Brunei Math Club

 The YouTube channel of Brunei Math Club is at: https://www.youtube.com/c/BruneiMathClub where you can find lecture videos of the modules that I teach at UBD (Universiti Brunei Darussalam) and some other random math-related pieces. Below is the list of playlists that are currently actively being updated: Mathematical Methods for the Sciences I  (mostly introductory linear algebra and one-variable calculus) Mathematical Methods for the Sciences II  (mostly many-variable calculus) Algebra  (Abstract algebra including group theory and ring theory) Stochastic Processes  (elementary stochastic processes (using first-year calculus) I'm planning to post lecture notes of these videos on this blog.

In a recent assignment, I saw a student who used parentheses (round brackets) to represent a set: \begin{equation} (1, 2, 3, \cdots). \end{equation} Of course, as Georg Cator put it, " the essence of mathematics lies in its freedom ," so it is OK to use whatever symbols to represent a set, if you define it first, consistently. However, using parentheses for sets is unconventional. We conventionally use curly brackets instead: \begin{equation}\{1, 2, 3, \cdots \}\end{equation} I recommend you stick to this convention to avoid any confusion. By the way, a list of elements enclosed by parentheses, such as in \((1, 2, 3)\), is often used to represent a tuple . A tuple is an ordered list of elements. As such, \((1, 2, 3)\) and \((2, 1, 3)\), for example, represent different tuples. By comparison, in sets, the order of elements does not matter so that \(\{1, 2, 3\}\) and \(\{2, 1, 3\}\) represent the same, identical set. Furthermore, redundant elements are allowed in tuples. That

  To blog math posts, I need to write equations. Lots of equations. I found this page: https://www.quora.com/How-can-you-write-math-equations-on-Blogger-or-Blogspot . Then, I did what this page said. An inline equation should be here \(e^{i\theta} = \cos\theta + i\sin\theta\).... And a display equation should be below: \begin{equation}e^{i\pi} = -1\end{equation} and so on. Can I write equations like this? \(e^x = 1 + x + \cdots\) Here are sets of numbers. \begin{equation} \mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C} \end{equation} Vectors and matrices \begin{equation} \begin{pmatrix} 1\\ 2\\ 3\\ \vdots\\ n \end{pmatrix} \end{equation} \begin{equation} \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n}\\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{bmatrix} \end{equation} Looks good! $a+b=c$ `a + b = c`