MTH5114 - Linear Programming and Games - 2023/24
| Topic | Name | Description |
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| Lecture Notes | ||
| Week 1 : Introduction to Linear Programming | ||
Note that I slightly edit the notes I wrote in the lecture to correct small mistakes or clarify explanations, but these are essentially the notes I wrote on the ipad. |
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You will submit your solutions to these questions (together with your solutions for coursework questions from week 2 and week 3) in week 5 on QMplus. Details will be announced closer to the time. |
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These questions are designed to test your knowledge and understanding from Week 1. These questions will be discussed during seminars in Week 2. You do not need to submit any solutions, but you can and should get feedback on your attempts during seminars. |
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This is a link to a video of the gameshow Golden Balls, where we see an interesting game theory strategy being used. Later in the module we'll see why this "weirdest strategy ever" is the right thing to do! |
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| Week 2 : Modelling with Linear Programming | ||
These are the slides I will write on during the lecture. Note that I may have to alter these a little, so they might not match up exactly with the lecture |
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| Week 3: Geometry of Linear Programming | Most notes will be written in lectures. However, it will be useful to have several sheets of grid paper for drawing graphs, which is provided in the pre-lecture notes. |
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| Week 4: Extreme Points and Basic Feasible Solutions | ||
Note that I made some corrections to the notes mainly towards the end in the proof by example that extreme point solutions are the same as basic feasible solutions. In addition, I completed that proof by example in the notes (which we were not able to complete in lecture). |
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| Week 5: The Simplex Algorithm | ||
| Week 6: The 2-Phase Simplex Algorithm | ||
| Week 8: Duality I | ||
| Week 9: Duality II and Advanced Modelling | ||
| Week 10: Game Theory I | ||
The lecture starts 22 mins into the video because of a fault with the AV system this week. |
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| Week 11: Game Theory II | ||
Note that |
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| Coursework | ||
General feedback for first coursework submission Week 1 - this question was done quite well and most students obtained full marks. There was 1 mark each for parts (a) and (b) for stating that these are not linear programmes and 4 marks for (c) for transforming the linear programme into standard inequality form. Week 2 - Part (a) was done reasonably well with around 75% of students obtaining close to the full 5 marks. Part (b) was more difficult as it was not directly comparable to any examples from lectures or the seminars. Around 30% of students got this fully correct obtaining the full 2 marks. A few more got this partially correct (missing out e.g. the fact that we need c to be at least 0 in the solution). Note that for both parts, there is more than one correct answer. Week 3 - Part (a) was worth 4 marks. Many students got the sketch correct, but incorrectly concluded that the linear programme was unbounded and so obtained 2/4 marks. Part (b) was worth 3 marks. It was done better with many students finding the correct optimal solution and obtaining full marks. [In this question there were no marks for explaining your method for finding the optimal solution, but in an exam there might be, so make sure you can explain how you arrive at the solution. An incomplete understanding of the method is probably the reason why part (a) was done poorly.] |
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| Week 12: Game Theory III and Revision | ||
