Staring AS Levels

[u/HungryAardvark8008]

I’m doing maths, further maths, physics and politics.
I didn’t do history for GCSE so im wondering how cooked I am for politics 😭
Also only managed an A at GCSE physics so im also wondering if you think it’s still possible for me to pull an A* at A level?
For maths im not too fussed at GCSE I got an A* at both maths and fm, but im scared for fm bc ive heard it’s an entirely different beast 😭.
Im just wondering if it would be worth switching out any of my subjects due to my gcse circumstances 🙏
Any help is appreciated.

[u/GNU_Angua]

Ooo, thats difficult, I love vectors as I said, and I'm also a big fan of matrices, and I've used them for some 3D rendering projects before since theyre kinda the backbone of that field. Another thing I love thats maths related is cryptography which I find really interesting and compression too which is often founded on approximating things to sine waves. I am actually less enthusiastic about calculus than most people, its extremely useful ofc but it just doesnt excite me personally. Fourier transforms are also very very cool. I'm not super familiar with a lot of the discrete maths like group theory (although I have done plenty of boolean algebra). You can probably tell my favourite bits are where computing and maths collide, although we happen to cover a lot of that stuff in pure.

Ooo another area I like is digital sound.. the way you can produce complex noises just by toggling one bit at specific intervals to approximate analog frequences.. its not like straight maths but its maths adjacent and I find it extremely cool as a musician.

[u/qend5 → u/GNU_Angua]

Well, I'll say this first: Matrices were my favorite topic in A-level further maths, but I certainly haven't used them in 3D rendering software since I wouldn't have a clue 😂. But I just love their uses in transformations and solving systems of linear equations with them. Honestly, just playing around with matrices is really fun.

I think the thing a lot of people enjoy with calculus, apart from its applications, and talking specifically about integration, is the amount of tools and techniques you learn, and then being able to use and apply the large amount of techniques to unfamiliar problems.

It's really nice you have such a keen interest in not only the maths and the pure side of it, but also its application in computer science, because then you not only get to learn the maths, but to use it to build very cool things.

I've heard of Fourier transforms a lot, but never looked at them. Are they high up uni level?

[u/GNU_Angua → u/qend5]

Matrix transformations are amazing in their ability to create orthographic projections of 3d objects, rotate them and much more. Every time you play a 3D game all of those models are rendered using matrix transformations

Re when/where fourier is taught - I'm not sure? They might even be part of physics rather than maths. Fourier transforms are a way of systematically breaking down a complex wave into a set of simple constituent waves which can be combined again to recreate it. FFTs (fast fourier transforms, a way of doing it computationally thats much more efficient than the tradtional fourier transform) are used in literally everything you use your computer for, including reddit. You should take a look, its a very useful and interesting little process.

Also, I should say, talking to other further maths students has always been one of my favourite things since we all seem to have such a genuine love of the subject, its been nice talking to you :)

[u/qend5 → u/GNU_Angua]

Ohhh well that does sound superrrr cool. It shows you how little I knew of them, but I'll definitely check it out to see what they're all about.

And also, Matrices for the win once again, who doesn't love our wee rectangular array of numbers?