Shuttleworth Postgraduate Scholarship Programme


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By | August 23rd, 2018|Uncategorized|0 Comments

Is MAM1000W Making You Anxious?

Hello, my name is Jeremy :-)

I am new to the MAM1000W team of tutors – if you want to read more about my background you can take a look at my bio in the MAM1000W document on Vula. In short, I returned to UCT last year to do my second undergraduate degree, a BSc in Applied Maths and Computer Science, at 25 years old, after not doing any maths for seven years. In the beginning, I found MAM1000W really hard; the pace of the content and the tutorials made me anxious and when test one came around I scored 50%. More anxiety. Luckily I have a great support system (inside and outside the Math department) and with some good advice and determination, I was able to figure out a new, way of studying and managing my time that worked better for me. When it came time for test 2, despite being super stressed out, I scored 81%.…

By | July 22nd, 2018|Uncategorized|1 Comment

The Recamán sequence

In case you have watched the following video about the Recamán sequence.

and want to play around with it in Mathematica. Here is my code for doing so:

nums = {0};

For[i = 1, i < 66, i++,
If[nums[[-1]] – i > 0 && Position[nums, nums[[-1]] – i] === {}, nums = Append[nums, nums[[-1]] – i],
nums = Append[nums, nums[[-1]] + i]]

{{#[[1]], 0}, #[[2]]} & /@ Partition[Riffle[Mean[#] & /@ Partition[Riffle[nums, nums[[2 ;;]]], 2],
Abs[Differences[nums]]/2], 2];

Table[Graphics[Circle[%[[i, 1]], %[[i, 2]], {(i) \[Pi], (i + 1) \[Pi]}]], {i, Length[%]}], ImageSize -> 1000], Plot[0, {x, 0, 91}],
Axes -> True]

(You may have to copy this by hand rather than copy/paste.)

This produces the following rather beautiful graphic (and answers the question posed in the video):

RecamanEvidence away my dear Watson…evidence away.

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By | June 14th, 2018|Uncategorized|0 Comments

PDE: Physics, Math and Common Sense. Part I: Conservation Law

Source: CFDIinside blog


The course of Partial differential equations (PDEs) usually is a tough one. There is a number of factors contributing to this toughness:

  • PDE course combines the knowledge from calculus, algebra, ordinary differential equations (ODEs), complex analysis and functional analysis. Simply put, there is a lot that you need to know about!
  • PDE methods often (or should I say, mostly?) come from physics, but this aspect is not always emphasized and, as a result, the intuition is lost.
  • There is lots of abstraction in the PDE course material: characteristics, generalized functions (distributions), eigenfunctions, convolutions and etc. Many of these concepts actually have simple interpretations, but again, this is not emphasized.
  • PDEs themselves are tough. In contrast to ODEs, there are no general methods for all kinds of PDEs. The field is young and a bit messy.

This series of posts aims to demystify PDEs and show some general way of handling PDE problems by combining physical intuition and mathematical methods.…

By | May 21st, 2018|Level: intermediate, Uncategorized|0 Comments

Advice for MAM1000W students from former MAM1000W students – part 4

In high school, as I believe was the case for many students, there wasn’t much incentive to work very hard regularly on math – concepts were easy to grasp first hand in class. That’s the kind of attitude I brought towards MAM1000W last year (2017). Unfortunately things didn’t turn out as anticipated…by as early as April I had already started playing “catch-up” for I hadn’t been putting in any practice on the staff done in class. Tests were nightmares. With every course demanding its share of my attention, I found myself crying the other day alone in my room, asking myself, “what went wrong?”. Well, the answer was pretty simple – EVERYTHING.

Eventually, I figured a way to potentially get back on my feet – I became a very good friend of my WebAssign voluntary quizzes. In combination with past papers (WHICH I HIGHLY RECOMMEND) and the daily uploaded ‘practice questions and solutions’, I was able to gain back some bit of confidence.

By | May 9th, 2018|Uncategorized|0 Comments

Advice for MAM1000W students from former MAM1000W students – parts 2 and 3

Part 2:

So one thing that really helped me was having a partner in tuts. We would do the tuts as far as we could and we would then try to help one another in the tuts and ask the tutors for help if there was a difference in opinion.

Another thing that helped studying, going through past papers and tuts were so important.

If I was ever stuck and couldn’t really understand the textbook I would go on YouTube and watch a guy named Professor Leonard.  He’s videos are super long but extremely helpful and worth your time.

And last but not least, it’s important that you try your best to work everyday with maths because once you fall behind its difficult to catch up. Even if you do just one problem a day I promise it will help In the future.

and part 3:


I would suggest to MAM1 students that they should not fall behind the maths syllabus if they have tests in other subjects because it is very difficult to catch it up and requires much more effort than one thinks.…

By | May 8th, 2018|Uncategorized|1 Comment

Advice for MAM1000W students from former MAM1000W students – part 1

This is the first in a series of posts where I will be putting up the sage words of advice of former MAM1000W. Often, these students struggled their way through the course, before making a breakthrough in their study methods. I hope that maybe it will be easier to listen to students who have been through the struggle, than the advice of lecturers who seem to know it all (though I promise you, we do not!).

Here is the first:


As an Actuarial Science student I was aiming for 70% last year. I clearly remember that at orientation I asked some of the older ActSci students at orientation what they had done when they scored below what they needed to. I was so shocked, and a little scared when the group I asked said they never had. I wasn’t worries at this stage though because I thought I’d done well at maths at school, and I’d do well at maths here.…

By | May 8th, 2018|Uncategorized|3 Comments

Hypatia, The Life and Legend of an Ancient Philosopher – by Edward J. Watts, a review by Henri Laurie

Review written by Henri Laurie.

This is an important book for anybody interested in the history of mathematics and in the history of women intellectuals.

To recap very briefly: Hypatia is well-known as the mathematician/philosopher who was murdered by a Christian mob in 415 CE in Alexandria. She is one of the best-attested woman philosophers in the Greek tradition.

Watts turns this on its head: he tells the story of a life, one of singular achievement, and one in which the manner of death is not the most important part. The picture he paints is of a very remarkable woman, who became the head of her father’s school at a relatively young age and came to dominate the scholarly activity of her city, at the time one of the three most important centres of learning in the Mediterranean.

It is important to realise that although women did study philosophy at the time, and therefore also mathematics, which was seen as preparation for philosophy, very few of them were able to continue well into adulthood.…

By | May 6th, 2018|Uncategorized|2 Comments

Cartesian product

We know we can use binary operations to add two numbers, x and y: x+y,  x-y,  x \times y,  x \div y. Furthermore there are other operations such as \sqrt{x} or any other root and exponents. Operations can involve other mathematical objects other than numbers, such as sets.

def^n Given two sets, A and B, we can define multiplication of these two sets as the Cartesian product. The new set is defined as

A \times B = \{(a,b): a \in A, b \in B\}

Before looking at abstract examples, consider this case:

e.g.1. Assume there is a student in a self-catering residence and they want to make food preps for the first four days in the week. They want to know how many possible combinations they can make using fruits (between grapes and apples) and meals (pasta and meatballs, chicken wrap).

To solve this, let  A = \{ \text{ grapes, apples } \} \text{ and } B = \{ \text{pasta  and  meatballs, chicken  wrap} \}

Then the possible meal options are: (grapes, pasta and meatballs), (grapes, chicken wrap), (apples, pasta and meat balls) and (apples, chicken wrap).

The Cartesian Product of sets A and B would be:

\text{A x B} = \{( \text{ grapes, pasta and meatballs}), (\text{ grapes, chicken wrap }), (\text{ apples, pasta and meat balls }), (\text{ apples, chicken wrap}) \}

We can think of the above example in more abstract terms.…

By | April 14th, 2018|Uncategorized|3 Comments

3. power sets

Recall powers (or exponents) of numbers: 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32

Similarly, sets have the power operation to create new sets.

def^n If A is a set, then the power set of A is another set denoted as

\mathbb{ P }(A) = \text{ set of all subsets of A } = \{ x: x \subseteq A \}

Recall: A is a subset of B if every element in A is also in B. Furthermore, if A is a finite set with n-elements, then we can find the number of subsets in A by using this formula:


To find the power set of A, we write a list of all the subsets of A first – remembering that:

  • the empty set is a subset of every set,
  • and every set is a subset of itself

Let’s look at some examples:

e.g.1. A = \{1, 2, 3 \}

Using the formula 2^n , we know that there are 2^3 = 8 possible subsets of A, namely:

\varnothing,  \{1, 2, 3 \},  \{1 \},  \{2 \},  \{3 \},  \{1, 2 \}, \{2, 3 \} \text{ and } \{1, 3 \}

Hence the power set is the set that contains all the above subsets:

\mathbb{ P }(A) = \{ \varnothing,  \{1, 2, 3 \},  \{1 \},  \{2 \},  \{3 \},  \{1, 2 \}, \{2, 3 \},  \{1, 3 \}  \}

Note: The cardinality (size) of  \mathbb{ P }(A)  = 8 = 2^3 where size of A= 3 elements


By | April 10th, 2018|Uncategorized|1 Comment