Blogs

1. From Calculus to Analysis: Limits

   At high school you were taught how to integrate and differentiate. You were exposed to all sorts of tricks and special techniques—such as the chain rule for differentiation, and integration by parts for integration. If you revelled in mastering and applying such techniques, you might find that what succeeds high school calculus, is a horse of an entirely different colour, called analysis, at university.

2. How Are Numbers Built?

   Decimals and continued fractions are two different ways to represent numbers succinctly, with complementary strengths.

3. Doron’s Mathematical Amnesia

   Poor Doron has suffered a strange cognitive deficit. His language and speech skills have survived intact, but he has developed ‘selective mathematical amnesia’. He has forgotten much of high school mathematics—which for a person with a Master’s degree in engineering—is a rather tragic state of affairs. In fact, his knowledge of mathematics now resembles Emmental cheese—full of holes.

4. Using Typst for Letters

   So, I was eager with anticipation when I first stumbled upon mention of Typst [1,2] which exhorted “Compose papers/theses faster”. The Typst home page claims it is a “A new markup-based typesetting system that is powerful and easy to learn.” Piqued by these promising assertions, I decided to take the plunge with Typst for the specific but express purpose of writing letters. I have chronicled my experiences here.

5. Euler Two with Julia

   The Julia programming language is refreshingly adaptive in its syntax and allows the programmer to solve a problem in very many ways. In the case of Euler Project Problem 2, I got into trouble, mostly because I was running foul of doing things the “right way”. The language gently nudges one to think again before coding. It coaxes rather than coerces the programmer to adopt efficient and safe coding practices. The existence of a knowledgeable user-community who were ready to help, and who could illuminate the problem from different angles, made learning Julia enjoyable, educational, and enriching. It is a language that I will spend time learning properly, and use in the future.

6. The Most Scary Experience

   My redoubtable friend Solus “Sol” Simkin wandered into my office late one afternoon and asked me, “What is the most scary experience for a human being? I thought but for an instant as I replied, almost reflexively,”Death. What else? Or a close shave with death.”

7. A Foray into Rust: Euler One

   Rust is the emerging programming language. I decided to start learning Rust by solving Euler Project One. This is a chronicle of my first efforts, including false starts, errors, backtracks, etc.

8. 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.

9. 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.

10. 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 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.