• Kapil Hari Paranjape

      Articles written in Resonance – Journal of Science Education

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

      Kapil Hari Paranjape

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    • Win or Lose? Listen to a Martingale!

      Kapil Hari Paranjape

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      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

      [1] also talks about martingales.

    • Meet Your Match

      Kapil Hari Paranjape

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      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

      Kapil Hari Paranjape

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      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

      Kapil Hari Paranjape

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      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.

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