REPORT OF THE NATIONAL SEMINAR ON ADVANCES IN MATHEMATICS: HISTORICAL DEVELOPEMENTS AND ENGINEERING APPLICATIONS 9-11, January 2012 MBICT, New Vallabh Vidyanagar, GujaratA three day National Seminar on Advances in Mathematics: Historical Developments andEngineering Applications was organized by the Department of Mathematics, Madhuben andBhanubhai Patel Women Institute of Engineering (MBICT), New Vallabh Vidyanagarjointly with the Indian Society for History of Mathematics (ISHM). The seminar receivedﬁnancial 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 wasinaugurated by Prof. George Gheverghese Joseph, Manchester University, UK. Hecongratulated MBICT for organizing the national seminar.The programme was chaired by Dr. C. L. Patel, Chairman, CVM, Vallabh Vidyanagar andProf. 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 Souvenirbook of abstracts of the seminar was also released by Prof. George Gheverghese Joseph andDr. C. L. Patel:
The ceremony of Lightning of the Lamp was performed by Dr. C. L. Patel, Prof GeorgeGheverghese Joseph, Prof. S. G. Dani, Prof. S. L. Singh and other dignitaries on the dais. Lightning of Lamp by DignitariesProf. A.K. Kulkarni, Secretary, NBHM, Mumbai also graced this seminar with his valuablepresence.Various eminent personalities gave their precious blessings and wished for the success of thisseminar. Honourable Shri Narendra Modi, Chief Minister, Gujarat said that it is delightful toknow that a national Seminar on Advances in Mathematics, Historical Developments& Engineering Applications is being organized by MBICT. He said that History andrecent developments of Mathematics to be covered in this seminar will help tocultivate deep interest in the subject in all the participants and make them feel proudabout Indias valuable contribution in the ﬁeld of Mathematics and that participantswill ﬁnd it a good platform for knowledge sharing and learning. He said that thehistory and the recent developments in Mathematics will provide clarity of theprogress in this ﬁeld and its direction. He extended his congratulations fororganizing 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 onAdvances in Mathematics: Historical Development & Engineering Applications with anoble cause of spreading knowledge regarding application of advanced mathematicsin engineering and its historical developments. He congratulated the organisers andwished the Seminar a grand success.Prof. Samir K. Brahmachari, Director General, CSIR, said that the National Seminarwill undoubtedly, enhance the existing scientiﬁc network for promoting and
strengthening research in the ﬁeld, and also provide much needed exposure to theyoung students. He wished the National Seminar all success and congratulated theorganizers on this timely initiative. Dr. Akshai Aggarwal, Vice Chancellor, GTU,Ahmedabad conveyed his wishes with the message that this seminar has manyinteresting areas, which can lead our faculty members towards the frontiers ofresearch in mathematics and towards the applications in engineering and physicalsciences. He hoped our faculty members will be able to take advantage of thisSeminar and wished all the participants, resource persons and organizers a highlyfruitful seminar.Shri Prayasvin B. Patel, Chairman CVM and Chief Managing Director, ELECON,conveyed his heartfelt congratulations to each and every member of MBICT Collegefor organizing such a seminar and wish this national level seminar a great success.Professor Subhash Kak, Oklahoma State University, USA sent his greetings to theISHM and participants and wished the seminar a resounding success.Prof. S. G. Dani, in his presidential address, spoke about the right angle in ancient IndianMathematics. 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. SatishBhatnagar, 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 thedeliberations.The “Professor U. N. Singh Memorial lecture” was delivered on Theory of Equations fromNewton 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 thebiquadratic equations were obtained by Tartaglia, Cardon and Ferrari in the sixteenthcentury, many unsuccessful attempts were made to solve a ﬁfth degree equation ingeneral. That elementary symmetric functions of the roots were closely related to thecoefﬁcients of the equation was well-known. Newton realized that all symmetricfunctions of roots are algebraic functions of the elementary symmetric functions andtherefore 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 Keplers 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 thenindeed discovered in nature.A special lecture was delivered by world renowned Prof. George Gheverghese Joseph onComparing Mathematics on different cultures: Different preoccupations, proofs and practices.In his talk, he proposed to examine critically the ways in which different mathematicaltraditions of the past have been characterised by historians of mathematics. He saida litmus test of a valid mathematical practice today is proof and a number ofcriticisms have been levied against certain traditions because of the perceivedabsence or lack of rigour in their proof procedures (seen today as the litmus test ofwhether we are "doing" real mathematics or doing it well).Prof. B. S. Kiranagi presented a talk on Harish Chandra- a Mathematical genius. Hesaid to every Indian Harish-chandra means Satya Harishchandra, the king of Kosalaregion, which is on the bank of river Sarayu, of ancient India who was known for hisextraordinary truthfulness and duty.Prof. D. S. Hooda presented a talk on Vedic and Ancient Mathematics. In his talk hediscussed the origin and development of Vedic mathematics. He illustrated itsapplication by solving multiplication problems in very short time. He gave itsapplication in computing and future plan of its expansion. He discussed ancientmathematics and the most important discoveries of decimal system, numerals andzero symbols in brief.Prof. G. S. Pandey presented a talk on Mathematics in Vedic Era. He emphasizedthat ever since the dawn of Vedic civilization on this planet mathematics has beenheld in the highest esteem among all disciplines. According to him initially, thefollowing three branches were developed to sustain the Vedic society: Arithmetic foruse in the everyday life, Geometry for the construction of Vedics of various shapesand size to perform Yajnas, Astronomy to develop a suitable calendar system.Prof. Hans Raj Joshi presented a talk on Fascinating Concepts in our Scriptures. Heproposed that whatever science is found in Vedic period is supposed to haveoriginated and grown to help religion. This was true to certain extent and up to acertain time only. Prof. Mamta Rani presented a talk on Hilbert Curves. The purposeof this talk is to use the idea obtained from superior approach in generation of newvariants of the Hilbert curve. These curves are examples of new superior fractals.
New Hilbert curves have been generated and rewriting system has been developedfor them.Prof. M. G. Nadkarni presented a talk on Did Cantor sow the seed of Measure andIntegral?Prof. Prem Chandra presented a talk on Lp- Approximation of Functions and Eulermeans. In his talk, he proposed to throw some light on the various subspaces ofspace used to obtain the degree of approximation of f. Prof. Ravi Kulkarni presenteda talk on Euclidean Geometry, a historical perspective. He reviewed the historicalcontroversy about Euclids ﬁfth postulate, Hilberts objections to Euclids formulation,and philosopher Kants "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 somefunctional Equations. The talk presented a survey of the Hyers-Ulam-Rassiasstability of some different type of functional equations in various spaces such asnormed space, Banach space, Fuzzy space, Random normed space, Intuitionisticrandom normed space etc.Prof. Satish Bhatnagar presented a talk on A Deck of Mathematicians. The talk wasabout the nuts and bolts of a long project on the investigation of the rise and fall ofthe centres of mathematical learning and the mathematicians who have doneseminal works since BC millennia. Prof. Shraddha Ingale presented a talk on ARetrospective view of Fuzzy sets and Logic. It is being used as a tool in the ﬁeldslike Engineering, Medical, Management, Artiﬁcial intelligence, Social sciences etc.Prof. Sunil Datta presented a talk on Stokes Source Flow: a jump from 19th centuryto 21st century. The presentation traced various analytical and application aspects ofits development. It was followed by a talk on Introduction to Quantum Computing byProf. V. D. Pathak. In his presentation, a concise Introduction Quantum Computationwas given. After this Prof. Vithal N. Kamat presented a talk on Encompassingbiological sciences within Mathematics-A Uniﬁed Paradigm. He talked about ArtiﬁcialIntelligence, Inductive Learning and The Evolutionary Transformation System.Prof K. Subramaniam presented a talk on the origin and growth of Mathematics inIndia. The talk provided a brief overview of these and other important contributionsfound in the Indian mathematical treatises, generally composed in Sanskrit in theform of verses. It was followed by a talk on Reliability and Proﬁt Analysis ofTechnological Systems by Prof. Gulshan Taneja. In his presentation he said thatreliability has become an established discipline in many systems. He speciﬁed thatReliability of a system is the probability of the system performing its anticipatedpurpose adequately for the intended period of time under the given operatingconditions. Prof. Rekha Mehta on Coordinate Geometry- a bridge between classicaland modern Mathematics. In this talk, a brief description of Coordinate Geometryfrom classical Mathematics was given and how it leads to several ideas of modernmathematics.On the second day parallel paper presentation sessions took place in which scholarsfrom 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 IndianMathematician Bhaskaracharya, The place of Zero in number systems, History ofStatistical Analysis in Science, to Mahavira- Charya and Ganita Sar Sangraha. Thetopics also included recent trends in Mathematical Applications such as 2-BoundedOperators and 2-Normed Space, n-Quasinormal Operators, Lanczos Potential forgeneral axially symmetric space-times, Role of Cryptography in Network SecurityPrinciples and Practise, Generalization of recent result of C’iric for single valued andmulti valued maps, Convergence of Logistic Map in N-Orbit, Characterization of WeylTensor for Vaidya Metric, Joint and conditional exponential survival entropies,Analysis of two Mathematical distribution on edge detection of images, MetricDimension of Graceful Graphs, New Fractal Hedgehogs and various other topicsincluding parallel Invited talks.There was a Cultural programme organized by the students of MBICT for giving allthe Scholars and Mathematicians a short ride to our culture. Cultural Program by MBICT StudentsOn the third day a MBICT Student Seminar was organized where parallel sessions ofpresentation by the students of MBICT took place. Prizes were given to the 3 bestpresentations by Prof. Sunil Datta. The ﬁrst prize was bagged by Priyanka L. Vermaand Subbulakshmi S. Pillai and their topic was Fourth Dimension. The second prizewas bagged by Dipal Dalal, Avani Kansara, Riddhi Shah and Jinal Shah and theirtopic was Genetic Algorithms. The third prize was bagged by Aashir Sutar andShikha Arora and their topic was Emotions, Psychology, Computer Based Modellingand Mathematics. The judges and the session chairs praised the students for theirexcellent efforts and wished them success for their future.
Students winning prize for best presentationThe valedictory function was addressed by Prof. S. L. Singh. In his address he spokeabout the successful organization of the three days national seminar at MBICT, NewV. V. Nagar. He acknowledged the participation shown by the all the participantsacross the country. He also encouraged MBICT College for organizing aninternational conference in the upcoming future. As Chief Guest, Dr. Dimple, Director,Eurokids, Anand appreciated the efforts put in by the organizing committee andcongratulated for the grand success of the seminar.Certiﬁcates were distributed to all the participants and invited guests and speakersby Prof. George Gheverghese Joseph. Certiﬁcate Distribution
The organizing Secretary, Prof. Darshana J. Prajapati read a detailed seminar reportand expressed a vote of thanks as well. A feedback was given by the participantswherein they showed their gratitude for the efforts made by the committee fororganizing this successful seminar. All the participants as well as guests attended all Group Photo of participants and gueststhe sessions and events of the three day national seminar.A short tour for the participants as well as the guests was organized to the SardarPatel Memorial Hall, Karamsad.