Mathematics in Higher Education in India: A Historical Perspective

I begin this journey of thought through the annals of Mathematical Education in India, with a quote by Swami Vivekananda, “... how many sciences had their origin in India? Mathematics began there. You are even today counting 1, 2, 3, etc. to zero, after Sanskrit figures, and you all know that algebra also originated in India.”

Mathematics is rooted deeply in the life and culture of people in the Indian subcontinent, attested by a long history of engagement with mathematics in art, craft, work and abstract disciplines of thought. This has also meant a tradition of socially embedded modes of education and learning in aspects of mathematics as well. The fact that India has the third largest higher education system in the world (after China and the USA) suggests that there is a great deal of mathematics around as well. This study provides a viewpoint on the vast and varied landscape of the subject, and offers an insight into not only the problems and potential of mathematics education in India but also how they are approached by scholars in the past years.

India is characterized by diversity and cultural riches, as well as prevalent poverty and social division, and this is reflected in mathematics education as well. Despite the tremendous challenges, also visible are a number of innovative initiatives, some small and some on a large scale. This study cannot hope to evaluate the effectiveness of such initiatives, rather it does point to them with a sense of hope towards the future.

According to India 2009 Reference Annual (Ministry of Information and Broadcasting, 2009), India has 20 universities run by the Central Government and 215 run by States. In addition there are 100 autonomous institutions deemed-to-be universities that do not get their funding directly from Governments. Nearly 16000 colleges are affiliated to these universities, among them 1800 exclusively for women.

India is also home to some institutions where world class research in mathematics is carried out. A strong group of Indian mathematicians have been contributing to the development of many areas of mathematics. The legendary genius Srinivasa Ramanujan has inspired generations of young Indians towards taking up mathematics as a calling. India boasts of institutions of technology and medicine that have been globally acclaimed for their standard of undergraduate education. These, and the boom in Information Technology industry (and its generation of jobs) in the last two decades, have led to a greater emphasis on mathematical training, and the nation seeks to expand a pool of scientifically equipped manpower. This creates a situation in India where higher education in mathematics forms a very sharp pyramid. A few elite institutions offer excellent opportunities for mathematics research and a small number for mathematics education as a part of technology or some instances, management studies. However, among the large number of universities and a vast number of affiliated colleges, which provide the bulk of higher level  mathematics education, there is an overall rigidity in curriculum, pedagogy and modes of assessment that make mathematics education often ineffective. This affects the prospects of building a strong pool of mathematics teachers for the future.

Small innovative initiatives towards constructing a meaningful interactive pedagogy at the under graduate level give hope for solving this problem on a larger scale in the future. An important agenda for mathematics education in India is research in mathematics education. University departments, while undertaking research in education, by their typical structure, tend to attract largely people who are neither mathematically trained nor thus inclined. Further, the idea of research providing solutions to curricular conundrums or pedagogic trauma remains outside the framework of decision making in education. The system needs to build a way of actively pursuing research on several fronts towards well formulated questions and use the answers to influence policy. It should be noted here that India provides a large enough arena, with tremendous diversity, to even allow a self-contained universe for analysis and research, and international influences can only add to this richness.

The past four decades (beginning 1970s) have seen enormous changes in the field of education in India.  Numerous organizations (governmental and non-governmental) have taken steps in response to or in reaction against the policies adopted by the government.  Universalization of education and education for democracy have become the new agendas for the country which gives much  importance for the growth of biological and physical sciences and technology.

As far as mathematics education concerned higher education has largely been a neglected area in India.  Indira Gandhi National Open University made some efforts to collect data on a bridge programme (the Bachelors Preparatory Programme, BPP) that they had launched to allow access to the undergraduate degree programme for people who had no formal high school leaving certificate. Feedback collected over a 3-year period suggested the need for curricular revision so as to meet the needs of the students. When India manages to provide quality mathematics education for all, mathematics education as a discipline would have new insights and new formulations to work with has happened by way of improving teaching and learning of mathematics. But a lot more needs to be done. Impressions of researchers or teachers involved in developing alternative curriculum and carrying out the classroom interventions indicated significant improvements in children’s attitudes towards mathematics. They also indicated better understanding of the content but systematic studies are required to assess their actual impact on students’ learning. In the absence of strong empirical evidence and sound theoretical background, policy formulation becomes a difficult task.  Teacher preparation continues to be the weakest link in our education system. The departments and colleges have not been able to come up with a good model of training teachers at both the pre-service and in-service levels. Simultaneously, efforts have to be made to develop capacities among teacher educators and administrators in the system. There are relatively few individuals who are contributing to innovation in mathematics education in this vast country. There is no systemic structure to support and strengthen such work. Although the list of contributors is not an exhaustive list and there are many others, including private support in the form of corporate social responsibility today, one needs to worry about quality of the various efforts made and critically look at the underlying philosophy. There is also no forum where different groups and individuals showcase their work and discuss issues relevant to mathematics education in the country. Similarly, assessment is another area which has not radically changed.  This is also one area which needs serious rethinking and research. At present, the goal of mathematics education is to tell the story of  mathematics in such a way so as to open up new  vistas of thought and knowledge through a dynamic confluence of history, philosophy, and science, to get her with the mathematics that merges them together  into a coherent living whole - a personalized story of human endeavor.

References

Ministry of Human Resource and Development (1986).National Policy on Education.

New Delhi: MHRD. Retrieved March 9, 2014 from University Grants Commission

Website: http://www.ugc.ac.in/policy/npe86.html

Ministry of Human Resource and Development (1993).Learning without burden:

Report of the National Advisory committee appointed by the Ministry of Human

Mathematics education in India – An overview 11Resource Development.New Delhi: MHRD.

National Council of Educational Research and Training (2005).National curriculum

framework. New Delhi: NCERT.

National Council of Educational Research and Training (2006a).National focus group

on teaching of mathematics report. New Delhi: NCERT.

National Council of Educational Research and Training (2006b).National focus group

on aims of education. New Delhi: NCERT.

National Board of Higher Mathematics (n.d.). Retrieved from :http://

www.nbhm.dae.gov.in/about.html

University Grants Commission (2011). 11th plan guidelines. Retrieved  on March 9, 2014

from http://www.ugc.ac.in/fi nancialsupport/xiplan/guideline.html,

http://math-site.athabascau.ca/documents/HistoryMathematicsEducation.pdf, Retrieved ,March 27 2014.

http://nime.hbcse.tifr.res.in/articles/INPBook.pdf, Retrieved ,March 27 ,2014.

Shirali, S. (2000).A primer on number sequences. India:Universities Press.

Srinivasan, P. K. (2004). Romping in numberland.India:National Book Trust.

Antony Puthussery

1345304

Computer Science Education - a Historical Perspective

Balaji V, Reg. No.1345001.

Introduction

The electronic computer was developed in 1940s, and has changed in many ways the functioning of the world. It is undoubtedly one of the top ten greatest inventions of mankind without which today, we cannot even think to live.

The history of computers in education has been characterized as an “accidental revolution” or “unthinking man and his thinking machines”. The computer has changed the saying that “necessity is the mother of invention” to “in a computer world, invention is the mother of necessity”. Some of the most provocative and inspiring ideas in the history of education have been created by the creators of the computer science field.

Prof. V Rajaraman, the renowned Indian author of many programming languages text books, in his article on “Computer Science Education in India” [1], highlights the goals of an education program in Computer Science, with the following statements:

• To fulfil the manpower needs in the field of Computer Science to ensure the Country’s economic advancement.

• To popularize the use of Computers in engineering design for applications like, design of Civil Structures, Electrical Machines and Chemical Plants. This will accelerate the development of the design process and end up in improved productivity.

• To become self-reliant in Software Development, which demands intellectual labour and India is abundant in this factor.

• To create the manpower for Designing, Manufacturing and Maintaining Computer Systems.

• To facilitate the use of Computers in Research & Development in India.

• To develop special continuing Education Programs for Managers, Engineers, Scientists, Administrators and General Public to learn the potentials of Computers and facilitate them to use the same as they had had their formal education in the pre-computer era.

• Artificial Intelligence and Natural Language Processing

• Computer Networks – Performance modelling

• Computer Graphics, Computer Vision and Image Understanding

• Theoretical Computer Science

• Computer Systems

• Intelligent Systems

• Medical Imaging, Digital image processing, Medical Informatics and Multimedia Databases

• Assistive learning for the physically challenged

• Cryptography and information security

• Technology for VLSI CAD

• Software Engineering

• M.Sc. Computer Science

• Doctor of Philosophy (Ph.D.)

• B.Tech. Computer Science and B.Sc. (H) Computer Science through its constituent colleges.

He has provided indicative syllabi for many of these courses and concludes this article mentioning the potential of the Computer Science field be utilized in the rapid industrial development of the country and for achieving our social goals.

This article discusses the applications of Computers, the impact of Computers in the field of Education and how the penetration of computers into institutions happened in the chronological order.

Computer’s entry into India

India bought its first computer in 1956 for a high sum of Rs. 10 lakh. Named HEC-2M, it was installed at Calcutta’s Indian Statistical Institute, where India’s weather forecasting model, based on statistical analysis of meteorological data, was developed. The same machine was used to design the next generation of computers, including India's first indigenous computer, the ‘TIFRAC’ (or Tata Institute of Fundamental Research Automatic Computer), in 1962.

By world standards, India is behind many countries in the field of Education. Central and state governments make consistent efforts to raise the literacy rate. The main obstacles are the huge population and lack of good teachers to reach out to this population. Computing technology comes handy to solve these kinds of problems.

Need: The Scientific Information Explosion

We are experiencing a scientific information explosion, which has not been sensed in the other disciplines. Today, scientists and engineers use computers to access the rapidly growing data bases that store numbers, words, maps, chemical and physical structures and they search them millions of times a year. The base of scientific knowledge today is huge. It is estimated that it would take 22 centuries to read the annual biomedical research literature or seven centuries to read a year’s chemical literature [2].

An unmanned Soviet satellite, Sputnik was launched on October 4^th 1957 in the orbit around the Earth, which provided scientists with valuable information. The propagation of its radio signals gave information about the ionosphere and the density of the upper atmosphere. More such information stirred national interest in educational reform and thus began the “golden age” of education. Major national efforts were made to reform education.

Fresh modes of communications such as radio, film, television and computers created an information-rich society. Schools were no longer the only center of information, but had to compete for student attention. Additionally, the new emerging educational technologies were to become an important catalyst for rethinking education. The rethinking started some time in 1960s though the inventions in Computers and Computing had started in 1940s.

Computers in Education

At Dartmouth, USA, in 1963, John Kemeny and Thomas Kurtz transformed the role of computers in education from primarily a research activity to an academic one. In the same year, at Stanford, Patrick Suppes and Richard Atkinson established a program of research and development on computer–assisted instruction in mathematics and reading. They sought to create a new system to free the students from group–paced instruction and use individualized, instructional strategies with feedback. These programs facilitate students to take an active role in the learning process and Mastery was obtained through drill–and–practice.

Computer–aided Education this way proceeded to the MIT – Massachusetts Institute of Technology, University of Michigan, Carnegie Mellon University and other well-known institutions. The penetration of computers into Education as an aid has been facilitated by many reputed Indian institutions which are discussed below.

Role of the IITs:

The Indian Institutes of Technology at various locations in the country have been the pioneer to bring in Computer Science in to the formal education stream in India. They offer both graduate and post graduate courses in Computer Science & Engineering, and facilitate active research through MS, PhD and Post-Doctoral programs. Following are the specifics of each of the institutes.

1.   Indian Institute of Technology Kanpur

This was the first Institute in the country to start Computer Science education in August 1963 on an IBM 1620 system. The department continues to lead the nation in terms of excellence in research and teaching in Computer Science and Engineering.

2.   IIT Bombay

The first computing activity in IIT Bombay started with the arrival of the Minsk II computer in 1967, which had 2^nd generation discrete transistor based circuitry, paper tape input-output, and off-line printers. Prof. J.R. Isaac spearheaded the initial efforts in setting up the Computer Center. The Department of Computer Science and Engineering was officially formed in 1982. Active research areas of the department are:

3.   IISC Bangalore

The Department of Computer Science and Automation (CSA) is a pioneering academic centre for higher education, research, and innovation in computer science, which was created in 1969 and was initially called the School of Automation. The department states its vision as “To enable India’s excellence in the world of computer science and automation”. The “Supercomputer Education and Research Centre (SERC)” functioning at IISc conducts research in the following domains:

4.   Department of Computer Science and Engineering, IIT Madras

The Department was started in 1973 with the acquisition of an IBM 370 Mainframe Computer, the then most powerful computer in India. It offered M.Tech, M.S and PhD degree programmes and started the B.Tech degree programme in the year 1983. The student strength of the department has now grown to about 400, with 50 full-time engineers working on R&D projects. Vision of the department is stated as “Global Excellence and Local Relevance in research, teaching, and technology development”.

5.   IIT Delhi

The department of Electrical Engineering, Indian Institute of Technology Delhi started Computer Technology as a course in 1976, which was even before the establishment of Computer Science & Engineering department. Courses offered were PhD, M.S. (Research) and M.Tech. The later established department of Computer Science and Engineering is now renowned for cutting edge research and for imparting state of the art education to the students of B.Tech, M.Tech, M.S.(Research) and PhD.

6.   IIT Kharagpur

The Department of Computer Science & Engineering was initiated in the year 1980 and it has played a pivotal role in developing and deploying the technology for one of the largest telemedicine networks in India. Apart from the graduate and post graduate programs, the Department has been engaged with considerable research work in

Pune University

The Department of Computer Science of Pune University is one of the earliest CS Departments started in Indian Universities. When computer science was little known and the word IT did not exist, the department started a one–year programme [B.Sc. (Applied) degree in Computer Science] in 1980. Other programs include, M.C.A. in 1983, the M.Tech. in 1985 and M.Sc. Computer Science in 1986.

University of Delhi

In the year 1981, University of Delhi with an objective of imparting quality education in the field of Computer Science, established its department of Computer Science. The Department started the three year MCA program in 1982, which was one of the first in India. Following are the other courses offered by the department:

University of Mysore

In the year 1986, the University of Mysore with the support of DRDO, Ministry of Defence, Government of India, started the department with a Post Graduate programme in Computer Science (M.Sc.) mainly to cater to the demands of good software engineering in DRDO labs all over the country. The Department of Studies in Computer Science was formed in the year 1991 and subsequently, MCA was started in 1992.

Bangalore University

The Department of Computer Science & Applications was established in the year 1986. It started with a P.G Diploma in Computer Science followed by MCA program in 1989 and M.Sc Course in 2006.

Computer Science in School Education

CBSE, the Central Board of Secondary Education, India, has included Computer Science in its Curriculum 2005, for students of XI and XII standards. Earlier in March 2004, the board’s proposal for “Work Education in Schools” included “Computer Applications” as an elective for class VI–XII[3]. Many state governments[5] have also incorporated similar changes in their secondary and higher secondary curriculum for the inclusion of many flavours of this subject like, Computer Science, Informatics Practices and Multimedia and Web Technology.

The Department of School Education & Literacy under the ministry of HRD, Government of India has framed “The Information and Communication Technology (ICT) in Schools” Scheme in December, 2004 to provide opportunities to secondary school students. This is to mainly build the necessary ICT skills in students and make them learn through computer aided learning process.  The Scheme provides support to States/Union Territories to establish computer labs on sustainable basis.  It also aims to set up smart schools in KendriyaVidyalayas and NavodayaVidyalayas.

CSI

Computer Society of India is the first and largest body of computer professionals in India. A group of computer professionals started it on 6th March 1965 and has now grown to be the national body representing computer professionals. Across India, it has 71 chapters, 418 student branches, and more than 90,000 members.

Summary & Conclusion

The information and data provided in this write–up though not exhaustive, is expected to serve the reader as a ready reckoner into the topic of “permeation of Computers in to Education in the Indian Scenario”. It starts with the very basic history of invention of computers, describes their importance to and applications in human life, and discusses how various educational institutions explored the opportunities to include into their curriculum and operations. It has also examines in short the impact of Computers in school education and described one popular professional organization, CSI and its activities.

References:

1.      The Institution of Electronics and Telecommunication Engineers, “Computer Education in India, Past, Present and Future”, Edited by Dr. Utpal K. Banerjee, Concept Publishing Company, 1996.

2.      Bernier, C. L., “Reading Overload and Cogency”, Information Processing and Management, 14, (1978), pp. 445-452.

3.      Work Education in Schools, published by CBSE (Central Board of Secondary Education), March 2004.

4.      Websites of CBSE, IIT Delhi, IIT Madras, IIT Kanpur, IIT Kharagpur, IIT Bombay and IISC, Bangalore.

5.      Official Website of School Education, Govt. Of Uttarakhand.

6.      “Computers in Education: A Brief History”, THE Journal, Date: 06/01/1997.

7.      Makarand Bhonsle, “Computer Technology in India”, web resource accessed on 30^th March 2014:  http://www.vigyanprasar.gov.in/Radioserials/Computer Technology in India.pdf.

The Development of Commerce Teaching History in India

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.

In 1920's (1921-22) the first Fiscal Commission was set-up and this commission made certain important recommendations In the light of these recommendations some major improvements were vis­ible in various industrial fields especially in the field of iron and steel industry, sugar industry, tea industry, cotton industry and jute indus­try.

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.

·         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.

Today,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 best 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.

 -          SANJANA GUPTA,    COMMERCE 1340103

History of Mathematics

Anjana K.

1345301

Research Scholar

Christ University

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. 

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 and the Lucasian chair of Mathematics being established by the University of Cambridge in 1662. 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. 

In the 18th and 19th centuries, the industrial revolution led to an enormous increase in urban population. Basic numeracy sills, such as ability to tell time, count money and carry out simple arithmetic, became essential. Within the public education systems, mathematics became a central part of the curriculum from an early age. 

During the 20th 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 for mathematical education was established in Nottingham

·         The first International congress for 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

The Development of Commerce Discipline in India

Sir,

I am resubmitting the assignment as I was not able to format it properly in my first assignment.Please consider the same.

Thanks

Josephine Geetha

Roll No.1340101

Commerce (Ph.D)

History of Legal Profession in India

Sir,

PFA.

Thanks: Shivageetha

History Of Education

Sir,

 I am attaching my assignment.

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The history of higher education in Commerce - India

The first Commerce school was established in Chennai in 1886 by Trustees of Pachiyappa”s Charities.Commerce classes started in the Presidency College, Kolkata in 1903.The Sydenham College of Commerce and Economics was established in 1913 as the first institution for higher education in Commerce.Madras became a pioneer state where it started in 1886. In post-Independence period, Commerce education has emerged as one of the most potential pursuits in the wake of industrialization, economic development and techno-managerial revolution. Commerce has grown from a subject to a full -fledged faculty in most of the universities and had acquired a pride of place amongst different academic disciplines.   The Government of Madras laid the foundation of commerce education by setting-up commercial institute in Madras. Two other institutions were established during the next ten years (by 1896). One was set-up at Calicut and the other in the state of Kerala.

In the beginning of this century Calcutta Presidency College also introduced the teaching of commerce (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.

In 1920's (1921-22) the first Fiscal Commission was set-up and this commission made certain important recommendations In the light of these recommendations some major improvements were vis­ible in various industrial fields especially in the field of iron and steel industry, sugar industry, tea industry, cotton industry and jute industry.

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.

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.