What should the Mathematics requirements be for a Physics degree

[symbolipoint]

What should the Mathematics requirements for Physics degree really be?

The usual official requirement is three semesters of Calculus, and then one more combination course which combines some linear algebra and not-too-complicated differential equations. Often the Physics majors, at least for bachelor's degree, take more than that and find some way of using some.

If an undergraduate student really wants to be good at Physics, which courses more should or need he do? Why then, are these not listed as the official requirements for the degree?

 

[bhobba]

IMHO distribution theory/generalized functions is a must.

Just about all applied mathematicians/physicists come up against that damnable Dirac delta function somewhere in their education as well as Fourier transforms. Distribution theory makes Fourier Transforms a snap and the Dirac Delta function no longer a mystery.

I also want to mention when you study such things.

Here in Australia we have what's called Math B and C. Math B is a bit below US Calc AB, Math C, which is done in conjunction with Math B, is about Calc BC level with a few slightly different modules a school can choose from such as dynamics or beginning Markov Chains. What some schools are now doing is for good/interested students they do Math B and C in grade 11 and what is usually first year university math in grade 12. That consists of your Calc III, and a subject beginning linear algebra plus differential equations.

IMHO this is much better preparation when you get to university. You can start on distribution theory immediately, also straight into intermediate QM having studied some linear algebra, differential equations and either are currently studying distribution theory or if leaving it to second semester already studied it. It would allow QM to concentrate on the physics rather than issues that really should have been taught in Math. And for good students you can go straight onto something like Landau - Mechanics rather than the boring general physics you do because you didn't do calculus based basic physics at HS - which IMHO should be done at HS as well.

Why isn't it done? I think most physics majors who are also not math majors (it's very common here in Aus to do both) are sort of expected to pick it up from their physics texts as they go along. A really inefficient way of going about it IMHO. The physics courses should concentrate on the physics - they should already know the math required for the physics. For example if I remember correctly, Griffiths EM book, which I have a copy of but dusty since I haven't read it for a long time, spends a fair number of pages on the Dirac Delta function giving his personal guarantee coming to grips with it now will greatly enhance their future math/physics education. Really - in an EM book - not the place for it - he is right about its importance but it's in the wrong place - you should already know it - and what it actually is as well which he never does explain. I know most students just want a bit of paper to get a job later and don't really care about issues of real understanding, but some do, some were like me and actually thought about such things. Students like this really do need a proper math course.

I could even support the idea of not having physics majors alone - but combined physics/applied math majors.

Thanks
Bill

 

[deskswirl]

This is what I would consider to be "typical":
2-3 semester courses in Differential, Integral, and Multivariable Calculus
1 course in Ordinary Differential Equations that includes nonlinear 1st order, systems of ODEs (some Matrix Algebra), and stability theory

This is what it should be:
1 course in Partial Differential Equations that including the method of characteristics, quasilinear PDEs, and numerical techniques
1 course in Vector and Tensor Calculus
1 course in Dynamical systems and Chaos theory preferably covering both recursion relations and continuous models
2 courses on statistics, data analysis, and Numerical Analysis including Monte Carlo simulations
1 course on Design of Experiments

And ideally also:
1 course in pure Linear Algebra
1 course in Complex Variables including complex valued vector fields
1 courses in Mathematical Methods covering Special Functions, Green's functions (scalar, dyadic and tensor), Integral Transforms and Operational Calculus, Integral Equations, and the Calculus of Variations
1 course in Differential Geometry
1 course on probability theory
1 course on stochastic processes
an assortment of pure math courses in Algebra, Analysis, and Geometry

They are not required because time is devoted towards learning physics not mathematics. I did as much extra math as I could and also learned more in physics classes. There is only so much material that can be covered in a 4 year undergraduate degree.

 

[bhobba]

They are not required because time is devoted towards learning physics not mathematics. I did as much extra math as I could and also learned more in physics classes. There is only so much material that can be covered in a 4 year undergraduate degree.

Agree entirely.

Here is Australia degrees are 3 and not 4 years - but, while there is some of what I consider we are doing it right, you wrong, discussion about this, we complete what US would consider first year stuff in 11 and 12. We do six subjects at about the UK AS level or IB SL level each of which is considered equivalent to a US single freshman subject. We also have math B and C which is two subjects at about UK A level and equivalent to US Calc BC which I believe gets you 2 credits at most schools. So we have really done 6 subjects before entering uni. Then you do 24 subjects in 3 years at uni to give 30 4 unit subjects or the 120 credits typical US 4 year degrees require - ours is more like the British system than the US. US schools say our 3 year degrees are not equivalent to your 4 year degrees, and we say, for spending a semester here in Australia as part of your US degree, you must be at least second year because we have already done the equivalent of your first year. Its a a bit maddening actually how some don't really understand what's going on and engage in simplistic things like ours are 4 years while yours is 3. Conversely here in Aus we don't understand your AP system and students can easily enter university in the US ready for second year subjects.

The answer IMHO is you do a double degree in math and physics where all that stuff is covered. Its possible - but you need better preparation of university entrance both here and in the US - that's the real key.

Naturally this applies to good, thinking students. Like I said many, possibly even most don't even care - they just want a bit of paper. For them leave things as they are.

In practical terms here in Aus many do a double degree in math and physics where a lot of what you mention is covered anyway - double degrees here take 4 years eg from where I went:
https://www.qut.edu.au/study/courses/bachelor-of-science-bachelor-of-mathematics

I did the math and computer science one:
https://www.qut.edu.au/study/courses/bachelor-of-information-technology-bachelor-of-mathematics

But back in my day it was a bit different - you could do it in 3 years - you did about the same number of subjects but many were 3 credits instead of 4. Obviously the 3 credit subjects didn't go as deep into it as the 4 credit ones - or maybe standards have simply slipped.

Thanks
Bill

 

[Vanadium 50]

And ideally also:

That leaves no time for studying physics. I wouldn't call that ideal.

 

[Herman Trivilino]

What should the Mathematics requirements for Physics degree really be?

That's impossible to say because there is so much math in physics that a physics major could benefit from lots and lots of math, too much to fit into any degree plan. So a compromise is needed.

I would say that differential equations is very important. Also important is linear algebra. You you have already acknowledged these, but I think combining them into a single course doesn't do justice to either of them. You really need as much of them as you can learn, so separate courses in them would be better. I found that a course I took in numerical methods was very useful. Differential geometry is also good.

What you really need to focus on though, is the area of physics you wish to specialize in, and then talk to the professors who teach those physics courses and ask them which math courses they would recommend. The other people who have responded in this thread have made some good recommendations.

Why then, are these not listed as the official requirements for the degree?

Time and money. Administrators are under pressure to make degrees affordable. They therefore have to come with degree plans that will fit into the time allotted for the degree. The statistics about the average time to complete a degree, for example six years to complete a four-year degree, loom over their heads.

http://www.politifact.com/wisconsin...e-college-degree-takes-six-years-us-sen-ron-/

They are being criticized for crippling their graduates with debt that will take years and years to pay off.

 

[Andy Resnick]

What should the Mathematics requirements for Physics degree really be?

The usual official requirement is three semesters of Calculus, and then one more combination course which combines some linear algebra and not-too-complicated differential equations. Often the Physics majors, at least for bachelor's degree, take more than that and find some way of using some.

If an undergraduate student really wants to be good at Physics, which courses more should or need he do? Why then, are these not listed as the official requirements for the degree?

The question is incomplete, as there are many 'flavors' of physics degrees: BS vs. BA, for example. While many of the responses here seem to fall back on "more math", I take the position that there needs to be more laboratory/computational activities. Statistical analysis of data is a topic that broadly covers all three.

Let's also remember that there's no simple linkage between earning the degree and subsequent job/career activities, leading to the (still unresolved) question "What does a Physics degree prepare you for?" The reason for electives is a precise response to that question: there is a broad palette of skills that could be asked of a Physics major, who can only become proficient in some subset. Deciding on the subset is the prerogative of the student.

 

[vela]

This is what I would consider to be "typical":
2-3 semester courses in Differential, Integral, and Multivariable Calculus
1 course in Ordinary Differential Equations that includes nonlinear 1st order, systems of ODEs (some Matrix Algebra), and stability theory.

At the schools I attended, undergraduate physics majors were also required to take a year-long course in math methods which covers many of the topics mentioned in this thread. I think most physics majors would have benefited from a course in probability, statistics, and numerical analysis.

I question the usefulness of having formal mathematics courses in many of the topics mentioned so far. I recall the joke about how mathematicians spend a long time to come up with answers that are 100% correct but still utterly useless. If a student is interested in a particular subjects and wants to see a more rigorous treatment, he or she can choose to take that math course, but to require it of all physics majors seems like overkill. They're majoring in physics, not math.

 

[bhobba]

At the schools I attended, undergraduate physics majors were also required to take a year-long course in math methods which covers many of the topics mentioned in this thread. I think most physics majors would have benefited from a course in probability, statistics, and numerical analysis.

Its the same here - you pick up more advanced topics in the textbooks themselves such as what I mentioned about the Dirac Delta Function in Griffiths.

But things would be more efficient if the physics courses could concentrate on the physics rather than take a detour to the math.

When I was doing my Masters and wanted to do QM I spoke to my adviser - he said when he sends people over to the physics department to learn QM they skip introductory courses because the math they have done more than compensated for it. For example in the PDE course you have already solved the Schrodinger Equation for the Hydrogen atom - its a standard PDE they teach. There is no use at all rehashing the same thing again. You are just given a bit of reading to do on physical concepts such as wave-functions etc which I already new and that's it.

By doing more math the actual physics becomes more concentrated and you can cover more. Of course it has to be RELEVANT math - not just math for math's sake. I did a number of subjects undergrad totally useless for physics such a Mathematical Economics.

Thanks
Bill

 

[Dr Transport]

But things would be more efficient if the physics courses could concentrate on the physics rather than take a detour to the math.

A question then arises, consider Jackson chapters 2 and 3 on electric fields. Ideally a student would have had a semesters course if not a years course in PDE's and separation of variables. What Jackson covers in two chapters is close to what I remember my 1 semester course in Fourier series and PDE's covered (and we didn't really hit upon all that is necessary to deal with Greens functions). How do you divorce the math necessary and just cover the physics?? Those two chapters are just an example of how you need to develop the math at the same time you discuss the physics.

 

[jtbell]

At some or many schools in the US, physics majors learn topics like Fourier analysis and PDEs not in a course taught in the math department, but instead in a course taught in the physics department under a name like “Mathematical Methods”.

 

[Dr. Courtney]

It's easier to define a body of mathematical knowledge that should be required, bodies that may be recommended for various specializations, etc. than it is to specify how that knowledge needs to be imparted (math courses vs. physics courses). I managed to get by with Calc 1, Calc 2, Calc 3, Diff Eq, Linear Algebra, and Numerical Analysis as the formal math courses I took. But we also has a physics course called, "Mathematical Methods in the Physical Science" (used Boas) that was essential. I also picked up along the way that instructors in physics courses just taught on the fly (Calculus of Variations, PDE, Runge-Kutta, Fourier Analysis, Complex Analysis, etc.)

Most of the better Physics departments (top 100) in the US seem to know what they are doing as it relates to how to ensure their majors have the math they need one way or the other. I tend to get more suspicious when the Calc 3 courses are powder puff and the Physics majors never get the math they need to properly understand Maxwell's Equations or the Hydrogen atom at the more advanced undergraduate levels. These shell games are much more common at universities ranked below 75 or so, and I'd be hesitant to recommend schools ranked below 100 for students aspiring to PhD programs without having a hard look at the specific school to know whether the math (and the Physics that depends on it) is getting short shrift.

But course names on a transcript may also not be meaningful. Lots of Calc 3 and Diff Eq credit is being gifted, and lots of slacker physics students are passing E&M 1 and 2, and QM 1 and 2 who are woefully under prepared for graduate school. The grade gifting is not even giving these students Cs any more to keep them out of graduate school, lots are being gifted As and Bs.

 

[Crass_Oscillator]

The usual offerings at a decent university are good enough. Physics students should not waste a minute of their time in philosophy courses from the math department that might cover such irrelevant topics as generalized functions/distributions; the Dirac delta function is obvious to people who do not get their jollies off estimating the number of angels who fit on a pin head, and a good physicist can pick up the mathematics if needed from a strong foundation (Calculus through vector calculus, applied linear algebra, ordinary and partial differential equations, probability theory,and more recently, computational methods)

 

[symbolipoint]

The usual offerings at a decent university are good enough. Physics students should not waste a minute of their time in philosophy courses from the math department that might cover such irrelevant topics as generalized functions/distributions; the Dirac delta function is obvious to people who do not get their jollies off estimating the number of angels who fit on a pin head, and a good physicist can pick up the mathematics if needed from a strong foundation (Calculus through vector calculus, applied linear algebra, ordinary and partial differential equations, probability theory,and more recently, computational methods)

I do not believe that; which is why I asked the question. I had only found hints from some physics students many so many years ago, that more advanced and alternative Mathematics courses were getting into play for some of these students academic studies.

 

[atyy]

I do not believe that; which is why I asked the question. I had only found hints from some physics students many so many years ago, that more advanced and alternative Mathematics courses were getting into play for some of these students academic studies.

You can just learn the maths with the physics. If one is interested, one can take the maths courses one likes. These are not official requirements, since there are many types of physicists. If you make too many requirements, you leave less time for people to explore their own interests.

Also, the maths in some parts of physics was still not rigorous even 15 years ago - eg. renormalization, Landau damping, the KPZ equation etc.

 

[bhobba]

irrelevant topics as generalized functions/distributions;

Really? Irrelevant? Are Rigged Hilbert Spaces irrelevant to QM? If you say yes then for anyone that actually thinks a bit the usual formalism is an utter mess. Ballentine knows this and explains, not in detail mind you, but enough so someone that actually thinks, gets the gist of what's happening, and why its important. And learning Fourier transforms - try that one without distribution theory - you soon become bogged down in issues like how the hell does one have the Fourier transform of say e^ix which crops up all over the place. You can look it up in a table of such things - but anyone with even a very basic knowledge of integration is lost - you can't do it.

Of course you may think its just philosophy - that's OK - but I don't classify things that create confusion as just philosophy - it IMHO is critical.

Thanks
Bill

 

[Herman Trivilino]

I do not believe that; which is why I asked the question. I had only found hints from some physics students many so many years ago, that more advanced and alternative Mathematics courses were getting into play for some of these students academic studies.

It depends a lot on what it is you plan on doing with the physics you learn, but also what you like to learn. Your interests may lean more toward the practical or more towards a deeper understanding of things. Be careful, though, because too much of either one may turn out to be a bad thing.

 

[bhobba]

Be careful, though, because too much of either one may turn out to be a bad thing.

Sure - but IMHO things that even a smidgen of thought show is nonsense should have at least an overview of what's going on. Some students don't care about such hings - even if it doesn't really make sense, as long as it works who cares. Others get quite confused by this and you loose them. Yes it depends on the student and purpose, but we need at least a bit of an aside explaining something like - if you are on the ball you recognize its nonsense but rest assured it can be fixed. If interested they can then go away an look into it.

It just isn't generalized functions but crops up all over the place eg the Hall Effect. The usual explanation is its absences of electrons, 'holes', moving in the other direction. This then proceeds onto explaining semiconductors and what not. But a little though shows it utter hogwash - holes moving one way are exactly the same as electrons moving in the usual direction - it explains nothing. Many don't care - but a few thinks a bit and realizes it's a big porky. Whats really going on - well the holes are actually quasi particles of positive charge and conductors contain both electrons and holes moving about. It doesn't take much to explain it - good students can investigate it a bit further (although that will involve a lot of advanced QM) - but at least are not confused.

The one thing we can't do to students is make them think things are not quite 'cosha'. We don't need to tell them the full detail - but we do need students to know these questions do have answers.

Thanks
Bill

 

[Buffu]

What should the Mathematics requirements for Physics degree really be?

Formal logic and set theory.

Physics students should not waste a minute of their time in philosophy courses from the math department that might cover such irrelevant topics as generalized functions/distributions; the Dirac delta function is obvious to people who do not get their jollies off estimating the number of angels who fit on a pin head,

Why generalized functions/distributions are irrelevant ?

 

[bhobba]

Why generalized functions/distributions is irrelevant ?

Of course they are not irrelevant. Its just some students simply do not care. That's fine - but some do and dismissing those means possibly loosing them - they are turned off. That simply IMHO is unacceptable - we must do better.

Its not confined to students either - read the opening pages of Von-Neumann's - Mathematical Foundations of QM - Dirac - yes the great Dirac - get's a big serve - correctly. Of course Von-Neumann can do that from his exalted position, but it leaves a big problem to be solved. It was solved - but it took a while. IMHO we are doing a disservice to students not at least outlining the solution.

Thanks
Bill

 

[George Jones]

The usual offerings at a decent university are good enough.

You can just learn the maths with the physics. If one is interested, one can take the maths courses one likes. These are not official requirements, since there are many types of physicists. If you make too many requirements, you leave less time for people to explore their own interests..

I agree that the amount of math required for a typical North American physics degree is about right.

Goofy math like topology, real analysis, abstract algebra etc are basically just academic subjects that exist for fairly contrived, formal reasons. Occasionally academics looking to get their jollies off will "apply" them to problems in physics, but usually with inscrutable or irrelevant consequences.

Physics students should not waste a minute of their time in philosophy courses from the math department that might cover such irrelevant topics as generalized functions/distributions; the Dirac delta function is obvious to people who do not get their jollies off estimating the number of angels who fit on a pin head, and a good physicist can pick up the mathematics if needed from a strong foundation (Calculus through vector calculus, applied linear algebra, ordinary and partial differential equations, probability theory,and more recently, computational methods)

While the amount of required math is about right, I think it would be sad if no physics students took pure math courses like point-set topology or abstract algebra, just as it would be be sad if no physics students took non-required biology courses or non-required chemistry courses.

Science, including pure mathematics and non-applied fundamental physics is part of who we are as a species. Fundamental science is as much part of our culture as musics, art, and literature. If we lose the desire and ability to ask fundamental "Why?" questions in science, we have failed as humans.

 

[Dr. Courtney]

In the US, most BS degrees top out at 120-128 credit hours, and this limit on credits is set by the institution, not by the Physics department.

The institutions also have core requirements (humanities, foreign language, etc.) so that the major requirements represent a fixed number of hours much lower than 120. In most cases, the requirements for a BS in Physics already has maxxed out the number of credit hours in Physics + Math, so you cannot simply add more. Each addition needs to remove something else, so that the total number of credit hours in Physics + Math is constant.

Folks are full of great ideas for what to add, but few have realistic proposals for what should be removed to keep the number of credit hours in Physics + Math constant while still representing an improvement with their proposed additions.

Students do have a small number of electives that they can use for additional math or science courses. They tend to make these based on combinations of perceived need, interest, and keeping their perceived workloads manageable. I am mentoring a couple outstanding science majors who are having a hard look at minoring in math and using electives to fulfill the requirements for a math minor. If they complete this proposed path, they'll be better prepared for possible theory in graduate school, but not really at much advantage should they choose experimental paths. Programming courses would suit them better in those cases.

On the whole Physics (and other science) majors need more opportunities, not more requirements: opportunities for research, opportunities for programming coursework, opportunities for advanced math coursework, opportunities for graduate coursework (possibly with instructor approval). One student I mentor was denied enrollment in a graduate course due to an administrative rule, even though the instructor wanted her in the course and even invited and strongly encouraged her.

 

[Dr Transport]

Formal logic and set theory.

Really, in 30+ years since I got my degree I have not had the need for either... I've used group theory and that is about the most advanced math I've used.

 

[Buffu]

Really, in 30+ years since I got my degree I have not had the need for either... I've used group theory and that is about the most advanced math I've used.

I am sorry, it was a bad joke.

 

[ZapperZ]

The mathematics background required to survive physics undergraduate curriculum, at least here in the US, is what is covered in Mary Boas's "Mathematical Methods in the Physical Sciences" text.

https://www.physicsforums.com/threa...-the-physical-sciences-by-mary-l-boas.665434/

Zz.

 

[Charles Link]

A good background in Linear Response Theory along with Fourier Transforms is something very important for a well-rounded physics education. I did not have such as course in my undergraduate education, but learned this material in bits and pieces as it came up time and time again in various physics courses including in graduate courses. The convolution theorem for linear response along with the equation in frequency space $\tilde{V}_{out}(\omega)=\tilde{m}(\omega) \tilde{V}_{in} (\omega)$, (where $\tilde{V}_{out}(\omega)$, $\tilde{m}(\omega)$, and $\tilde{V}_{in}(\omega)$ represent Fourier transforms of $V_{out}(t)$, $m(t)$, and $V_{in}(t)$), comes up repeatedly in many places, including electrical circuits, dielectric and magnetic frequency response of a system, and many other places. I think it would be advantageous for this material to be presented to the students in a required mathematics course, rather than needing to pick it up in bits and pieces. It's application is quite universal.

 

[stefan r]

...
If an undergraduate student really wants to be good at Physics, which courses more should or need he do? ...

English/writing so that they can write decent papers. Economics/business and maybe political sci so they can run a lab. History/social sci so they know when they are why. Psychology and communications also to run a lab. Some phys ed because brains need food and exercise and also because this is easy to work into a schedule.

If the college/university teaches students to think then they can learn how to do the jobs/careers that they find themselves in. People often find themselves doing things they did not expect to be doing.

 

[symbolipoint]

English/writing so that they can write decent papers. Economics/business and maybe political sci so they can run a lab. History/social sci so they know when they are why. Psychology and communications also to run a lab. Some phys ed because brains need food and exercise and also because this is easy to work into a schedule.

If the college/university teaches students to think then they can learn how to do the jobs/careers that they find themselves in. People often find themselves doing things they did not expect to be doing.

I mostly agree, that those are all very or at least potentially useful, and sometimes are neglected. My emphasis for the topic is on the MATHEMATICS courses to help educate the Physics students better.

 

[stefan r]

I mostly agree, that those are all very or at least potentially useful, and sometimes are neglected. My emphasis for the topic is on the MATHEMATICS courses to help educate the Physics students better.

What should the Mathematics requirements for Physics degree really be?

The usual official requirement is three semesters of Calculus, and then one more combination course which combines some linear algebra and not-too-complicated differential equations...

I am saying that you will get better educated physics students if you do not neglect the liberal arts education.

 

[symbolipoint]

I am saying that you will get better educated physics students if you do not neglect the liberal arts education.

The connection is weak. The connection between Mathematics and Physics is much stronger. A bachelor of ARTS degree in Physics might be a degree arrangement encouraging the students to study more of the liberal arts. A bachelor SCIENCE degree in Physics might be a degree arrangement encouraging more technical courses such as Math or Computer Science or other sciences or Engineering course as some possible electives, and still nothing should stop such a student from dipping into a little bit more of liberal arts.

The ability of the graduate to discuss societel and economics conditions, and write and be able to read is already granted so the focus, as asked initially, is about what set of mathematics courses beyond the usual stated official required ones, should a motivated physics student include. The answers seem to be, anything the student wants if contains topics which his areas of specialty can use the topics, and ultimately, no limit on what more Mathematics course - but one must cut off some because just not enough time when one wants to deal with Physics and not endlessly learn more Math without clear purpose.

 

[berkeman]

@stefan r and @symbolipoint -- let's please stay on-topic for the OP's question. Thanks.

 

[Dr Transport]

These were my UG math courses, Calc I-III, Differential Equations, Linear Algebra, Advanced Multi-variate calculus, PDE's (Fourier series, separation of variables, no Green's functions). That was the required coursework. I also took a course in Special Functions and another special studies course in PDE's.

My department didn't teach a course in math methods (it still doesn't), that was the required advanced multi-variate calculus and PDE's, both of which were taught by a true mathematical physicist who was a professor in the math department. Computational physics wasn't required, neither was numerical methods or complex variables. We did see some complex calculus in the advanced multi-variate course which was essentially an advanced vector calculus, integral theorems (Gauss's law, Stokes theorem and some complex variables and residues).

In graduate school, one place I went to taught a year long course in advanced calculus, special functions and complex in the fall. The spring consisted of linear algebra and group theory. Depending on who taught the group theory, it could have been point and space groups or Lie groups. The other school taught a year long course out of Arfken (yes it was Arfken, not Arfken and Weber, that is how long ago I went to school).

That should shed some light on what math is required for an undergrad physics degree.

 

[alan2]

For what it's worth, I had to take the usual 3 semesters of calculus, linear algebra, ODE's, advanced calculus and one semester each complex variables, vector analysis, and boundary value problems for a BS in physics. But that was 30 years ago and, as I recall, the last three were to satisfy a requirement of three additional math courses at the senior level. I think the experimental people took statistics and other courses instead. I also have degrees in mathematics and, frankly, I see zero use in making a physics major take any course in pure mathematics. Physicists need methods, not formal proof.

 

[bhobba]

That should shed some light on what math is required for an undergrad physics degree.

That's quite reasonable.

Interestingly here in Aus, as I said before, double degrees in applied math and physics or math and engineering for that matter are very popular. They even have a separate strand for it (they have a number of different strands as well eg - stats and decision science). The advanced subjects that must be done for that strand look a lot like physics subjects - they are (from the student handbook of where I attended):

Applied Transport Theory
Applied Transport Theory is the study of the exchange of mass, momentum and energy in physical systems. An understanding of the equations that govern these transport phenomena is fundamental to understanding how the physical world behaves. This unit builds upon knowledge you will have developed in studies of advanced calculus. You will learn how to derive equations from fundamental conservation laws and develop an understanding of the commonality between the equations. Furthermore, in deriving analytical solution techniques for these equations you will develop further skills in calculus and differential equations. Completion of this unit will prepare you for the final semester capstone project.

Partial Differential Equations
Previously you have discovered the power of differential equations for modelling real world processes. In this unit you will extend your capabilities to problems that simultaneously exhibit both spatial and temporal variation. Such problems can be described by partial differential equations. You will learn a variety of analytical solution techniques for these equations, which bring together many of the skills you have learned in earlier study of advanced calculus and ordinary differential equations. You will also learn the techniques of Fourier and complex analysis, which have applications far beyond the realm of differential equations.

Dynamical Systems
Dynamical Systems” is a descriptive term used to represent the analysis of time varying systems. Such systems exhibit a variety of behaviours including exponential approaches to equilibrium states, periodic or oscillatory solutions, or unpredictable chaotic responses to simple inputs. The study of dynamical systems employs topological and function space concepts to provide the analytic structure to systems of nonlinear (and linear) ordinary differential equations, and as such forms the basis for the mathematical interpretation and understanding of numerous real world systems. This unit is an exploration of the more technical aspects of the theory of solutions to systems of ordinary differential equations and as such builds on your prior understanding of such equations while providing the support for the exploration of an exciting area of modern mathematics.

Computational Fluid Dynamics
This capstone unit provides students with the opportunity to apply their knowledge and skills in applied and computational mathematics to simulate complex real-world problems. Students will be presented with several real-world case studies, which will involve model formulation, examining the impact of varying model parameters, and formulating and presenting recommendations for the best course of action to take based on model predictions. Your previous learning in deriving and solving partial differential equations that describe transport phenomena will be extended to include numerical methods of solution. Combined with the computational expertise you have acquired over your degree, you will be able to formulate and solve these complex mathematical models using MATLAB.

Thanks
Bill

 

[DaveC49]

I found having a good grounding in Calculus, ODE's, Linear Algebra, Vector spaces, Group Theory, Numerical method were the maths couses I found most useful for Physics. I also did introductory computer science subjects at first year level and 1st semester 2nd year which proved useful. Like Bhobba, I did a combined Maths- Physics double major degree which I changed to a Physics major at third year level. I only did a very basic statistics course at first year level yet as an applied physicist, I would have benefited from far more depth in statistics. The numerical analysis was however extremely useful in my later career. UQ where I did my undergraduate degree also offered courses in both math and physics at a basic core level and at an advanced level. In maths the core level concentrated on knowing the theorems and fundamantal concepts while the advanced levels required you to learn and understand the proofs of the theorems. Physics also had the same two level structure where the core level subjects gave you a grounding in the concepts and the advanced levels gave you more depth and usually a more rigorous mathematical treatment. Both departments also offered a fourth year to selected students which was pitched largely at a Masters level or Ph.D. course work level in the US generally with prerequisites from the advanced level. One of the difficulties with the combined degree was the mismatch in timing between the relevant maths and physics courses as each department largely arranged their couse structures to meet the requirements of their own graduate programs. Consequently QM in physics preceeded Hilbert spaces in maths by a semester. The mathematics requirement for a mathematical physicist working in areas of string theory or quantum loop gravity or astrophysics are going to be very different from those for someone who ends up working in an accelerator lab . A good solid grounding in core mathematics though gives you a better chance of being able to identify and pick up anything you didn't get as an undergraduate later in your career.

 

[stefan r]

@stefan r and @symbolipoint -- let's please stay on-topic for the OP's question. Thanks.

What should the Mathematics requirements for Physics degree really be?...

My answer was very much on topic: 3 years calculus and linear algebra. More requirements diminish the "degree".

You are, of course, welcome to disagree. My being wrong does not imply that I am talking about the wrong subject. Natural science professors tend to think their majors should be bigger. Humanities professors usually state the opposite position. This argument really happens at colleges and universities.

The original post also had this question:

Why then, are these not listed as the official requirements for the degree?

Listing off lots of possible math courses does not answer that question at all.

Physics and Mathematics professors at colleges and universities try to add more mathematics requirements. Professors from other departments block those proposals. Reasons are stated more eloquently than I am likely to be capable of.

 

[Mark44]

@stefan r, your post #27 was off-topic, and was the reason @berkeman listed your name. The title of this thread is "What should the Mathematics requirements be for a Physics degree" -- (emphasis added).

English/writing so that they can write decent papers. Economics/business and maybe political sci so they can run a lab. History/social sci so they know when they are why. Psychology and communications also to run a lab. Some phys ed because brains need food and exercise and also because this is easy to work into a schedule.

Also, what does "History/social sci so they know when they are why" mean?

 

[symbolipoint]

@stefan r, your post #27 was off-topic, and was the reason @berkeman listed your name. The title of this thread is "What should the Mathematics requirements be for a Physics degree" -- (emphasis added).

Also, what does "History/social sci so they know when they are why" mean?

Right. berkman does have a point. This point can be made better if done as a separate topic. Some departments and universities seem to like to ADD a separate WRITING course supposedly suited to a particular major field. My belief is that such a separate course should not be needed, since the major field's program should have some significant report-writing as part of more than one of the major-field's courses. A very significant routine lab exercise in some phys sci courses is the writing of formal lab reports. Any student can easily adapt to these. Note that one of the "humanities" areas is the courses which emphasise modern foreign languages; which definitely bring up instruction about both CULTURE & HISTORY, and also the workings of the LANGUAGE. The student will then develop some precise language translation, which is much like what we do mathematically anyway in our physical sciences. When "we" do this, it is between a described or representable physical situation and mathematical expressions and equations.

 

[bhobba]

I only did a very basic statistics course at first year level yet as an applied physicist, I would have benefited from far more depth in statistics.

Yes - I originally only did the minimum required which believe it or not were 4 subjects - Mathematical Statistics !A, 1B, 2A, 2B. Didnt like it much personally, but the lecturer for the advanced subjects was great - I even remember his name - Dr Ogalvie. I really liked him so, not because I liked stats much, but purely because I liked him , I did 3A and 3B. Turned out to be a very good choice not only for physics but for computing later on - they wanted all these statistical reports etc and it was great to know the background behind them. Not to 3A and 3B level, but it was very useful in understanding QM and it's probability bit such as exactly what does the Heisenberg Uncertainty Principe mean. - you need to know and understand variance for that one.

Thanks
Bill

 

[Charles Link]

Besides having courses in advanced calculus, differential equations, and complex variables as an undergraduate physics major, I also had a course in Probability Theory given by the Mathematics Department. One of the most useful things about probability theory is the concept of the distribution function, $F(x)=P(X \leq x)$ compared with probability density function $f(x)=F'(x)$. This concept is very useful in a number of places, including particle scattering, where a section (area ) on the target $\sigma$ maps into a solid angle $\Omega$. (Thereby concepts like the differential scattering cross section $\frac{ d \sigma}{d \Omega}$ are much more readily understood). And I do think in this area, the mathematicians generally have at least a slight edge over most physicists in presenting material such as this. $\\$ The mathematical concepts presented in the Probability course have also been very useful in understanding things such as the Planck spectral function for blackbody radiation, as well as the Maxwell/Gaussian type distribution (density) functions of particle velocities. The Probability course also covered the Standard Normal Distribution function, including how to normalize a function of the Gaussian form. The various probability concepts, including binomial trials, etc., and discrete distributions were also very good things to have learned. I would recommend that anyone who is serious about their physics education have such a course as soon as possible after the basic calculus sequence. Whether such a course should be made a requirement I think would depend somewhat on the academic ranking of the university. I think a really top notch program could do well to have such a course be part of their graduation requirements. $\\$ Editing: And although it might start to be a somewhat heavy load from the math department if the advanced calculus, differential equations, and complex variables courses were required, I think it could be advantageous to have them be required. I still am of the opinion that a course in Linear Response Theory and Fourier transforms should be a requirement as mentioned in post 26. I had one additional course from the mathematics department as an undergraduate, besides those mentioned above, and that was Linear Algebra and Matrices. That, IMO, was the least important of all of these courses. A course in Linear Response Theory and Fourier Transforms would have been much more beneficial than the Linear Algebra and Matrices course.

 

[Jenab2]

Linear algebra, probability and statistics, Fourier and Laplace transforms, vector calculus, and partial differential equations.

 

[AgentSmith]

It depends on how your physics courses are organized. There are bits of math needed here and there that can be fit into a physics course. But you need a minimum of ODE, Linear Algebra, some PDE, some tensor analysis. Its possible to take ODE and linear algebra, then a two semester course in physical mathematics involving PDE, vector analysis. complex analysis, tensors, abstract algebra. A separate and serious sequence in experimental methods & data analysis should be required.
In my opinion, to which I give considerable weight, an applied mathematics degree with a year of intense physics work is also feasible. It just depends. There is no single answer, beyond the minimum most people take anyway.