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: $$(1,2,3,\cdots ).$$ 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: $$\{1,2,3,\cdots \}$$ 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: $$e^{i\pi }=-1$$ and so on. Can I write equations like this? $e^x=1+x+\cdots$ Here are sets of numbers. $$\mathbb{N},\mathbb{Z},\mathbb{Q},\mathbb{R},\mathbb{C}$$ Vectors and matrices $$\left(\begin{array}{c}1\\ 2\\ 3\\ ⋮\\ n\end{array}\right)$$ $$\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{n1}& a_{n2}& \cdots & a_{nn}\end{array}\right]$$ Looks good! $a+b=c$ `a + b = c`