MAST20018: Discrete Maths and Operations Research

Exam worth 80%, Assessments were also an unpredictable mess

The lecturer and subject coordinator this year was new, and without going into too much detail, kinda messed up the whole subject experience. Lectures were frequently a mess, assessment requirements and weighting changing on a daily basis, foisting unwanted software and platforms on us and just created an all-round complete mess and chaos on a daily basis. At least tutorials were good though.

The Operations Research side of the subject was interesting and enjoyable, but the Discrete Maths portion was a hodge-podge of subjects, that whilst sometimes interesting felt a little out of place on a uni curriculum and honestly a little pointless. Overall, the subject honestly ended up as a bit of a failure this semester, which is disappointing as it had some potential.

Alysson Costa

90 H1

Yes, about 5, solutions were not really provided

1.5/5

Linear & Integer Optimization by Sierksma for the OR part, but not required and not really necessary

1 hour tutorial, lectures were a mess

2020 Semester 2

Four written assignments (20%), and a 3-hour written examination (80%).

A step-up from first year:
I thought I would pass through by cramming, which I would do with Calculus 2 and Linear Algebra last semester. This was not the case at all. There is quite a good amount of proof that you will need to comprehend and do if you want to truly understand the course, which I struggled at. So as a good measure you probably want to spend a good amount of time understanding the proofs you are given, and get decent at writing proofs (eg. proof by contradiction). Speaking of this, it may appear strange that this subject is more applied based, far from being abstract compared to first year math subjects. So I guess if you are into pure mathematics, you may not enjoy this subject and otherwise if you are into solving practical problems.

What is operations research?
Well, it is simply about using mathematical methods to find solutions, or making better decisions towards real-life problems. As an introduction to this field, you are taught linear programming, and how to solve a linear program (LP) using the Simplex Method. Solving non-linear or integer programs are not taught, due to its general difficulty in finding its solution. If you want to learn that then you can pursue more subjects about operations research.

You are also taught some concepts of discrete math, including finding the shortest paths, a bit of graph theory, systems of dividing things fairly and some voting systems. The lecturer, Charl Ras seemed friendly, at least when I attended his lectures up to the later weeks. He would regularly ask questions regarding a problem (of course, the same people respond and everyone stays silent... including me, ha).

Weeks 1-6: Operations Research
As mentioned above, you will learn what linear programming is about, as well as the Simplex Method. The methods covered in the Simplex Method is rather straightforward (given that you have done tons of calculations before), so you will probably want to understand the process and why it works (eg. the Fundamental Theorem of Linear Programming). You will also learn about sensitivity analysis (parametric changes), which deals with how the solution changes if you alter a linear program. Overall, I found to be the easier than the discrete portion of the course. If you slept in Linear Algebra, you might also sleep in this portion too (if you just want to calculate like me).

Second half of semester: Discrete Math
Various concepts are taught, broken up into four sections:

Activity networks: You have a problem where you want to find a minimum amount of time to get from A to B, where activities/tasks between them require previous tasks to be completed before they can start. That is basically what problems you solve in this part of the course. You also learn how to find shortest paths, and the betweenness centrality (a method for finding the importance of a node connected to other nodes). Compared to the rest of these sections, you just had to follow methods to achieve your answer. Easy as that.

Graph theory and scheduling: Finding the vertex chromatic number (minimum of colours of a graph so that no adjacent edge/node has the same colour), bipartite graphs, and finding which jobs to assign to people according to their abilities (as an example). There is some proof here which threw me off, which was made worse by not attending lectures and getting behind. So if you are new to graph theory and proofs, you probably want to keep up with the content.

Fair division: You are taught different ways to distribute portions of goods fairly/equally to other people. This part is more subjective, as you are required to explain why a system is not envy free, equitable etc.

Voting systems: I found this to be the most interesting of all the discrete math topics, despite having no interest in politics. In this part you are taught 5 voting systems--most of them relatively basic--as well as some principles which makes a voting system fair to both candidates and voters.

I found this part of the subject to be more difficult, mainly due to its broadness and lack of interrelations between the sections.

Tutorials and assignments:
I had a rather friendly and approachable tutor (A. Kumar), and unlike Vector Calculus I was far more interested in coming to these tutes because of it. Other than that, these tutes are a good warmup for the concepts taught and so it's probably worth coming to them.

As well as some typical calculating work , you are also given proofs to solve in the four assignments. I found these questions to be the most difficult of all, but there was usually only one in each assignment. If you've been paying attention the rest of the questions should be similar to the example questions shown in lectures. Each one is worth 5%, and were usually marked out of 50-60.

Exams:
You are permitted to bring a scientific calculator and a one double-sided A4 sheet of notes to the exam. As for past exams, they are provided on the LMS without its answers. Charl simply suggested us to ask questions, in person or through e-mail if we had any problems. As for the actual exam, I found the exam to be fairly reasonable (even if I choked).
I will probably be expecting a poor mark, but that was not the reason why I rated this subject 3.5/5 (lol). To me at least, you may want to spend a consistent amount of time studying the proofs, and why this is that. I found this to be the most difficult, so get a good idea on how to do proofs and understand them. As a consequence of this, I also regret not spending enough time on this subject; I concede that the study demand for it was higher compared to first years. But don't let this put you off, of course (just be consistent and you'll be fine). This subject might give you an indication if you like solving real life problems, or if operations research is for you.

Yes.

Dr Charl Ras

Exams from 2009-2013 were given, but without answers on LMS. Charl encouraged to ask questions instead.

3.5/5

None.

3 x one hour lectures per week, 1 x one hour tutorial per week

Semester 2, 2014

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