Blogs

1. Varieties of Multiplication

   I want to look at some of the varieties of multiplication that mathematicians have developed over time. It is a survey that will serve as a pinhole through which we can view how a single, simple mathematical idea has been expanded and elaborated into uses far beyond its historical moorings.

2. The Two Most Important Numbers: Zero and One

   The unique properties of the numbers zero and one make them mathematically interesting and indispensable. In this slow-paced stroll though the ideas streaming out of these two numbers, we uncover well-known as well as relatively obscure facts about them. It is hoped that in the process we may discover how they cement together disparate areas of Mathematics.

3. A tale of two measures: degrees and radians

   The transition from degrees to radians is often the most traumatic mathematical change that the student has to endure when moving from elementary to intermediate mathematics. The simplicity of 360° seems so much more welcoming than the equivalent of \(2\pi\) radians for the angle of a full circle. \(\pi\) is forbidding, because it is not the convenient fractional fiction \(\frac{22}{7}\), but rather a number which is both transcendental and irrational and therefore, somewhat “untidy”. Surely this tradeoff between simplicity and complexity must have been worth it, or it would not have been so ordained. Here we attempt to fathom the method in the madness.

4. Zero, One, Two, Many

   As has been observed above [1], in the context of computer programming, there are only three numbers worth being concerned about: zero, one, and many. And if you are into the arcana of “regular expressions” and “pattern matching”—which is, incidentally, something done implicitly every time you do a Google search, or look for a book at an online bookstore—that is very sage advice. But how serviceable is this dictum in everyday life?

5. Mastering Time

   As Sol wound up his enriching tale, I resolved not to fall into the trap of procrastination ever again. First, I should prime my mind to enjoy the task. Then, I should shed the need for approval from others. Next, I would allocate adequate time to prepare for it, well ahead of the deadline. Then I would do it once, and do it well. And finally when it was done and dusted, I would dismiss it from my mind. ‘Whew! What a teaching!’ I said solemnly to Sol. He smiled the beaming smile of the cognoscenti.

6. Solving a Mathematics Olympiad problem

   During a casual tour of the Web, my attention was drawn to a problem that was stated so simply that it beckoned an attempt at a solution. It was purported to be from a Mathematical Olympiad, which raised its attractiveness index, as such problems are known to strenuously exercise the grey cells, while still retaining the charm of a sport. Only later did I find out that the problem I had written down had omitted an important constraint that made the problem all the more memorable. This is an account of my escapade into the land of mathematics in search of solution.

7. Pattern Matching and Substitution in bash

   The programs, sed, awk, grep, and perl have been the traditionally used tools for matching and manipulating lines and strings in Linux. But the bash shell [1,2] also embodies powerful pattern-matching and substitution capabilities [3–6], many of which are relatively unknown and unused. This blog gives practical examples for using these powerful, but somewhat understated features, to achieve common tasks efficiently and tersely, directly from within bash itself.

8. The Secret Trapdoor to Success

   The nursery rhyme tells us that life is but a dream. Imagine, however, if someone told you that your dreams could become your life. Would you be inclined to believe that statement? If you are imbued with the scientific spirit, you would at the very least subject that assertion to experimental validation or refutation. If you are of that mind, read this blog carefully, because it could be the single most important secret of success—academic or otherwise—that you might encounter in your entire life.

9. Asking Questions in English

   This blog is devoted to the art of asking questions in English. This seemingly undemanding task often trips up the aspiring learner of English, especially one who is studying it as a second or third language.

10. What Ails Indian Education?

    The QS World University rankings for 2013 have just been released. This is one of several league tables ranking universities according to various criteria of academic performance. Such rankings are symptomatic of the relentless trend to quantify more and more aspects of our lives. May this madness be checked before intangible attributes best left qualitative—like love and loyalty—are also subjected to mindless, simplistic metrology!