Kapil Hari Paranjape
Articles written in Resonance – Journal of Science Education
Volume 19 Issue 9 September 2014 pp 862-865 Classics
Volume 24 Issue 6 June 2019 pp 681-684 Classroom
The author did not learn probability theory properly whenit was taught to him as an undergraduate. However, nowthat he has to teach, it has become a fascination. The problemstated below was given to second year students of theIISER BS-MS programme as an examination question; theyanswered it in interesting ways. An earlier article in Resonance
 also talks about martingales.
Volume 24 Issue 11 November 2019 pp 1311-1315 Classroom
The author did not learn probability theory properly when itwas taught to him as an undergraduate. However, now thathe has to teach it has become a fascination. The followingproblem is based on a section in the book Asymptopia by JoelSpencer and Laura Florescu. The original problem had a
“life or death” formulation. This version is less murderous!
Volume 25 Issue 1 January 2020 pp 133-139 Classroom
Diophantine geometry is a fascinating interplay between algebra,geometry and number theory. The author was introducedto it in a blackboard-less one-on-one talk given inthe aerodrome at IIT Kanpur during a thunderstorm! Thespeaker was Professor V. Srinivas of the TIFR. At that pointin time, the latter was a graduate student at the University ofChicago and happened to be in Kanpur.
Volume 25 Issue 7 July 2020 pp 1045-1053 Classroom
What is the meaning of an inﬁnite sum? This question has fascinated mathematicians for a long time; from Zeno's para-dox and the series of Madhava and Leibnitz to more contem-porary times. Euler, Fourier and others played insouciantly with inﬁnite series until Abel, Cauchy and Weierstrass gave us a safe and dependable way to ``do the right thing" with in-ﬁnite series. Like other such instances in Mathematics, this did not shut the door on the older playground. Rather it pro-vided a framework to play in it with greater clarity.The author learned a lot about this the topic through the bookon $Divergent Series$ by G. H. Hardy, while teaching a course on ``Computational Methods" at IISER Mohali.
Volume 27 Issue 2 February 2022 pp 177-184 General Article
We give a rapid introduction to some basic concepts related to the Narasimhan-Seshadri theorem such as unitary groups, plane curves, compact Riemann surfaces, vector bundles, differential equations, and connections.
Volume 27 | Issue 6