Just finished my A Levels, maths study advice before uni?

[Tibbz]

Hi everyone,

So I'm currently in the middle of my summer holiday (waiting for A Level results) and I'm getting pretty bored of not knowing what to do. (I have contacted some charities for volunteer work but still waiting to hear, anyway that's beside the point)

At A Level I studied Maths (Core 1-4, Mechanics 1 and 2) and Further maths (Further Pure 1-3, Mech 3, Stats 1, Decision 1) , so I have some knowledge of calculus, vectors (3d lines, planes), 1st/2nd order differential equations, mechanics, complex numbers etc.

Basically I want to continue to expand on my maths/physics knowledge before I (hopefully) go to university in September to study physics. However I don't really know where to start from, could anyone offer some advice on what topics of maths(or physics) that I could look into and hopefully understand/learn from my current level of knowledge?

Thanks! :)

 

[axmls]

Are you going for physics?

Then read the Feynman lectures!

 

[Tibbz]

Are you going for physics?

Then read the Feynman lectures!

Ah yes I do have those bookmarked, and have read some of the early pages already :) I will continue do read them!

 

[artfullounger]

You've pretty much covered all the relevant maths you're realistically going to need or indeed be able to grasp at this stage. Anything else you'll either not need or will be taught to you in a lot more depth once you begin your course anyway.

Reviewing the Feynman Lectures is a great idea on the physics side however as they help develop your physical intuition. You could find an old copy of Young and Freedman on ebay or something and work through some of that, since University Physics with Modern Physics is basically every single topic you'll do in first year (although some,
e.g. mechanics and EM, you'll probably go into more depth on).

Getting some problem based book for basic calculus may be useful so you can keep your computational skills sharp. The Schaum's guides are useful int his respect as while they aren't very didactic they have tons of (usually worked) problems. The Schaum's Guide of Advanced Mathematics for Scientists and Engineers in particular covers basically all the maths you're likely to encounter in a typical single honours physics degree in the UK, so if you get a copy now you can work on the stuff you know over the summer and then have it for exam prep for your future courses at a later date. It's also pretty cheap usually.

While arguably not really relevant you could look at some pure maths topics. Yet Another Introduction to Analysis by Victor Bryant was basically designed for post A-level Maths students to develop the concepts of Real Analysis. I found it tediously slow personally, but for a beginner it's probably a decent introduction. I never finished reading it so I can't really comment on how good it is. Similarly Linear Algebra Done Wrong covers Linear Algebra allegedly at a fairly introductory level and is supposedly quite good. It's also a free web resource unlike the previously mentioned things, which may be available for free on the web but aren't necessarily legally so :P

Many people recommend Spivak's Calculus which covers broadly similar levels of calculus as at A-level but from a more theoretical/analysis-oriented point of view. It's supposedly very good didactically and has a good breadth and depth of problems. On the downside I think it's often quite pricey.

 

[Tibbz]

*Much helpful advice*

Thank you! :)

Certainly plenty of things to look into, and I do have a nice thick book full off problems from trig to way past single variable calculus, so I'll dive into that too!

 

[f95toli]

Basically I want to continue to expand on my maths/physics knowledge before I (hopefully) go to university in September to study physics. However I don't really know where to start from, could anyone offer some advice on what topics of maths(or physics) that I could look into and hopefully understand/learn from my current level of knowledge?

Thanks! :)

My advice would be to do something that is actually useful instead
You will have plenty of opportunities to study math once you've started university, self studying for a few weeks now is not going to make much of a difference. Hence, I would instead focus on learning something that would be very useful to know but won't be taught at university (at least at most universities in the UK). Buy yourself a a Raspberry Pi or an Arduino (or something similar) and learn to program it to be point where you can say make an LED blink (note that the price of a Pi is about the same as for a textbook)..

Knowing a little bit about practical electronics will be a big help if you e.g. decide to apply for summer internships while at university since it would make you much more "useful" in a lab. I tend to get something like 10 applicants whenever I advertise for summer students, and I always end up hiring the student who has shown at least some aptitude for doing something a bit more practical (the student I had this year actually used a Pi to make some control electronics for one of our experiments).
If you don't want (or can) do something practical I would instead suggest you try to learn a bit of Python programming (if you get a Pi this is something you will learn anyway). It is -again- something that they are unlikely to teach you at university (at least properly) but would be extremely useful to know.

 

[Tibbz]

My advice would be to do something that is actually useful instead
You will have plenty of opportunities to study math once you've started university, self studying for a few weeks now is not going to make much of a difference. Hence, I would instead focus on learning something that would be very useful to know but won't be taught at university (at least at most universities in the UK). Buy yourself a a Raspberry Pi or an Arduino (or something similar) and learn to program it to be point where you can say make an LED blink (note that the price of a Pi is about the same as for a textbook)..

Knowing a little bit about practical electronics will be a big help if you e.g. decide to apply for summer internships while at university since it would make you much more "useful" in a lab. I tend to get something like 10 applicants whenever I advertise for summer students, and I always end up hiring the student who has shown at least some aptitude for doing something a bit more practical (the student I had this year actually used a Pi to make some control electronics for one of our experiments).
If you don't want (or can) do something practical I would instead suggest you try to learn a bit of Python programming (if you get a Pi this is something you will learn anyway). It is -again- something that they are unlikely to teach you at university (at least properly) but would be extremely useful to know.

I have been learning python for a few months now, so already have that covered ;)

I've been looking into getting a pi at some point, they do seem quite useful, and I've seen a few good applications of them that could be useful to me in hobbies!

Cheers :)