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Member's Copy ISSN: 0025-5742 THE MATHEMATICS STUDENT Volume 84, Numbers 1-2, January-June, (2015) (Issued: May, 2015) - Editor-in-Chief J. R. PATADIA EDITORScopy Bruce Berndt George Andrews M: Ram Murty N: K: Thakare Satya Deo Gadadhar Misra B: Sury Kaushal Verma Krishnaswami Alladi S: K: Tomar Subhash J: Bhattcirculation L: Sunil Chandran M: M: Shikare C: S: Aravinda A: S: Vasudeva Murthy Indranil Biswas Timothyfor Huber T: S: S: R: K: Rao Clare D0Member'sCruz Atul Dixit not PUBLISHED BY THE INDIAN MATHEMATICAL SOCIETY www.indianmathsociety.org.in THE MATHEMATICS STUDENT Edited by J. R. PATADIA In keeping with the current periodical policy, THE MATHEMATICS STUDENT will seek to publish material of interest not just to mathematicians with specialized interest but to the postgraduate students and teachers of mathematics in India. With this in view, it will ordinarily publish material of the following type: 1. the texts (written in a way accessible to students) of the Presidential Addresses, the Plenary talks and the Award Lectures delivered at the Annual Conferences. 2. general survey articles, popular articles, expository papers, Book-Reviews. 3. problems and solutions of the problems, 4. new, clever proofs of theorems that graduate / undergraduate students might see in their course work, 5. research papers (not highly technical, but of interest to larger readership) and 6. articles that arouse curiosity and interest for learning mathematics among readers and motivate them for doing mathematics. Articles of the above type are invited for publication in THE MATHEMATICS STUDENT. Manuscripts intended for publication should be submitted online in the LATEX and .pdf file including figures and tables to the Editor- J. R. Patadia on E-mail: [email protected] Manuscripts (including bibliographies, tables, etc.) should be typed double spaced on A4 size paper with 1 inch (2.5 cm.) margins on all sides with font size 10 pt. in LATEX. Sections should appear in the following order: Title Page, Abstract, Text, Notes and References. Comments or replies to previouslycopy published articles should also follow this format with the exception of abstracts. In LATEX, the following preamble be used as is required by the Press: n documentclass[10 pt,a4paper,twoside,reqno]famsartg n usepackage famsfonts, amssymb, amscd, amsmath, enumerate, verbatim, calcg n renewcommandfn baselinestretchgf1.2g n textwidth=12.5 cm circulation n textheight=20 cm n topmargin=0.5 cm n oddsidemargin=1 cm for n evensidemargin=1 cm n pagestyleMember'sfplaing The details are available on Indian Mathematical Society website: www.indianmath society.org.in not Authors of articles / research papers printed in the the Mathematics Student as well as in the Journal shall be entitled to receive a soft copy (PDF file with watermarked \Author's copy") of the paper published. There are no page charges. However, if author(s) (whose paper is accepted for publication in any of the IMS periodicals) is (are) unable to send the LaTeX file of the accepted paper, then a charge Rs. 100 (US $ 10) per page will be levied for LaTex typesetting charges. All business correspondence should be addressed to S. K. Nimbhorkar, Treasurer, Indian Mathematical Society, Dept. of Mathematics, Dr. B. A. M. University, Aurangabad - 431 004 (Maharashtra), India. E-mail: [email protected] Copyright of the published articles lies with the Indian Mathematical Society. In case of any query, the Editor may be contacted. ISSN: 0025-5742 THE MATHEMATICS STUDENT Volume 84, Numbers 1-2, January-June, (2015) (Issued: May, 2015) - Editor-in-Chief J. R. PATADIA copy EDITORS Bruce Berndt George Andrews M: Ram Murty N: K: Thakare Satya Deo Gadadhar Misra B: Sury Kaushal Vermacirculation Krishnaswami Alladi S: K: Tomar Subhash J: Bhatt L: Sunil Chandran M: M: Shikare C: Sfor: Aravinda A: S: Vasudeva Murthy IndranilMember's Biswas Timothy Huber T: S: S: R: K: Rao 0 Clare D Cruz not Atul Dixit PUBLISHED BY THE INDIAN MATHEMATICAL SOCIETY www.indianmathsociety.org.in ISSN: 0025-5742 ii c THE INDIAN MATHEMATICAL SOCIETY,- 2015. This volume or any part thereof may not be reproduced in any form without the written permission of the publisher. copy This volume is not to be sold outside the Country to which it is consigned by the Indian Mathematical Society. circulation Member's copy is strictly for personal use. It is not intended for sale or circular.for Member's not Published by Prof. N. K. Thakare for the Indian Mathematical Society, type set by J. R. Patadia at 5, Arjun Park, Near Patel Colony, Behind Dinesh Mill, Shivanand Marg, Vadodara - 390 007 and printed by Dinesh Barve at Parashuram Process, Shed No. 1246/3, S. No. 129/5/2, Dalviwadi Road, Barangani Mala, Wadgaon Dhayari, Pune 411 041 (India). Printed in India. The Mathematics Student ISSN: 0025-5742 Vol. 84, Nos. 1-2, January-June, (2015) CONTENTS 1. S. G. Dani Prizes, recognitions and promotion of mathematics. 01-06 2. S. G. Dani Dynamics of Numbers. 07-21 3. Ritabrata On some recent applications of circle method. 23-38 Munshi 4. Ajit Iqbal How permutations, partitions, projective 39-52 Singh representations and positive maps entangle well for quantum information theory. 5. Pablo Andr´es A generating function related to π. 53-56 Panzone 6. Jay Praksh On a type of Sasakian manifolds- admitting a 57-67 Singh quarter symmetric non-metric connection. 1 7. Amrik Singh Deriving Forsyth-Glaisher type series for π 69-86 Nimbran and catalan's constant by an elementary method. 8. Dinesh On escaping sets of some families of entire functions 87-94 Kumar and Dynamics ofcopy composite entire functions. 9. Priti Singh Existence of reduction of ideals over semi-local 95-104 and Shiv rings. Datt Kumar 10. Manjil P. A study of the Crank function in Ramanujans 105-121 Saikia lost notebook. circulation 11. Josef Bukac Integrability of continuous functions. 123-127 12. M. Ram Murty A very simple proof of Stirlings formula. 129-133 and Kannappan Sampath for 13. ManishaMember's Diophantine equations of the form 135-155 Kulkarni f(x) = g(y) - an exposition and B. Sury 14. - notProblem Section 157-161 ******* - copy circulation for Member's not iv The Mathematics Student ISSN: 0025-5742 Vol. 84, Nos. 1-2, January-June, (2015) EDITORIAL NOTE The publication of the Mathematics Student began from 1933 as a quarterly to serve the students and teachers of mathematics. In fact, one observes the following sentence clearly printed on the front cover page of each volume of The Mathematics Student till 1952 A Quarterly Dedicated to the Service of Students and Teachers of Mathematics in India and notes that it used to have in its contents sections on Questions and solutions, Mathematical notes, Classroom notes, Book-Reviews, etc. right from the beginning till around mid-fifties, but it appears to have gradually disappeared- then after. During the past couple of years, it was widely felt among some of the well-wishers of the Indian Mathematical Society (the IMS) that the Mathematics Student has become a research level journal with no appeal to students; and it was suggested that since the IMS has no such journal for students nor perhaps is there any such journal published in India, the IMS seriously should address this deficiency. The thread was picked up by the Council of the Society, an Editorial Boardcopy for the Mathematics Student is now formed and, as a humble beginning, we are happy to resume the Problem Section beginning with this issue. The Council is aware that the success to make this periodical more relevant, acc- sessible and accptable to the larger section of mathematical community, our students and teachers of mathematics, lies in thecirculation active participation from the entire mathemat- ical community of the motherland and earnestly appeals and invites one and all for the active participation to serve the cause of mathematics in this way. It may be noted here that for making it feasible for everyonefor to participate, the soft copy of the Mathematics Student isMember's made available, for free open access to all, on Society's website: www.indianmathsociety.org.in not - copy circulation for Member's not vi The Mathematics Student ISSN: 0025-5742 Vol. 84, Nos. 1-2, January-June (2015), 01-06 PRIZES, RECOGNITIONS AND PROMOTION OF MATHEMATICS* S. G. DANI Manjul Bhargava was awarded the Fields Medal this year, at the inaugural function of the International Congress of Mathematicians at Seoul, South Korea, on 13 August 2014. Joyous messages were exchanged, following the announcement, by the Indian mathematical community and the Indian people in general. Many mathematicians from India present at the function wrote- home enthusiastically from the venue with whatever additional information they could gather. Many newspapers and magazines came out with special write-ups with different levels of outreach. It was an historic occasion, with a mathematician of Indian origin receiving the medal for the first time. Let me begin this talk by recording my heartiest congratulations to Prof. Manjulcopy Bhargava for the achievement. In fact the occasion was historic in more ways. Maryam Mirzakhani, another concurrent recipient of the medal, is the first woman to receive the honour. She is also the first mathematician from Iran to be awarded the Fields Medal. My ardent felicitations to her for the accomplishment; may she inspire our daughters and granddaughters to excel in mathematics.circulation The Fields Medal had been the unique coveted Prize in mathematics for a long time**, and has often been described loosely as the \Nobel Prize in mathematics" (the Nobel Prize not being awardedfor in mathematics), notwithstanding the vast differenceMember's between the prize amounts of the two. In recent years however there have been other significant new prizes (including some with large monetary not components).
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