Maths for Optimisation

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Cleland
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#1
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#1
Hi Everyone,

I'm looking for some advice from someone who has studied Optimisation as an undergrad or postgrad, and who has a good understanding of the underpinning mathematical concepts.

I'm starting an MSc in September, and perhaps unlike many people who will start the course, my maths knowledge does not extend beyond my A-Levels.

The MSc is in Business Analysis, so I don't think that the maths will be too rigorous, not like a pure Operations Research course might be. It will be more about understanding the concepts and being able to implement the techniques using software packages.

Still, I'm conscious I've missed out on undergraduate maths and I'd like to further my knowledge (to the extent that I can in the next three months!) and try and improve my understanding in some key areas.

What would be the best areas to focus on do you think? I was considering the MIT opencourseware lectures on linear algebra: http://ocw.mit.edu/courses/mathemati...ideo-lectures/

Differential equations perhaps?

Any advice would be really appreciated, particularly if you can explain why the suggested skills are useful from an Optimisation perspective.

Thanks for you thoughts.

Tom
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rayquaza17
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#2
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From what I understand of optimisation, I don't think you can go wrong if you go through some calculus (single and multivariable). So like maybe read through http://ocw.mit.edu/courses/mathemati...lus-fall-2010/ and http://ocw.mit.edu/courses/mathemati...al-derivatives

But maybe if you posted the link to the course you are actually going to take, we could offer more specific advice.
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FireGarden
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#3
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To further the post above, certainly multivariable calculus; there is a method known as Lagrange Multipliers, which is used to optimise a function of several variables with respect to constraints.

Also yes, do study linear algebra. Everyone should know some linear algebra. A very large portion of mathematics is simply about reducing hard things to linear things, because linear algebra is so well understood and useful.

Business Analysis though, to me anyway, is a little vague when it comes to what you will actually study. Will economics feature much? An interesting variant of calculus is Ito calculus (or stochastic calculus) which is essential to study the behaviours of weiner processes, which are used often in financial mathematics. If this is necessary, then yes, definitely study some differential equations!
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Cleland
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#4
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#4
Thanks both for your thoughts. Yes, a little more detail would probably be helpful.

It's the Business Analytics course at Warwick Business School http://www.wbs.ac.uk/courses/postgra.../details/#more . The core modules with a mathematical focus in the first term are Business Statistics, which I'm relatively comfortable with. I've just finished S1 and S2 A-level, so I have a bit of a foundation to build on there. I also have one of the core texts from this module which seems fairly manageable. Also, there are modules on Operations Research Modelling and Spreadsheet Modelling.

The OR module is summarised as:

The module aims to develop the learner’s interest in, knowledge and understanding of a wide range of MS/OR techniques to support decision making in organisations. Students will learn the theoretical underpinnings of the main Operational Research techniques and the range of applications for which they are useful. They will gain practical experience in modelling and problem solving using Excel Solver.

Topics covered include:
Optimisation modelling
Linear programming with Spreadsheets
Simulation modelling (Monte Carlo)
Problem structuring
Modelling process
Validation and verification of models


The Spreadsheet Modelling module:

This module recognises the essential role that computing plays in Operational and Business Analysis projects, and the need for the students to develop hands on experience, good modelling and design skills and an understanding of the role of popular business computing tools. It includes both a top-down conceptual modelling/design and a bottom-up skills based course. The module demonstrates and develops both conceptual and practical understanding of the fundamental computing tool of spreadsheets and the problems they can address. There is an emphasis on OR applications such as simulation, stochastic and data management processes.

I'm not sure how much hands-on mathematics will be required. As it suggests in the OR module description, it's perhaps more focused on the theory and concepts, rather than being required to work through pages of algebra to find solutions. Still, there will certainly be some benefit in having an improved mathematical understanding. In the second term they have optional modules on forecasting, simulation, advanced data analysis etc, which will probably be quite mathematically challenging.

Thanks again for your thoughts and advice. I've just finished A-Level Maths, so have been doing a lot of calculus of late, although not much of the multivariable variety. It's interesting to see how some of the terms like 'stochastic', which I've comes across so many times when reading about analytical techniques, fit into the picture I've been building throughout the A-Level though - I had no idea it was linked to calculus. Thanks both for the insights. Much appreciated.

Tom
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