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Main Question or Discussion Point
I am torn between theoretical physics and math. Are there any theoretical physicists here who regret not going into math? Are there any mathematicians here who regret no going into theoretical physics?
Yay that's really useful to know. And yes, I am planning to do a PhD.It's not unheard-of for people in physics or engineering (or econ) departments to have math profs as their primary research advisors.
Is that true?there are VERY few positions in academia in theoretical physics.
Yes, especially "math intensive" physics like string theory etc. It is a bit easier if you are interested in more applied modeling and/or computational physics (e.g. surface physics etc).Is that true?
I faced that choice, I double majored and was unsure about if I wanted to go into grad school in math or physics. I chose physics. Both fields are intellectually stimulating, and if you choose your adviser very carefully it will not be that important. I thought that I would end up regretting my choice, but honestly I have not.I am torn between theoretical physics and math. Are there any theoretical physicists here who regret not going into math? Are there any mathematicians here who regret no going into theoretical physics?
Right now I have to say math i.e. I love presenting proofs in algebra and analysis and topology. I just cannot say the same for physics. But I think that may be symptomatic of being at a school where the quality of pedagogy in the physics department trails far behind the mathematics department. The physics classes I have taken are somewhat of a joke, which is in fact the main reason that I created this thread. However, I can imagine at other schools such as MIT, the physics and math classes are not as different as they are here. The courses I have looked at on MIT opencourseware are good examples of this. I think you can make teaching a physics quite close to teaching a math class if you are good at it and that is what the MIT professors do. I think that will be my goal, to teach a physics class that models a math class.Which would you enjoy teaching-- physics or math?
I think I will be well-prepared for physics grad school not from my courses but from a lot of self-study.Well I should warn you that if you teach introductory physics or math you will not be presenting formal proofs, and at small colleges the demand for teaching will be heavily focused around introductory courses.
If your physics classes are a joke, then you might not be ready for physics grad school, and you will end up struggling in the beginning, and the first year already is a hard year. You have to balance TA duties with completing the course load (which move at a faster pace than undergrad courses).
If you enjoy math, and feel much better prepared for math grad school, and you seem to enjoy the logical structure of proofs, it seems that math might be for you.
Yes that is exactly what I want. The issue is what department are these people in?There are plenty of people around working in mathematical physics. You can in essence do both. Study problems that arise in the study of physics from the prospective of a mathematician.
They are in the math department.Yes that is exactly what I want. The issue is what department are these people in?
This is not what you will be doing throughout your PhD, though. You will not be "presenting proofs" in the way you have done in undergrad. You also may not know whether you have got the right answer: you may have an answer, but it'll be to stuff that hasn't been done before.I think I will always "enjoy" doing math more i.e. solving Putnam problems, presenting proofs, manipulating equations, getting the correct answer is my foremost passion.
Have you ever taught maths? I get the impression that you're in your second year undergrad, so don't have the experience to say whether or not you enjoy it! Also, if you don't like brainstorming for new ideas then I doubt that any sort of research is right for you. Theoretical physics is no different to maths in the sense that you will be trying to find solutions to problems that have no solutions.However, that has not been compelling enough to go into math for two reasons: 1)I think that enjoyment might fade as I get older. Also, I like learning and teaching math a lot and 2) I lot solving problems that are given to me but I am not sure I actually like "doing" math. That is, coming up with new theorems and conjectures is rather a dry task for me. Brainstorming for new results in mathematics seems so awkward and undirected to me.
If you want my advice: it is utterly pointless planning out your career right now-- you don't even know whether you'll make it through grad school, let alone land yourself a faculty position! At the moment, I would concentrate on trying to learn the courses you are taking as well as you possibly can.I guess my ideal job would be this: teaching math, teaching theoretical physics, doing research in theoretical physics.
Can you give an example of what a typical physics lecture at your school is like? I am looking over an MIT lecture on Dielectrics now as part of the E&M class, and it looks very much like what I get at my school, but with more colorful chalk.Right now I have to say math i.e. I love presenting proofs in algebra and analysis and topology. I just cannot say the same for physics. But I think that may be symptomatic of being at a school where the quality of pedagogy in the physics department trails far behind the mathematics department. The physics classes I have taken are somewhat of a joke, which is in fact the main reason that I created this thread. However, I can imagine at other schools such as MIT, the physics and math classes are not as different as they are here. The courses I have looked at on MIT opencourseware are good examples of this. I think you can make teaching a physics quite close to teaching a math class if you are good at it and that is what the MIT professors do. I think that will be my goal, to teach a physics class that models a math class.
Its not the content of the lectures at my school that are different than what I imagine they are like at MIT, it is more the presentation that is different. I lot of my professors essentially recite almost verbatim parts of my textbook during class and it is clear that they could never reproduce the derivation if they had not copied it down in their notes.Can you give an example of what a typical physics lecture at your school is like? I am looking over an MIT lecture on Dielectrics now as part of the E&M class, and it looks very much like what I get at my school, but with more colorful chalk.
I mean, my intro classes at Community College were like this:
"Here is the formula. Believe me, it works. Now let's use it."
I don't know whether Freshman physics at my university is the same or not. But the courses I've been taking for the past 2 years have been just derivations during lecture with an example usually. I can't imagine going back to "Proof by trust" type of lectures.
All of my professors read from their notes during class. The bad ones get confused by their own notes, the good ones don't look at them too often in the first place.Its not the content of the lectures at my school that are different than what I imagine they are like at MIT, it is more the presentation that is different. I lot of my professors essentially recite almost verbatim parts of my textbook during class and it is clear that they could never reproduce the derivation if they had not copied it down in their notes.
The best math professors I have had teach almost or completely without notes. This is only possible when the professor understands the material very well. I have never had physics teacher that came anywhere close to this level of excellence in teaching. At MIT, it seems like the physics professors could easily teach from memory.
My point is that in my classes we get do get derivations but they are usually just really sloppy and although my professors can write down the math, I do not think they understand the "logic behind the math" if that makes any sense.
That's the difference between professors who want to devote time and energy into teaching well and those that only teach because they have to.I lot of my professors essentially recite almost verbatim parts of my textbook during class
That's a very arrogant and foolish thing to say. Their understanding of the material probably far exceeds yours, and I bet they could reproduce any of those derivations without much trouble. It is clear that you value memorization highly, but understanding is far more important.and it is clear that they could never reproduce the derivation if they had not copied it down in their notes.