# Math or Physics degree?

I am hoping to become a physicist focusing mainly on the theoretical side in the future. I am trying to decide whether to go for a physics or math undergrad course.

Assuming that I am capable of doing either, what are the pros and cons of either route?

I know that mathematics is essential to doing physics, and in most math courses, there are applied math modules that are very much related to physics. Also that many research physicists have math degrees. But surely there is a reason why people choose the physics course over the math course and vice versa?

Thank you.

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Go for a Mathematical Physics/Theoretical Physics degree. Most such courses cover both core maths and physics modules. Note, if the institute you choose offers such course it is likely to be hard and alot of work - but great!! :] Good luck... – Killercam Sep 19 '12 at 11:11
Thank you, @Killercam . My institution (if I may call it that), offers 2 courses: Physics (Experimental and Theoretical with supplementary Math modules) and Mathematics (within which I can opt for applied modules). The thing is, the Math route is mainly concerned with solving differential equations (also some QM, electromagnetism, etc) and the Physics course does not have as intense a Math regime but offers a wider range of topics. Which do you think is best? – Rinaldo Sep 19 '12 at 11:23
If you want to go into theoretical physics, maths is all important. For generic mathematical/theoretical physics (in my oppinion) mathematics forms the foundations. So I would opt for the maths option. You can read about the experimental stuff and learn the physics you want to from the avalible options/modules, books and doing some physics modules. However, even doing the maths course, you will eventually be able to taylor what you study - here you can opt for applied rather than pure. I think you should speak to someone face-to-face about this, as it is a big decision. Phone the university... – Killercam Sep 19 '12 at 11:32

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someone should take time to talk you through your concerns and offer advice. If they don't I would question whether it is the right institution. Having said mathematics; there are some core aspects of physics that are crucial to becoming a theoretician. Quantum Physics/Theory, Relativity (General and Special - meths courses should provide this), Thermodynamics, Mechanics, etc. Good luck... – Killercam Sep 19 '12 at 11:35
I will offer the opinion that it is better to start with physics if one wants to study physics, because of course mathematics is absolutely essential, even for experimental physicists, but there is a danger with starting with mathematics and then going on to physics of getting caught in a special groove of physics and never having an over all strong foundation in it. So it depends on you ambition: somebody ambitious to leave his/her mark in physics should really know as much of physics data and open problems as possible, imo. – anna v Sep 19 '12 at 12:05
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## 5 Answers

After reading this dialogue I can't help but feel like a burden on society....you're all so frickin smart. Anyway, here is two cents from Napoleon's corpral. There is no wrong answer here. Either course/path will enlighten and strengthen your capability to perform to greatest potential. However, I would ask you to acknowledge your passion...physics and race ahead with gusto. Also, this is not an either or. Do both! However, I would say physics first and then go back and police up any math skills later... Hope this helped???? Unless you have some sort of terminal illness you have about 60 years to get toward your goal.

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Some time ago I had the same doubt, but I finally chose Physics for following reasons:

Pure math very abstract, you may go along very complex structures that will bring you to no where, in sense of there practical useability. Modern math is very far of it's old philosophy "intuitionism" , and they try always to prove things that are very obvious , this decreasing productivity very much, and dragging you back of understanding the "big picture", that of course not a wrong thing, but they are really exaggerating in that in my opinion. Besides other reasons I will not mention to keep it short.

My advice to you:

Try to read a math book for mathematicians and another one about the same subject for specially for physicists, you will understand immediately what fits you. even from the first 50 pages, that how I understood what I want, and as example of such subject is "differential geometry".

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Thank you, TMS. This is very true! – Rinaldo Sep 19 '12 at 17:46

I don't know if there is a right answer of math vs. physics at an introductory level. However, what is important is content, concepts and context. The problem I have seen in many math classes is that they frequently have the content you will eventually need to understand, but they are taught generally independent of the physical concepts and context. Since I don't have the benefits of current course descriptions, I would take a day to map the key material being taught in physics courses to those taught in math courses. A simple table would suffice I think, this may be difficult since it is hard to know a priori what the underlying math in a physics course might be, but some quick searching for online references might help. In any case, one is looking for gaps in the mapping, and then try to understand why the gaps are there and how long it would take to fill them. One thing that is frequently an issue with physics is that they frequently do not keep pace with connecting back to what is being taught concurrently in mathematics and the mathematics will outpace the physics courses in introduction of new content. This might not be true in all universities, but there is often little coordination that would benefit the student.

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Hal, the removal from context point is very true! – Rinaldo Sep 19 '12 at 12:23

It depemnds a lot on your interests. If you are more drawn towards abstract thinking, it may be better to start [like me] ith math and learn physics along the way, while if you are more drawn towards understanding physical phenomena, it may be better to start [like most physicists] with physics and learn math along the way. In the end you'll need both anyway for a thorough understanding.

You may also want to choose based on what you'd prefer to end up with in case you'll not have the stamina to complete both studies.

In any case, studying one subject properly (according to the syllabus of your university of choice) should not deter you from learning as much as you can about both sides of the coin.

People with different educational background and/or preferences will often develop different preferred approaches, though they learn of course the traditional ones, too. This diversity is an advantage, as different points of view complement each other.

If you plan your life actively rather than have it determined by circumstances, what you specialize on will mainly depend on what you want. Cultivating strong and well-defined interests is a definitive advantage, as it simplifies everything - choices, understanding, motivation, recognizing possibilities and open doors, etc..

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Thank you, Arnold. Very true, I hope to learn as much about both. In your experience, have you noticed different approaches to problems between people who took the different paths? Also is there a particular area of specialization each path leads to? For example, would physics people be disadvantaged in doing say string theory, which may be quite abstract? – Rinaldo Sep 19 '12 at 10:55
@Rinaldo: I added a response in my answer. – Arnold Neumaier Sep 19 '12 at 11:40
Thanks again, Arnold. – Rinaldo Sep 19 '12 at 12:21

you can get a PH Degree on physics and then make a MASTER (sorry i do not how it is told in english) in mathematical physics or perhaps you can switch to mathematics and make a thesis on mathematical physics.

for me it is easier to learn MATH from PHYSICS than becoming a MATHEMATICIAN and then trying to learn physics

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Thank you, Jose. Would you mind explaining why it could be harder for a mathematician to learn physics than vice versa? – Rinaldo Sep 19 '12 at 10:25
One reason is physicists don't use terms correctly (e.g., Lie groups and Lie algebras are synonyms for physicists). Mathematicians go crazy over this stuff. Another reason is the lack of rigor, and generality of algebra is used often in physics... – Alex Nelson Sep 19 '12 at 15:42
yep, we physicst care only for the result :D (experiment) and sometimes we do not care about rigour but i do not think is so bad , another think mathematician do not usually like is the notation for multiple fourier integral $exp(k.r)$ where k and r are vectors. – Jose Javier Garcia Sep 19 '12 at 16:16

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