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Maths After A-levels

Hi guys, before applying to university I knew I'd end up having to choose between maths and science.After much deliberation I decide that a degree in physics would be most suitable for me.
However, I am also deeply passionate about maths and have decided that independantly study the subject- more as a hobby than anthing else
Although, I feel this is possible I don't what topics would usually be studied beyond A level which is why I need some advice.
The topics I am most intetested in are mechanics and pure mathematics.
I have completed all mechanics modules M1-5 and all core maths modules C1-FP3 if this is of any use.

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No option for a joint degree?

Surely a Physics degree would have some kind of optional mechanics module?

You said just "Physics" so I'm assuming it's a degree in general Physics or whatever it's called.
(edited 6 years ago)
Original post by Sapereaude45
Hi guys, before applying to university I knew I'd end up having to choose between maths and science.After much deliberation I decide that a degree in physics would be most suitable for me.
However, I am also deeply passionate about maths and have decided that independantly study the subject- more as a hobby than anthing else
Although, I feel this is possible I don't what topics would usually be studied beyond A level which is why I need some advice.
The topics I am most intetested in are mechanics and pure mathematics.
I have completed all mechanics modules M1-5 and all core maths modules C1-FP3 if this is of any use.


Uni option modules?, as they should be open to you and you should have the probable requirement ( A level maths)
I'm pretty sure my course does have the option of taking mechanics modules.However, when it comes to pure maths options there really isn't much.However, I should be able to teach myself it's just I don't know where to begin.What topics would ypu typically learn in a first year maths course and what books would you recommend.It'll give me something to do on and off over the summer.
Original post by Sapereaude45
I'm pretty sure my course does have the option of taking mechanics modules.However, when it comes to pure maths options there really isn't much.However, I should be able to teach myself it's just I don't know where to begin.What topics would ypu typically learn in a first year maths course and what books would you recommend.It'll give me something to do on and off over the summer.


What institution are you going to study Physics at?, so I can find/give you better advice.
Original post by DreamlinerFinder
What institution are you going to study Physics at?, so I can find/give you better advice.


Durham or Imperial college, depending on my results
Looks good, I'll be sure to look into it!Do you have any other books you'd recommend?
Original post by Sapereaude45
Durham or Imperial college, depending on my results


Have a look at the two links below:
http://www.imperial.ac.uk/mathematics/undergraduate/course-structure-and-content/

https://www.dur.ac.uk/resources/faculty.handbook/degrees/frameworks/g103.pdf ( this is for 2016, so may not be indicative)
Original post by Gem Thief
No option for a joint degree?

Surely a Physics degree would have some kind of optional mechanics module?

You said just "Physics" so I'm assuming it's a degree in general Physics or whatever it's called.

It's really only general for the first and second year, but becomes extremely specialized during third and fourth year.For example, if you decide to study theoretical physics or particle physics.
Original post by DreamlinerFinder

This is great.There seems to be a lot of crossover with the topics in phsics.I should be able to take these as option modules.
Excellent, I'll check it out!
Reply 11
Avatar for jcm420
jcm420
2
Original post by Sapereaude45
Hi guys, before applying to university I knew I'd end up having to choose between maths and science.After much deliberation I decide that a degree in physics would be most suitable for me.
However, I am also deeply passionate about maths and have decided that independantly study the subject- more as a hobby than anthing else
Although, I feel this is possible I don't what topics would usually be studied beyond A level which is why I need some advice.
The topics I am most intetested in are mechanics and pure mathematics.
I have completed all mechanics modules M1-5 and all core maths modules C1-FP3 if this is of any use.


C1-FP3?????? surely thats enough maths lad 😂😂
Original post by Sapereaude45
This is great.There seems to be a lot of crossover with the topics in phsics.I should be able to take these as option modules.


Depends, but I'll link the physics ones below:
https://www.dur.ac.uk/resources/faculty.handbook/degrees/frameworks/f301.pdf
http://www.imperial.ac.uk/study/ug/courses/physics-department/physics-msci/
Reply 13
Avatar for Zacken
Zacken
22
Original post by Sapereaude45
Hi guys, before applying to university I knew I'd end up having to choose between maths and science.After much deliberation I decide that a degree in physics would be most suitable for me.
However, I am also deeply passionate about maths and have decided that independantly study the subject- more as a hobby than anthing else
Although, I feel this is possible I don't what topics would usually be studied beyond A level which is why I need some advice.
The topics I am most intetested in are mechanics and pure mathematics.
I have completed all mechanics modules M1-5 and all core maths modules C1-FP3 if this is of any use.


A first year course in maths would typically take you through some very basic number and set theory, and the idea of proof. Working the way up to proving and using fermat-euler, chinese remainder theorem and quadratic residues. A section on countability and cardinality of sets.

It would cover some basic linear algebra, covering the idea of vector spaces, some basic theorems about those, linear maps and their matrix representations and their eigenvalue/eigenvector concepts.

Some stuff on differential equations, from basic A-Level stuff to some multivariable calculus and a bit about PDE's.

A course on group theory, building from the basic axioms on groups to lagranges theorem, introducing group actions, orbit stabiliser theorem and its various applications.

A basic real analysis course, constructing the real numbers axiomatically, a treatment of limits of sequences and series, continuity and differentiability of a function and some basic riemann integrability.

A vector calculus course, covering multivariable calculus in depth, from integration in R^n, surface integrals, directional derivatives and the derivative as a linear map as well as the associated integral theorems and div,grad, curl concepts. Some stuff on Poisson and Laplace's equation and proofs of uniqueness and existence.

A mechanics course, doing mechanics properly, working with orbits and gravity as a central force, some special relativity.

A probability course, building the concept of a probability space axiomatically, introducing the various useful distributions, concept of pdf's, cdf's in the one-dimensional and multivariable case.
Original post by Zacken
A first year course in maths would typically take you through some very basic number and set theory, and the idea of proof. Working the way up to proving and using fermat-euler, chinese remainder theorem and quadratic residues. A section on countability and cardinality of sets.

It would cover some basic linear algebra, covering the idea of vector spaces, some basic theorems about those, linear maps and their matrix representations and their eigenvalue/eigenvector concepts.

Some stuff on differential equations, from basic A-Level stuff to some multivariable calculus and a bit about PDE's.

A course on group theory, building from the basic axioms on groups to lagranges theorem, introducing group actions, orbit stabiliser theorem and its various applications.

A basic real analysis course, constructing the real numbers axiomatically, a treatment of limits of sequences and series, continuity and differentiability of a function and some basic riemann integrability.

A vector calculus course, covering multivariable calculus in depth, from integration in R^n, surface integrals, directional derivatives and the derivative as a linear map as well as the associated integral theorems and div,grad, curl concepts. Some stuff on Poisson and Laplace's equation and proofs of uniqueness and existence.

A mechanics course, doing mechanics properly, working with orbits and gravity as a central force, some special relativity.

A probability course, building the concept of a probability space axiomatically, introducing the various useful distributions, concept of pdf's, cdf's in the one-dimensional and multivariable case.

Damn, all sounds quite exciting actually.I have read a book on linear algebra as I have heard that what is used as the bridge into undergraduate level mathematics.I'l probably have a read of it again over the summer.I'll probably tackle multivariable calculus next, then vector calculus.Do you have any textbooks you'd recommend for either?I was going to get the dover textbook, but they dovecieve criticism for being light on details.
Reply 15
Avatar for Zacken
Zacken
22
Original post by Sapereaude45
Damn, all sounds quite exciting actually.I have read a book on linear algebra as I have heard that what is used as the bridge into undergraduate level mathematics.I'l probably have a read of it again over the summer.I'll probably tackle multivariable calculus next, then vector calculus.Do you have any textbooks you'd recommend for either?I was going to get the dover textbook, but they dovecieve criticism for being light on details.


I normally use lecture notes rather than textbooks, so no recommendations.
Original post by jcm420
C1-FP3?????? surely thats enough maths lad 😂😂

Yeah lol, I did feel that way last week with all the exam clashes from maths modules.I went home at 6:30 pm last thursday after doing a whole days worth of exams.I'm still worn out lol.
Original post by Zacken
I normally use lecture notes rather than textbooks, so no recommendations.

No worries-the information you've given is a great template nonetheless!
Original post by Sapereaude45
Do you have any textbooks you'd recommend for either?


For multivariable/ vector calculus, a good textbook is very hard to find mainly because marriage between rigour and application is not presented in a well-balanced manner. Stewart's Calculus (full version or just the multivariable version) is really popular among US students while RHB (Riley, Hobson, Bence) and Advanced Engineering Mathematics by Kreyszig is the textbook used in most universities in the UK. The lecture notes closely follow these textbooks. However, the presentation of material at this level is very superficial and non-intuitive. Insight giving theorems are almost never given or proven in the case where they are given.

Calculus on Manifolds by Spivak and Analysis on Manifolds by Munkres are the textbooks that make you feel the multivariable calculus in your neural synapses. However one needs to have at least respectable understanding of one-variable calculus in order to get going with these books. However, no matter how elegant presentations are, these books are by no means replacement for above mentioned dry books. So, this path is not ideal either.

Calculus by Apostol (vol 2) seems to be just between these texts for being gentle in introduction, rigorous in approach and giving plenty of applications. Plus it has added benefit of teaching you linear algebra along the way. So three birds one stone. However, the hind-side is that this book is quite old so does not contain glamorous images and fancy layout if that's what interests you.

It is also key to note that vector calculus was developed in the light of electromagnetism. If you want to appreciate Vector Calculus in this way then the best book would be: "Divergence, Gradient, Curl and all that: an Informal introduction to vector calculus".

If you are already familiar with vectors, dot product, cross product, matrices and determinants, the best book for linear algebra would be: "Linear Algebra Done right" by Sheldon Axler. Introducing you with abstract vector spaces, it teaches you eigenvalue, eigenvector, diagonalization and all that stuff in an intuitive way without the use of the determinants. He further shows that these concepts are not there due to determinants but the determinant is just a tool to achieve these results.

Another highly appreciated book (more advanced) is "Vector Calculus Linear Algebra and Differential Forms" by Hubbard which is the most elegant unified approach I have ever seen.
Original post by Sapereaude45
Durham or Imperial college, depending on my results


Just thinking, do those two both not offer A*A*A ? I've applied to Imperial and have a friend who's going to Durham and was just wondering which is Firm and which Insurance. Sorry for not contributing in any way

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