.G. (1983). Clinical psychology – Then and now. Indian Journal of Clinical

Psychology, 10, 1–15.

 

Prasadarao, P.S.D.V. & Sudhir, P.M. (2001). Clinical psychology in India. Journal of Clinical

Psychology in Medical Settings, 8(1), 31–38.

History of Education

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HISTORY OF PSYCHOLOGY IN INDIA

Mary Varughese

 

The First Department

Psychology was first introduced as a subject in the Philosophy department of the Calcutta University in 1916. It had an alien quality to it, as Indians were not used to the empirical approach that was prevalent at that time. The then Professor of Mental and Moral Philosophy, Brojendra Nath drafted the first syllabus. He was also the first to establish the first experimental lab in 1905 that later became the seat of the department when it was established. Studies in this lab revolved around depth perception, psychophysics and attention. Recognizing the scientific nature of psychology, the Indian Science Congress included it as a separate section in 1923. The Indian Psychological Association was founded in 1924. Soon after this, Girindra Shekhar Bose, who was in close contact with Freud, founded the Indian Psychoanalytic Society in 1922.

 

Lumbini Park Mental Hospital

Bose, after receiving his PhD from Calcutta, established the Lumbini Park Mental Hospital in Calcutta in 1940 that brought out the journal ‘Samiksha’. Many Indian Psychologists had contacts with the famous contributors to psychology during those days. Jung, Meyers, and Spearman were present during the Silver Jubilee Session of the Indian Science Congress. M.V. Gopalswami, Head of the Department of psychology at Mysore, was trained in the London University with Spearman in the mental testing tradition. He helped develop Indian adaptations of Western intelligence tests. He was the first to establish the first animal lab in India.

 

The department at Patna began in 1946 along with the Institute of Psychological Research and Services headed by H. P. Maiti. Maiti was trained with Bose and was psychoanalytic in his approach and very soon the department at Patna became a major center for counselling services and research.

 

 

The Empirical Nature of Psychology

The empirical nature of psychology during those years meant that psychologists in India had to compartmentalize their aesthetic satisfaction of Hindu mythologies without seeking to bring the two together (Kakar, 1982). Psychologists were also aware that this singularity of the positivist approach was unable to fully explain the psycho-social nature of the Indian society or the Indian mind. Hence, there was no overlap between what the reality of Indian society was and the subjects being studied in the departments of Psychology during the British period. This also meant that they were unable to make any major societal changes or engage in research that would bring about social awareness.

 

 This bifurcation of the actual from the academic did not change even after Independence. In fact, it only become more pronounced. In most universities, there was a divide now between the Philosophy department and the Psychology department. Most of the philosophy professors became psychology professors and were very excited to be finally considered ‘scientific’. Hence, they continued to study areas like memory, psychophysics, perception, learning, pattern recognition and the like. They did not utilize their understanding of Indian Philosophy to help them better understand the Indian mind and behaviour.

 

Psychologists also did not focus on theory building and neither did they stick to any particular theory in their writings. Decisions were based more on what projects generated more funds. They also distanced themselves from issues of national interest. Hence, Psychology was distant in nature and it lacked a vision to take it forward.

 

But, in 1950, after the partition of India, the Ministry of Education sought the services of Gardner Murphy to help Indian scholars investigate the causes of communal violence. This endeavor resulted in a book called ‘In the Minds of Men’. This was a not just towards academic writing, but also towards understanding the mind-set of Indian people.

 

Post Independence, there was also a shift of the growth of Psychology outside the university campuses. Kamla Chowdhury conducted a large-scale survey on motivational levels in textile industry workers. NIMHANS in 1955 and the Hospital for Mental Diseases in Ranchi introduced advanced training programmes for the benefit of personnel selection tests. 

 

Psychology and UGC

In the 1950s-1960s the field of psychology saw huge progress as the UGC encouraged various universities to begin courses in psychology by funding them. As a result the number of colleges offering psychology increased to a 32. The interests of the person heading the department at any given time governed the specialties that the departments focused on. Hence, departments were not able to focus on one field of specialization over a sustainable period of time.

 

The UGC continued in its efforts to promote excellence in education. In the late sixties it began a scheme of Centers for Advanced Studies and Centers for Special Assistance. Under these schemes the psychology departments at Utkal and Allahabad were given the status of Centers of Advanced Studies in Psychology. The aim was to improve the quality to be on par with the rest of the world.  The UGC expected these departments to take the lead in areas of advanced research.

 

The exchange programmes engaged by the fellowships of Commonwealth, Fulbright and Ford Foundation, encouraged many Indian scholars to be trained in the west (Britain, Canada, and the United States) and sharpen their skills. On their return these scholars were able to impart skill and engage in projects that had social impacts. Another development during this time was that psychology was introduced to various professional colleges like engineering, agriculture, management and medical sciences. However, the subject was taught by junior staff, research assistants, and demonstrators and received a low priority. This has not changed much even to this day.

 

Psychology outside University campuses

In the seventies, many researchers became frustrated with being unable to conduct research within the university departments and hence research endeavors were taken outside the university departments. The universities were also not being able to control the quality of students entering the departments. The universities were also being affected by the politics of the nation and there was unrest on their campuses. Some of the institutes where A.N.S. Institute of Social Studies (Patna), Center for the Study of Developing Societies (New Delhi), and the National Institute of Community Development (Hyderabad).

 

Indian Adaptations to Western Tests

The area of psychological testing continued to increase. Many western tests were being adapted to the Indian population. Out of the 503 tests, 218 were personality tests. However, these tests did not establish validation and seemed to have a language barrier. Hence, these tests were suited only for the urban population. The quality of these tests were thus in question.

 

The Second Handbook of tests by Pestonjee showed considerable improvement. This handbook showed improvements in the areas of establishing validity and including Indian adaptations of western tests. These tests were then used to conduct research on the prevalence of mental health problems by Sethi in Lucknow (1972), Dube in Agra (1970), Rao in rural Bengal (1972), Verghese in Vellore (1973). However, these epidemiological studies lacked depth in the study of the problem. Areas of drug abuse, yoga and health, psycholsocial aspects of family planning and mental retardation was slowing gaining momentum in the seventies. 

 

Late Seventies and Eighties

Towards the late seventies and eighties there was a noticeable change in the focus of research. Scholars began to research on social problems, Indian concepts and theories. Some of the areas of interest were teacher-pupil model in clinical counseling (Neki, 1973), leadership style – nurturant task-master (Sinha, 1980), the role of traditional healers in maintaining mental health in traditional societies (Kakar, 1982, and 1991), concept of stress based on ancient scripture (Rao, 1983), concepts of stress based on ancient scriptures (Palsana, Bhavasari, Goswami, and Evans, 1986), and a measure to study the concept of detachment and its mental health consequences (1992). However, the majority of the research topics tend to be replicative and imitative. 

 

 The present trend in research and higher education in India is towards indigenization. An example in this trend is the book edited by Misra and Mohanty (2002) titled ‘Perspectives on Indigenous Psychology. 

 

Bibliography

Dalal, A.K. (2010. Foundations of Indian Psychology. New Delhi: Pearson.

Kakar, S. (1982). Shamans, mystics and doctors: A psychological inquiry into India and its healing traditions. Bombay: Oxford University Press.

Kakar, S. (1991). The analyst and the mystic. London: Penguin.

Misra, G., & Mohanty, A. (2002). Perspectives on indigenous psychology. New Delhi: Concept.

Neki, J.S. (1973). Guru-chela relationship: The possibility of a therapeutic paradigm. American Journal of Orthopsychiatry, 43, 755-766.

Palsane, M.N., Bhavsagar, S.N., Goswami, R.P., & Evans, G.W. (1986). The concept of stress in the Indian tradition. Journal of Indian Psychology, 5, 1-12.

Rao, R. (1983). The conception of stress in Indian thought: I. The theoretical aspects of stress in Samkhya and Yoga systems and II. The practical involvement in Gita and Ayurveda. NIMHANS JOURNAL 1, 115-131.

Sinha, J.B.P. (1980). Nurturant task leader. New Delhi: Concept.

 

 

 

 

 

--

Mary Varughese

Psychologist

Address: SAIACS, 363, Doddagubbi Cross Road,

Kothanur, Bangalore 560077

HISTORY OF COMMERCE (NEW)

The Development of Commerce Teaching History in India.

 

Commerce and trade are ageless concepts. They are as old as mankind. There has been a historic growth in the fields of commerce, industry and science in the recent past. This growth demands a specialised education in various fields concerned with science, commerce and industry.

If one turns the pages of history, Higher education in Commerce in India is nearly 102 years old.

 

Formal commerce education was first started in India in 1886 at Madras by the Trustees of Pachaiappa’s Charities in the form of commercial School. Thus the formal commerce education in India is nearly 118 years old.

 

At collegiate level the Presidency College, Calcutta started Commerce classes in 1903.

By about that time it was also introduced in Delhi. One more commercial institution was started in Bombay in 1912. At the graduate level the commerce edu­cation was introduced in 1913 in Sydenham College of Commerce and Economics in Bombay.

 

A very rapid growth of commercial educational institutions was observed during 1920-40. The Indian Institute of Bankers was estab­lished in 1926, the Institute of Chartered Accountants of India was established in 1934. Later on in 1944, Institute of Works and Cost Accountants of India was established. In 1955, the Federation of Insurance Institutes was established.

 

To cope with the increasing demand for the trained people to transact commercial and governmental jobs, it became essential to introduce the commerce education at school level.

 

To start with the teaching of short-hand and typing was intro­duced in Government schools and aided schools and afterwards the teaching of commerce was introduced in such schools. Now the com­merce education has been included in the school curriculum.

 

According to Dr. Khan, "Commerce education got some impe­tus in conjunction with the growth in the volume of the business. The constantly growing demand for typists, stenographers, book-keepers and clerical workers made commerce curriculum a very desirable addition to secondary school programme. The tremendous spurt in commerce and industry with the planned economic development of the country made the possession of commercial competencies essen­tial to commercial career.

 

Now, there is a great demand for office workers who can type readily and accurately, take and transcribe notes quickly and correctly, keep financial records and operate busi­ness machines effectively. In addition it has been discovered that type writing and other commercial subjects can make valuable contribu­tions to the general education of the students".

 

In the new scheme of education (I.C. 10+2+3 pattern of educa­tion) sufficient attention has been paid to commerce education in Indian schools. In addition to shorthand and typing some more sub­jects that have been included for teaching in commerce are as follows:

(I) Book-keeping and Accountancy,

(II) Commercial mathematics,

(III) Sectarian practice,

(IV) Commercial English / Hindi,

(V) Commercial Law,

(VI) Industrial law,

(VII) Taxation,

(VIII) Income Tax,

(IX) Salesmanship,

(X) Applied economics,

(XI) Public relations, and

(XII) Advertising.

 

The teaching of Commerce subjects starts from XI class and in class XII the syllabus is quite advanced. Many a commercial subjects are also taught in vocational institutes.

 

At present commerce education is considered as good education because of the distinct advantages that a commerce student has over his counter-part in the arts faculty. It is believed that a commerce student not only achieves just training and perfection, but also a general professional intelligence.

 

Origin of commerce as a discipline:

 

·         1819 – The world's first business school, ESCP Europe was founded in Paris, France. It is the oldest business school in the world and now has campuses in Paris, London, Berlin, Madrid, and Torino.

·         1855 - The Institut Supérieur de Commerce d'Anvers (State funded) and the Institut Saint-Ignace - École Spéciale de Commerce et d'Industrie (Jesuits education) were founded in the same year in the city of Antwerp, Belgium. After almost 150 years of business education and rivalry between catholic and state education, the successors of both institutions have merged in 2003 to the University of Antwerp.

·         1857 – The Budapest Business School was founded in the Austrian Empire as the first business school in Central Europe. It is the oldest public business school in the world

·         1871 – The Rouen Business School recently merged with Reims Management School under the name of NEOMA Business School. Rouen Business School is one of the oldest French business school.

·         1881 – The Wharton School of the University of Pennsylvania is the United States' first business school.

·         1898 – The University of St. Gallen established the first university in Switzerland teaching business and economics.

·         1900 - The first graduate school of business in the United States, the Tuck School of Business at Dartmouth College, was founded. The school conferred the first advanced degree in business, specifically, a Master of Science in Commercial Sciences, the predecessor to the MBA.

·         1902 - The Birmingham Business School is the United Kingdom's first business school. Originally established as the School of Commerce was established in Birmingham, United Kingdom.

·         1906 – The Warsaw School of Economics (SGH) was established as the first university in Poland dedicated to teaching commerce and economics.

·         1908 - Harvard Business School was founded at Harvard University. It was the first program in the world to offer the Master of Business Administration degree.

·         1946 – The Thunderbird School of Global Management, then called the American Institute for Foreign Trade, was the first graduate management school focused exclusively on global business.

·         1949 – The University of Pretoria in South Africa founded the oldest business school in Africa. In January 2008 the Graduate School of Management was formally replaced by the Gordon Institute of Business Science.

·         1949 - XLRI - India's oldest business management school is founded.

·         1954 - The Faculty of Management Studies (FMS), University of Delhi is among one of the oldest business schools in India.

·         1955 - The Institute of Business Administration, Karachi was the first business school to be established outside North America to offer an MBA degree.

·         1991 – The IEDC-Bled School of Management was the first business school to offer an MBA program in Eastern Europe.

·         1994 – CEIBS (China Europe International Business School) was the first business school in China to have received funding from a foreign government, namely the European Commission.

 

CONCLUSION:

 

At present commerce education is considered as best education because of the distinct advantages that a commerce student has over his counter-part in the other faculties. It is believed that a commerce student not only achieves just training and perfection, but also a general professional intelligence.

 

 

 

 

 

 

 

 

References:

 

1.      Lecturer notes shared by Professor Neetu Patyal through Skype on 29/03/2014

 

2.      en.wikipedia.org/wiki/Business_school, Last visited on 12/04/2014.

 

      SANJANA GUPTA,    COMMERCE 1340103