• Kapil Hari Paranjape

Articles written in Resonance – Journal of Science Education

• On Learning from Arnold's Talk on the Teaching of Mathematics

• Win or Lose? Listen to a Martingale!

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

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!

• Ramanujan-type Numbers

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.

• Euler's Summation Method

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.

• Learning to See the Elephant

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.

• # Resonance – Journal of Science Education

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Volume 27 | Issue 6
June 2022

• # Resonance – Journal of Science Education | News

• Posted on 13 July 2021
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Posted on 9 August 2021