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Further Maths for Computer Science watch

1. I took A level maths 11 years ago, went on to study music, and am now looking at a career change into programming. In order to prepare for the mathematical component of the MSc in Computer Science I've decided I want to self-study Further Maths.

In my first (AQA) maths A level I took C1-4, S1 and M1. Beyond the obvious Decision Maths 1 and 2, which units would be most beneficial for the mathematical component of a computer science degree?
2. (Original post by jgiddings)
I took A level maths 11 years ago, went on to study music, and am now looking at a career change into programming. In order to prepare for the mathematical component of the MSc in Computer Science I've decided I want to self-study Further Maths.

In my first (AQA) maths A level I took C1-4, S1 and M1. Beyond the obvious Decision Maths 1 and 2, which units would be most beneficial for the mathematical component of a computer science degree?
There's a fair bit of variation in Computer Science degrees, but the things I'd concentrate on are:

General proofs (proof by induction, proof by contradiction, use of the contrapositive, etc.)

Basic algebra manipulation (what you did at A-level will be sufficient, but it will really help if you make sure you haven't got rusty on this).

The D1/D2 material should be useful - I have my doubts about how much the nagging detiails of questions like "exactly how many swaps does it take in the worst case for bubble sorting a list of 7 elements?" are actually relevant, but it still exposes you to various algorithms and ideas.

The following are probably not covered (or only skimmed) at A-level but will stand you in good stead.

Vectors and Matrices: ideally you want to cover things like reflection of a line in a plane, closest distance of a point from a line, solving simultaneous linear equations by matrices (Gaussian Elimination)

Limits and Big-O/Little-o/theta notation. (A "maths methods" approach is sufficent, you don't need to be doing lots of analysis style looking at pathologoical cases).

Taylor's theorem and applications (e.g. Newton Raphson, approx solutions of diff equations etc).

The long list above notwithstanding, my personal experience of doing an MSc in Comp-Sci was that very little maths was actually required. All you really needed to know going in was how to manipulate polynomials. For sure, courses will differ, but (other than being up to speed with basic algebra) I'd be pretty surprised at anything else being a prerequisite unless it was explicitly pointed out in the course description.
3. (Original post by DFranklin)
There's a fair bit of variation in Computer Science degrees, but the things I'd concentrate on are:

General proofs (proof by induction, proof by contradiction, use of the contrapositive, etc.)

Basic algebra manipulation (what you did at A-level will be sufficient, but it will really help if you make sure you haven't got rusty on this).

The D1/D2 material should be useful - I have my doubts about how much the nagging detiails of questions like "exactly how many swaps does it take in the worst case for bubble sorting a list of 7 elements?" are actually relevant, but it still exposes you to various algorithms and ideas.

The following are probably not covered (or only skimmed) at A-level but will stand you in good stead.

Vectors and Matrices: ideally you want to cover things like reflection of a line in a plane, closest distance of a point from a line, solving simultaneous linear equations by matrices (Gaussian Elimination)

Limits and Big-O/Little-o/theta notation. (A "maths methods" approach is sufficent, you don't need to be doing lots of analysis style looking at pathologoical cases).

Taylor's theorem and applications (e.g. Newton Raphson, approx solutions of diff equations etc).

The long list above notwithstanding, my personal experience of doing an MSc in Comp-Sci was that very little maths was actually required. All you really needed to know going in was how to manipulate polynomials. For sure, courses will differ, but (other than being up to speed with basic algebra) I'd be pretty surprised at anything else being a prerequisite unless it was explicitly pointed out in the course description.
Thanks for this detailed reply. Just what I was looking for.
4. I'm aware that this post has pretty much already been answered, but I thought I'd try and at least add to the post above.

Just to give a bit of context, I'm part way through Year 12 doing Edexcel Further Maths and planning to go to university to do CS.

(Original post by DFranklin)
The D1/D2 material should be useful - I have my doubts about how much the nagging detiails of questions like "exactly how many swaps does it take in the worst case for bubble sorting a list of 7 elements?" are actually relevant, but it still exposes you to various algorithms and ideas.
I completely agree with this, the entirety of Decision is basically just about algorithms, which, even if you never do the bubble sort in the course, will still help by introducing the way that these subjects approach algorithms and how to solve certain problems.

(Original post by DFranklin)
General proofs (proof by induction, proof by contradiction, use of the contrapositive, etc.)
If you want to go into proof by induction, I know that that at the very least is covered my spec, and if you were interested it is Edexcel FP1 Chapter 6

(Original post by DFranklin)
The long list above notwithstanding, my personal experience of doing an MSc in Comp-Sci was that very little maths was actually required. All you really needed to know going in was how to manipulate polynomials. For sure, courses will differ, but (other than being up to speed with basic algebra) I'd be pretty surprised at anything else being a prerequisite unless it was explicitly pointed out in the course description.
As far as I've seen, they don't treat it as a prerequisite as such, but it does seem to be looked upon favourably by the universities. I know for example that one university (I'll go check if it's the one I thought that it was now) says that the typically higher end students do take Further Maths, normally as a fourth option. I can't really comment on how much of it will be relevant in the course, but I do hope that I helped at least a little bit

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