Vallabh vidyanagar seminar report

REPORT OF THE NATIONAL SEMINAR ON

ADVANCES IN MATHEMATICS: HISTORICAL DEVELOPEMENTS AND ENGINEERING APPLICATIONS

9-11, January 2012MBICT, New Vallabh Vidyanagar, Gujarat

A three day National Seminar on Advances in Mathematics: Historical Developments and Engineering Applications was organized by the Department of Mathematics, Madhuben and Bhanubhai Patel Women Institute of Engineering (MBICT), New Vallabh Vidyanagar jointly with the Indian Society for History of Mathematics (ISHM). The seminar received financial support from National Board for Higher Mathematics (NBHM), Charutar VidyaMandal (CVM), Council of Scientific and Industrial Research (CSIR), New Delhi andGujarat Council on Science and Technology (GUJCOST), Gandhinagar. The seminar was inaugurated by Prof. George Gheverghese Joseph, Manchester University, UK. He congratulated MBICT for organizing the national seminar.

The programme was chaired by Dr. C. L. Patel, Chairman, CVM, Vallabh Vidyanagar and Prof. S. G. Dani, TIFR, Mumbai. Dr. C. L. Patel in his inaugural address highlighted that thescience of Mathematics has played a vital role for scientific development. He also mentionedthat no branch of Science and Technology is complete without Mathematics. A souvenir cum

Release of the Souvenir

book of abstracts of the seminar was also released by Prof. George Gheverghese Joseph and Dr. C. L. Patel:

The ceremony of Lightning of the Lamp was performed by Dr. C. L. Patel, Prof George Gheverghese Joseph, Prof. S. G. Dani, Prof. S. L. Singh and other dignitaries on the dais.

Lightning of Lamp by Dignitaries

Prof. A.K. Kulkarni, Secretary, NBHM, Mumbai also graced this seminar with his valuable presence.

Various eminent personalities gave their precious blessings and wished for the success of this seminar. Honourable Shri Narendra Modi, Chief Minister, Gujarat said that it is delightful to know that a national Seminar on Advances in Mathematics, Historical Developments & Engineering Applications is being organized by MBICT. He said that History and recent developments of Mathematics to be covered in this seminar will help to cultivate deep interest in the subject in all the participants and make them feel proud about India's valuable contribution in the field of Mathematics and that participants will find it a good platform for knowledge sharing and learning. He said that the history and the recent developments in Mathematics will provide clarity of the progress in this field and its direction. He extended his congratulations for organizing this national seminar and conveyed his best wishes for its success.

Honourable Shri Bharatsinh Solanki, Minister of State for Railways, New Delhi, conveyed that he was glad to know that MBICT is organising a National Seminar on Advances in Mathematics: Historical Development & Engineering Applications with a noble cause of spreading knowledge regarding application of advanced mathematics in engineering and its historical developments. He congratulated the organisers and wished the Seminar a grand success.

Prof. Samir K. Brahmachari, Director General, CSIR, said that the National Seminar will undoubtedly, enhance the existing scientific network for promoting and

strengthening research in the field, and also provide much needed exposure to the young students. He wished the National Seminar all success and congratulated the organizers on this timely initiative. Dr. Akshai Aggarwal, Vice Chancellor, GTU, Ahmedabad conveyed his wishes with the message that this seminar has many interesting areas, which can lead our faculty members towards the frontiers of research in mathematics and towards the applications in engineering and physical sciences. He hoped our faculty members will be able to take advantage of this Seminar and wished all the participants, resource persons and organizers a highly fruitful seminar.

Shri Prayasvin B. Patel, Chairman CVM and Chief Managing Director, ELECON, conveyed his heartfelt congratulations to each and every member of MBICT College for organizing such a seminar and wish this national level seminar a great success. Professor Subhash Kak, Oklahoma State University, USA sent his greetings to the ISHM and participants and wished the seminar a resounding success.

Prof. S. G. Dani, in his presidential address, spoke about the right angle in ancient Indian Mathematics. He highlighted that the right angle, or perpendicular, is one of the primarynotions in the development of geometry. It has been of crucial importance in architecture,engineering and technology from the earliest times, in a variety of constructions.Eminent historians of mathematics like Prof. George Gheverghese Joseph, UK, Prof. Satish Bhatnagar, USA, Prof. Hans Raj Joshi, Canada, Prof. D. S. Hooda, Guna, Dr. Sunil Datta,Lucknow University, Dr. S. L. Singh, UGC emeritus Fellow, Prof. K. Ramasubramaniam, IITMumbai, Prof. Ravi Kulkarni, IIT Mumbai, Dr. Shraddha Ingale, Ahmednagar, Prof. MamtaRani, Noida, Dr. Renu Chugh and Dr. Gulshan Taneja, M. D. University, Rohtak, Prof. PremChandra, Ujjain, Prof. M. G. Nadkarni, Indore, Prof. B. S. Kiranagi, Mysore, Prof. M. B.Dhakne, BAMU, Aurangabad, Prof. G. S. Pandey, Ujjain, Prof. R.P. Sharma, Jaipur, Prof.Rekha Mehta, Prof. M. H. Vasavada and Prof. M. D. Patel, SPU, Vallabh Vidyanagar, Prof. V.D. Pathak and Prof. D. C. Vakaskar, MSU, Baroda, Prof. A. M. Vaidya, Gujarat University,Ahmedabad, Dr. J. C. Prajapati, CHARUSAT, Changa, Dr. Narendra C. Chauhan, New V. V.Nagar, and Principal V. N. Kamat of MBICT, New V. V. Nagar contributed significantly in the deliberations.

The “Professor U. N. Singh Memorial lecture” was delivered on Theory of Equations from Newton to Cauchy to Abel and Galois by Prof. Arun M. Vaidya, Gujarat University,Ahmedabad. In his talk he said that after the general solutions of the cubic and the biquadratic equations were obtained by Tartaglia, Cardon and Ferrari in the sixteenth century, many unsuccessful attempts were made to solve a fifth degree equation in general. That elementary symmetric functions of the roots were closely related to the coefficients of the equation was well-known. Newton realized that all symmetric functions of roots are algebraic functions of the elementary symmetric functions and therefore also of the coefficients.

The "Professor B. S. Yadav Memorial lecture” was delivered by Professor M. H. Vasavada, Sardar Patel University of Vallabh Vidyanagar on Understanding Nature through

Mathematics. His talk stated that man has always been curious to know how the nature worksand what the laws governing the natural phenomena are. Observations and experiments,coupled with some penetrating thinking, have helped man a great deal in understanding theworking of nature. Surprisingly, mathematics has also played a very significant role in thisendeavour. Sometimes mathematics has even taken a lead in this matter. Mathematics, on onehand, provides a sound basis to what is already known and on the other, predicts the existenceof something hitherto unknown. Newton derived Kepler's laws of planetary motion, whichKepler had obtained empirically, on the basis of observations, from his law of gravitationusing calculus, thus giving these laws a firmer base. The Russian chemist, Mendeleeffpredicted the existence of some new chemical elements just by observing the pattern ofnumbers giving the atomic weights of elements known till then. The new elements were then indeed discovered in nature.

A special lecture was delivered by world renowned Prof. George Gheverghese Joseph on Comparing Mathematics on different cultures: Different preoccupations, proofs and practices.In his talk, he proposed to examine critically the ways in which different mathematical traditions of the past have been characterised by historians of mathematics. He said a litmus test of a valid mathematical practice today is 'proof' and a number of criticisms have been levied against certain traditions because of the perceived absence or lack of rigour in their proof procedures (seen today as the litmus test of whether we are "doing" real mathematics or doing it well).

Prof. B. S. Kiranagi presented a talk on Harish Chandra- a Mathematical genius. He said to every Indian Harish-chandra means Satya Harishchandra, the king of Kosala region, which is on the bank of river Sarayu, of ancient India who was known for his extraordinary truthfulness and duty.

Prof. D. S. Hooda presented a talk on Vedic and Ancient Mathematics. In his talk he discussed the origin and development of Vedic mathematics. He illustrated its application by solving multiplication problems in very short time. He gave its application in computing and future plan of its expansion. He discussed ancient mathematics and the most important discoveries of decimal system, numerals and zero symbols in brief.

Prof. G. S. Pandey presented a talk on Mathematics in Vedic Era. He emphasized that ever since the dawn of Vedic civilization on this planet mathematics has been held in the highest esteem among all disciplines. According to him initially, the following three branches were developed to sustain the Vedic society: Arithmetic for use in the everyday life, Geometry for the construction of Vedics of various shapes and size to perform Yajnas, Astronomy to develop a suitable calendar system.

Prof. Hans Raj Joshi presented a talk on Fascinating Concepts in our Scriptures. He proposed that whatever science is found in Vedic period is supposed to have originated and grown to help religion. This was true to certain extent and up to a certain time only. Prof. Mamta Rani presented a talk on Hilbert Curves. The purpose of this talk is to use the idea obtained from superior approach in generation of new variants of the Hilbert curve. These curves are examples of new superior fractals.

New Hilbert curves have been generated and rewriting system has been developed for them.

Prof. M. G. Nadkarni presented a talk on Did Cantor sow the seed of Measure and Integral? Prof. Prem Chandra presented a talk on Lp- Approximation of Functions and Euler means. In his talk, he proposed to throw some light on the various subspaces of space used to obtain the degree of approximation of f. Prof. Ravi Kulkarni presented a talk on Euclidean Geometry, a historical perspective. He reviewed the historical controversy about Euclid's fifth postulate, Hilbert's objections to Euclid's formulation, and philosopher Kant's "a priori"-argument about the truth of Euclidean Geometry. He also pointed out the role of the fourth postulate.

Prof. Renu Chugh presented a talk on the Hyers-Ulam-Rassias Stability of some functional Equations. The talk presented a survey of the Hyers-Ulam-Rassias stability of some different type of functional equations in various spaces such as normed space, Banach space, Fuzzy space, Random normed space, Intuitionistic random normed space etc.

Prof. Satish Bhatnagar presented a talk on A Deck of Mathematicians. The talk was about the nuts and bolts of a long project on the investigation of the rise and fall of the centres of mathematical learning and the mathematicians who have done seminal works since BC millennia. Prof. Shraddha Ingale presented a talk on A Retrospective view of Fuzzy sets and Logic. It is being used as a tool in the fields like Engineering, Medical, Management, Artificial intelligence, Social sciences etc.

Prof. Sunil Datta presented a talk on Stokes Source Flow: a jump from 19th century to 21st century. The presentation traced various analytical and application aspects of its development. It was followed by a talk on Introduction to Quantum Computing by Prof. V. D. Pathak. In his presentation, a concise Introduction Quantum Computation was given. After this Prof. Vithal N. Kamat presented a talk on Encompassing biological sciences within Mathematics-A Unified Paradigm. He talked about Artificial Intelligence, Inductive Learning and The Evolutionary Transformation System.

Prof K. Subramaniam presented a talk on the origin and growth of Mathematics in India. The talk provided a brief overview of these and other important contributions found in the Indian mathematical treatises, generally composed in Sanskrit in the form of verses. It was followed by a talk on Reliability and Profit Analysis of Technological Systems by Prof. Gulshan Taneja. In his presentation he said that reliability has become an established discipline in many systems. He specified that Reliability of a system is the probability of the system performing its anticipated purpose adequately for the intended period of time under the given operating conditions. Prof. Rekha Mehta on Coordinate Geometry- a bridge between classical and modern Mathematics. In this talk, a brief description of Coordinate Geometry from classical Mathematics was given and how it leads to several ideas of modern mathematics.

On the second day parallel paper presentation sessions took place in which scholars from all across the country participated. The topics of presentations were very varied

and ranged from Asymmetry of Mathematics, Review of Ancient Indian Mathematics, Fibonacci Structure for some short English poems and ordered Fibonacci poems, Computer Science in the light of Ancient Mathematics, Place of Indian Mathematician Bhaskaracharya, The place of Zero in number systems, History of Statistical Analysis in Science, to Mahavira- Charya and Ganita Sar Sangraha. The topics also included recent trends in Mathematical Applications such as 2-Bounded Operators and 2-Normed Space, n-Quasinormal Operators, Lanczos Potential for general axially symmetric space-times, Role of Cryptography in Network Security Principles and Practise, Generalization of recent result of C’iric for single valued and multi valued maps, Convergence of Logistic Map in N-Orbit, Characterization of Weyl Tensor for Vaidya Metric, Joint and conditional exponential survival entropies, Analysis of two Mathematical distribution on edge detection of images, Metric Dimension of Graceful Graphs, New Fractal Hedgehogs and various other topics including parallel Invited talks.

There was a Cultural programme organized by the students of MBICT for giving all the Scholars and Mathematicians a short ride to our culture.

Cultural Program by MBICT Students

On the third day a MBICT Student Seminar was organized where parallel sessions of presentation by the students of MBICT took place. Prizes were given to the 3 best presentations by Prof. Sunil Datta. The first prize was bagged by Priyanka L. Verma and Subbulakshmi S. Pillai and their topic was Fourth Dimension. The second prize was bagged by Dipal Dalal, Avani Kansara, Riddhi Shah and Jinal Shah and their topic was Genetic Algorithms. The third prize was bagged by Aashir Sutar and Shikha Arora and their topic was Emotions, Psychology, Computer Based Modelling and Mathematics. The judges and the session chairs praised the students for their excellent efforts and wished them success for their future.

Students winning prize for best presentation

The valedictory function was addressed by Prof. S. L. Singh. In his address he spoke about the successful organization of the three days national seminar at MBICT, New V. V. Nagar. He acknowledged the participation shown by the all the participants across the country. He also encouraged MBICT College for organizing an international conference in the upcoming future. As Chief Guest, Dr. Dimple, Director, Eurokids, Anand appreciated the efforts put in by the organizing committee and congratulated for the grand success of the seminar.

Certificates were distributed to all the participants and invited guests and speakers by Prof. George Gheverghese Joseph.

Certificate Distribution

The organizing Secretary, Prof. Darshana J. Prajapati read a detailed seminar report and expressed a vote of thanks as well. A feedback was given by the participants wherein they showed their gratitude for the efforts made by the committee for organizing this successful seminar. All the participants as well as guests attended all

Group Photo of participants and guests

the sessions and events of the three day national seminar.

A short tour for the participants as well as the guests was organized to the Sardar Patel Memorial Hall, Karamsad.