**NATIONAL CONFERENCE ON RAMANUJAN: A GODDESS GIFTED MATHEMATICIAN**

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**OCTOBER 30 – 31, 2017**

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**Organised by**

**Department of Mathematics, T.D.P.G. College, Jaunpur-222002 (UP) India**

**(Affiliated to: ****Veer Bahadur Singh Purvanchal University Jaunpur)**

**and**

**Ramanujan Society of Mathematics and Mathematical Sciences**

**About the Conference:**

Srinivasa Ramanujan was one of the India’s greatest mathematical geniuses. Ramanujan was born on 22^{nd} December 1887 at Erode near Kumbakonam, a fair-sized town in Tanjore District of Madras. His father was an accountant to a cloth merchant at Kumbakonam and his mother was the daughter of an amin in the Munsiff’s court at Erode. When her marriage remained infertile for an unusually long time, her father prayed to “Goddess Namagiri” installed in the neighbouring town of Namakkal to bless her daughter with an offspring. The devoted family firmly believed that it was in response to his prayer that shortly afterwards she gave birth to her eldest child, Ramanujan.

Throughout history most famous mathematicians were educated at renowned centers of learning and were taught by inspiring teachers. The one exception to this rule is Srinivasa Ramanujan. At the age of about fifteen, he borrowed a copy of G.S. Carr’s Synopsis of Pure and Applied Mathematics, which was the most influential book in the development of Ramanujan’s genius. One or two years later, Ramanujan entered the Government College of Kumbakonam. By this time, Ramanujan was consumed by mathematics and would not seriously study any other subject consequently he failed his examinations at the end of the first year and lost his scholarship. Because his family was poor, Ramanujan was forced to terminate his formal education.

Ramanujan entered the college; at about the time he began to record his mathematical discoveries in notebooks. Living in poverty with no means of financial support, suffering at times from serious illness and working in isolation, Ramanujan devoted all of his efforts in the next five years to mathematics, while continuing to record his theorems without proofs in notebooks.

In 1910, Ramanujan married S. Janaki, who was only nine years old. More pressure was put upon him to find a job. V. Ramaswami Aiyer and R. Ramachandra Rao helped him allot and anyhow, Ramanujan became a clerk in the Madras Port Trust office where he was encouraged by Sir Francis Spring and S. Narayan Aiyer, chairman and chief accountant respectively. They persuaded Ramanujan to write about his mathematical discoveries to English mathematician Prof. G.H. Hardy who responded encouragingly and invited Ramanujan to come to Cambridge to develop his mathematical gifts.

Ramanujan’s family were Iyengars, a conservative orthodox branch in the Brahmin tradition and his mother was adamantly opposed to her son’s “crossing the seas”. Ramanujan’s mother later on had a vision from the Goddess Namagiri giving Ramanujan permission to accept Hardy’s invitation. After overcoming family reluctance, Ramanujan boarded a passenger ship for England on March 17, 1914.

Over the course of next five years Ramanujan would publish extensively on a wide variety of topics: the distribution of prime numbers, hypergeometric series, elliptic functions, modular forms, probabilistic number theory, the theory of partitions and q-series, among others. He would write over thirty papers, including seven with Hardy. After years of frustration working alone in India, Ramanujan was finally recognized for the content of his mathematics. He was named a fellow of Trinty College and he was elected a Fellow of the Royal Society (F.R.S.), an honour shared by Sir Issac Newton. News of his election spread quickly, and in India he was hailed as a National Hero.

In the spring of 1919, Ramanujan returned to South India where he spent the last year of his life. His health declined over the course of the following year, and he died on April 26, 1920 in Madras, with Janaki by his side. He was thirty two years old.

Ramanujan’s last letter to Hardy, dated January 12, 1920, where he wrote: “I am extremely sorry for not writing you a single letter up to now... . I discovered very interesting functions recently which I call “Mock” theta functions. Unlike the ‘False’ theta functions they enter into mathematics as beautifully as the ordinary theta functions. I am sending you with the letter some examples. ”

In this letter, Ramanujan defines four third order mock theta functions, ten fifth order functions and three seventh order functions. He also includes three identities satisfied by the third order functions and five identities satisfied by his first five fifth order functions. He states that the order five fifth order functions also satisfy similar functions.

The next fundamental question is: what is in Ramanujan’s lost notebook besides mock theta functions? A majority of results fall under the purview of q-series. These includes mock theta functions, theta functions, partial theta functions, false theta functions, identities connecting with the Rogers-Fine identity, several results in the theory of partitions, Eisenstein series, modular equations, Rogers-Ramanujan continued fraction, other q-continued fractions, asymptotic expansions of q-series and q-continued fractions, integrals of theta functions, integrals of q-products and incomplete elliptic integrals. Other continued fractions, other integrals, infinite series identities, Dirichlet series, approximations, arithmetic functions, numerical calculations, Diophantine equations and elementary mathematics are some of the further topics examined by Ramanujan in his “Lost Notebook”. This “Lost Notebook” was searched out by G.E. Andrews in 1976 from the Library of Trinty College at Cambridge University.

Here we shall conclude it by giving few remarks of top-class scientist and mathematicians about Ramanujan.

Hardy wrote in a letter: I think we may now hope that he has turned to corner, and is on the road to a real recovery. His temperature has ceased to be irregular, and he has gained nearly a stone in weight... . There has never been any sign of any diminution in his extraordinary mathematical talent. He has produced less, naturally, during his illness but the quality has been the same.

“Ramanujan: The patron saint of π explorers,” is an article written by Vishak Datta. In the introduction, he has written: π, the all-pervading mathematical constant, has always fascinated mathematicians. Srinivasa Ramanujan was no exception. In 1914, he derived a set of infinite series that seemed to be the fastest way to approximate π. However, these series were never employed for this purpose until 1985, when it was used to compute 17 million terms of the continued fraction of π.

“Mathematics is called: man-made-Universe, Ramanujan too created his own universe unaware of several creations already existing. What is amazing is that these man-made creations have contributed immensely to the understanding of God-made-universe and to the well being of inhabitants of this universe.”

In the end I would like to give the following remark of Prof. A.K. Agarwal: Ramanujan was a true genius. Lord Krishna in the Bhagvata Gita (Ch. 4, V.3) said to Arjun, “I am revealing the supreme truth to you because you are devoted to truth”. After about 5000 years Goddess Namagiri of Namakkal appeared in the dream of Ramanujan and gave him formulas as he was truly devoted to unfolding the mysteries of mathematics.

It will be act as an inspiration to future generations of mathematicians to tackle a job that will never be complete.

The main objective of this National conference will be to motivate young mathematicians, research scholars and teachers towards mathematics especially Ramanujan’s Mathematics and its applications in different branches of physical sciences and many more.

**About the Host Institution:**

The pride of eastern U .P. and one of the premier seat of higher learning of the state . Tilak Dhari College, which was established with 25 students in 1947 at present spread over an area of more than 60 acres with more than 12000 students enrolled in its six faculties including Arts ,Science, Agriculture, Law ,Commerce and Teachers Training. Named after its revered founder Thakur Tilak Dhari Singh and situated in the southern part of the city adjacent to the reserve police lines and the roads leading to Varanasi-Allahabad, Sultanpur-Lucknow on one side, to Ajamgarh-Gorakhpur on the other and on the third to Varanasi. Tilak Dhari College is a stone’s throw from the Bus Station and three and half kms from Jaunpur junction and about 40 Km from Babatpur Airport . Apart from 235 learned Professor national and international repute with a commodious library stocked with about- 1,50,000 books, and some rare manuscripts, and over 60 to the latest journals –periodicals and big reading room.

**About Ramanujan Society of Mathematics and Mathematical Sciences:**

India celebrated the “Mathematics Year” in 2012 and Ramanujan Society of Mathematics and Mathematical Sciences (RSMAMS) was established in the same year. The main aim of the society is the promotion of Mathematics Educations and its applications in different field of Sciences and also to create interest among students, research scholars and young teachers towards mathematics. Since its foundation in 2012 “RSMAMS” has done excellent work to improve mathematics Educations and research in India. In 2012, 2013, 2014, 2015 and 2016 “RSMAMS” has organized symposiums, conferences, and workshops successfully to achieve its goal. The society is continuously organizing lectures of eminent Mathematicians for students and research scholars. During this short tenure the name and fame of the society has spread across the frontiers of the country and also in abroad. Ramanujan Society of Mathematics and Mathematical Sciences is publishing following two periodicals:

1. Journal of Ramanujan Society of Mathematics and Mathematical Sciences

2. South East Asian Journal of Mathematics and Mathematical Sciences

**Call for papers:**

The organizers of the Conference invite papers for presentation. The abstract not exceeding 200 words intended for presentation should be sent latest by October 15, 2017 preferable by e- mail to

Dr. S. N. Singh,

263, Line Bazar,

Jaunpur – 222002 (U.P.) India.

Contact No.: 05452 – 261922

Mob. No.: 09451159058, 09451161967

E-mail: snsp39@yahoo.com; snsp39@gmail.com

**Expected Invited Speakers**

Prof. N. K. Thakare (Pune University) Prof. Satya Deo (HRI Allahabad)

Prof. A.M. Mathai (CMS-Kerala) Prof. M. S. M. Naika (B’lore University)

Prof. R. K. Saxena (JNV, University Jodhpur) Prof. K. C. Prasad (Ranchi University)

Prof. K. Srinivasa Rao (IMSC Chennai) Prof. A. K. Agarwal (Chandigarh University)

Prof. A.K. Rathei (Central University, Kerala) Prof. R.C. Srivastava(Gorakhpur University)

Prof. R.K. Yadav (Jodhpur University) Prof. M. Azhar Hussain (Bihar University)

Prof. M. I. Qureshi (Jamia-Milya Delhi) Prof. C. Adiga (Mysore University)

Prof. Subhi Khan (AMU Aligarh) Prof. K. R. Vasuki (Banglore University)

Prof. Mridula Garg (Jaipur University) Prof. D. D. Somashekara (Mysore Univ.)

**Advisory Committee**

- Prof. Raja Ram Yadav (Vice-Chancellor, V.B.S. Purvanchal University, Jaunpur)
- Prof. Sunder Lal (Ex-Vice-Chancellor, V.B.S. Purvanchal University, Jaunpur)
- Dr. Vinod Singh (Principal T. D. P. G. College, Jaunpur)
- Dr. A.K. Singh (DST, New Delhi)
- Prof. M. A. Pathan (Aligarh Muslim University)
- Prof. P. K. Banerji (J.N.V. University Jodhpur)
- Prof. Umesh Singh (BHU)
- Dr. N.N. Pandey (Principal, Dalmia College, Mumbai)
- Prof. K. C. Prasad (Ranchi University)
- Prof. U. C. De. (Kolkata University)
- Dr. B. P. Mishra (Mumbai University)
- Dr. G.C. Chaubey (Purvanchal University Jaunpur)
- Dr. Tarkeshwar Singh (BITS Pilani Goa)
- Dr. Rama Jain (MVPG, Lucknow)
- Dr. S. Ahmad Ali (BBD-Lucknow)
- Dr. Prakriti Rai (Amity-Noida)
- Dr. Vishnunarayan Mishra (SVNIT-Surat)
- Dr. K.B. Yadav (TDPG College, Jaunpur)
- Dr. Sunil Singh (Institute of Science, Mumbai)
- Dr. Jay Prakash Yadav (Dalmia College, Mumbai)
**Proceeding of the Conference:**The proceedings of the Conference will be published. The full length paper in duplicate along with a file formatted in AMS latex/ MS word/ Pdf may be submitted during the Conference by November 15, 2017.

**Registration fee:**Students : Rs.500

Research Scholars : Rs.1000

Faculty : Rs.1500

Paper Presentation : Rs.1500

**Local Hospitality**Each participant and accompanying person will be provided local hospitalities.

*Please inform well in advance about your travel programme to facilitate the organising committee and volunteers.***Contact Persons****Dr. Satya Prakash Singh (Organising Secretary) Dr. Vijay Yadav**Department of Mathematics, Department of Mathematics and Statistics

T. D. P. G. College, Jaunpur – 222002 (U.P.) India S.P.D.T. College, Andehri East, Mumbai-400059

Contact No.: 09451159058 Contact No. 8108461316

E. mail: snsp39@yahoo.com, snsp39@gmail.com E-mail: vijaychottu@yahoo.com

**Dr. S.N. Singh**Emeritus Scientists,

Department of Mathematics,

T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09451161967

E-mail: snsp39@gmail.com, snsp39@yahoo.com

**Dr. Brijendra Singh**Department of Mathematics,

T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09415895789

**Dr. Manoj Kumar Srivastava**Department of Mathematics,

T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09415334577