About Siphelele Danisa

I am a Mathematics student at the University of Cape Town. I enjoy both the abstraction and applications of the theory in Mathematics. On the more abstract branches my interests lie in algebraic geometry and modern analysis, while on the more applied side my interests lie in approximation theory, applied methods, and computing. Of course, this is not exhaustive, and is heavily influenced by the resources I have been reading lately.

Linear Algebra for the Memes

I recently saw a post on Quora asking what people generally find exciting about Linear Algebra, and it really took me back, since Linear Algebra was the first thing in the more modern part of mathematics that I fell in love with, thanks to Dr Erwin. I decided to write a Mathemafrica post on concepts that I believe are foundational in Linear Algebra, or at least concepts whose beauty almost gets me in tears (of course this is only a really small part of what you would expect to see in a proper first Linear Algebra course). I did my best to keep it as fluffy as I saw necessary. I hope you will find some beauty as well in the content. If not, then maybe it will be useful for the memes. The post is incomplete as it stands. It has been suggested that this can be made more accessible to a wider audience than as it stands by possibly building up on it, so I shall work on that, but for now, enjoy this!

By | March 10th, 2019|Uncategorized|0 Comments

Basics of Vector Representation

Not so long ago, I started reading some linear algebra, just out of interest. I was uncertain about whether or not I would understand the concepts, or if it would be worth it to go through all the trouble. I can now say that it was worth it. Honestly, it was the most frustrating, but at the same time rewarding, experience. I have come to realise that there are things that we often have to accept without knowing the beauty of the logic behind their existence, and the idea presented here is one of them. This post answers a simple question about vector notation.

You might have asked yourself at some point in your life (… or maybe you haven’t, but you should): Why is it “legal” to write a vector,A, as { A=(a_{1},a_{2},\ldots,a_{n}) }, and why can we switch between different notations without finding trouble (for example, we can represent the vector in the form: {A = \sum\ a_ia^*_i} ) ?…

By | October 25th, 2017|Uncategorized|3 Comments

Counting to Infinity

I haven’t  really been active, so please accept my apologies since my first post seemed to promise that I would write quite often than I have done. But it was all for a good cause, so I have decided to share something which I found interesting while reading up some Mathematics this holiday (any corrections, additions of definitions, etc. will be appreciated).

Now, the idea I am going to talk about is the Cardinality of a set. In simple terms:
Definition 1: Cardinality is a “measure  of the size” of a set.

Suppose that we have a set, A , such that A=\{a,b,c,d,e\} . The cardinality of the set, denoted by |A| , is 5 , because there are 5 elements.
It is indeed worth noting that unlike ‘lists’, in Mathematics, order and number of elements doesn’t determine much concerning the identity  of a set, so \{a,b,c\}=\{a,a,a,b,c\}=\{a,b,b,b,c,c\}=\{a,...,b,...,c, ...\} as long as you use the same elements, they are all equal, and of course, cardinalities would be the same, because all of them are a representation of the same mathematical entity.

By | July 28th, 2017|Uncategorized|0 Comments

The UCT experience in Mathematics

One of the biggest changes in my life has been the move from my remote little town in Eastern Cape to a big city such as Cape Town. It has been the most exciting, yet scary transition, because I know that this is a path which I have to take that will eventually lead me to my dreams, but the excitement is almost balanced by the horror with which we associate the university experience, as those who are ahead usually tell us.

The best part about being at the University of Cape Town is being surrounded by so many students and professionals who are into the same things that you are into–or even different. The diversity in everything is an aspect that I find really interesting.

The one thing that really makes it easy to breathe here, though, is how willing the lecturers are to assist. Most of us were ‘raised’ to believe that being at university is all about surviving the ‘end of the world’, which of course it sort of is, but what really matters is that it is not as if no one cares about your progress.…

By | April 3rd, 2017|Uncategorized|0 Comments