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Difference between Applied maths and Theoretical physics?

Are there big differences between the 'physics-related' modules of Applied maths (Maths degree course) and the modules of Theoretical physics at university undergraduate level? What are the differences?
(edited 8 years ago)
Original post by Spiral1977
Are there big differences between the 'physics-related' modules of Applied maths (Maths degree course) and the modules of Theoretical physics at university undergraduate level?


This is a question of such generality that it's hard to give much of an answer. (If I attempted to, I would probably say "no"!)

Do you have a particular university (or set of universities) in mind? It would then be easier to answer in detail.
Reply 2
Original post by Gregorius
This is a question of such generality that it's hard to give much of an answer. (If I attempted to, I would probably say "no"!)

Do you have a particular university (or set of universities) in mind? It would then be easier to answer in detail.


University of Birmingham; this is where I will start the first year of my maths degree course in a few weeks. Although I guess my question (and the answer to it) can apply to any university within the set of the top-20 UK universities.
Original post by Spiral1977
University of Birmingham; this is where I will start the first year of my maths degree course in a few weeks. Although I guess my question (and the answer to it) can apply to any university within the set of the top-20 UK universities.


I've had a look at the Birmingham website and I note that they offer a degree course in straight maths and one in "theoretical physics and applied maths". There's very little detail about the modules studied on the straight maths degree, but there's a lot more information available for the TPAM degree; so I'll work off the latter.

On this course there are sub-options: theoretical physics (with lab); theoretical physics (without lab); and applied maths. It looks pretty clear that they differentiate between these sub-options by the choice of module that you take and not by differences in individual module content.

So let's have a think about how the type of content of these modules might differ between the AM and the TP options.

(1) In applied mathematics, you're often concerned with how you might actually solve the equations that come out of theoretical physics. A TP might be satisfied with a careful derivation of the equations governing some physical system and then putting them into Matlab to see what comes out; an AM will be happy with a cursory derivation of the equations but will be concerned with how to solve them - an AM will have programmed Matlab to solve such equations in the first place! So you see that the AMs get modules in linear algebra and analysis (and "methods" courses) that the TPs do not get.

(2) There are some areas of TP that have very much come into the realm of maths (pure and applied). For example, the heat equation is amenable to attack by methods that are derived from the field of stochastic processes. This work tends to get done by mathematicians rather than physicists. AMs in this course get more on probability theory that TPs. There are examples by the truckload in fundamental particle physics and gravitation theory and an intense cross-fertilization between TP, AM and PM.

(3) AM may be applied outside of areas that physics departments would be comfortable calling "physics".

But note that, having said all that, by the third year of the Birmingham course the choice of optional modules available can pretty much negate differences between the courses! In a way, this reflects the great overlap between, and the historical course of, the disciplines in the last fifty or so years.

Differences between course offerings to students can come down to how a university has organized its departments (for example, Cambridge has a big Department of Applied Maths and Theoretical Physics and a big Department of Physics) and where faculty members themselves have come from in terms of discipline.
Reply 4
Original post by Gregorius
I've had a look at the Birmingham website and I note that they offer a degree course in straight maths and one in "theoretical physics and applied maths". There's very little detail about the modules studied on the straight maths degree, but there's a lot more information available for the TPAM degree; so I'll work off the latter.

On this course there are sub-options: theoretical physics (with lab); theoretical physics (without lab); and applied maths. It looks pretty clear that they differentiate between these sub-options by the choice of module that you take and not by differences in individual module content.

So let's have a think about how the type of content of these modules might differ between the AM and the TP options.

(1) In applied mathematics, you're often concerned with how you might actually solve the equations that come out of theoretical physics. A TP might be satisfied with a careful derivation of the equations governing some physical system and then putting them into Matlab to see what comes out; an AM will be happy with a cursory derivation of the equations but will be concerned with how to solve them - an AM will have programmed Matlab to solve such equations in the first place! So you see that the AMs get modules in linear algebra and analysis (and "methods" courses) that the TPs do not get.

(2) There are some areas of TP that have very much come into the realm of maths (pure and applied). For example, the heat equation is amenable to attack by methods that are derived from the field of stochastic processes. This work tends to get done by mathematicians rather than physicists. AMs in this course get more on probability theory that TPs. There are examples by the truckload in fundamental particle physics and gravitation theory and an intense cross-fertilization between TP, AM and PM.

(3) AM may be applied outside of areas that physics departments would be comfortable calling "physics".

But note that, having said all that, by the third year of the Birmingham course the choice of optional modules available can pretty much negate differences between the courses! In a way, this reflects the great overlap between, and the historical course of, the disciplines in the last fifty or so years.

Differences between course offerings to students can come down to how a university has organized its departments (for example, Cambridge has a big Department of Applied Maths and Theoretical Physics and a big Department of Physics) and where faculty members themselves have come from in terms of discipline.


Thanks for the detailed answer.

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