Math/Physics Direction: Advise for 21 Year Old Student

[Jake4]

Alright, So I have a predicament. I have read the physics degree sticky and all, this is just kind of a follow up.

Right now, I'm enrolled in a physics major with a math minor (that may or may not be turning into a double major). I have JUST started it, I'm in calculus 1 right now. I have a very mathematical mind, math has always come quite easily to me.

anyways, I have been going back and forth between focusing on mathematics, or focusing on physics for a while now. Obviously I know there is a great deal of overlap, but I feel like for what my interests are, there is A LOT of overlap.

I was browsing through the faculty in the math section of my university's website, and was looking at the areas of research for these professors, and I found myself very interested in the topics of interest. I noticed that a lot were concerned with topology, along with mathematical physics. When I saw that, I really got to thinking.

I always wanted to be on the mathematical/theoretical side of physics, and always found math VERY interesting. Now to be honest, as I said, I'm just beginning, I read laymen's explanations of theories and fields of studies, and what I CAN understand , I absolutely love, but I certainly don't understand the bulk of them. Physics theories and research topics however, I can conceptualize a bit better.(without the knowledge)

SO basically my question comes down to, what should I be getting my bachelor's in? I feel myself going toward mathematical physics/topology (I know these may be very different, but bare with me), but I see that these folks that are working on things that are interesting to me, are in the math department. One, has a Ph.D in philosophy, ( really don't know how this works) but did his dissertation on a math topic (if someone can clarify that, that would be great) and honestly, if I understand it correctly, that's very along the lines of what I'd like to do with my physics and/or math degree.

I know, I sound uneducated on the topic. I am... Today was my first day of classes(I'm 21, and just transferred into this school/major) I'm not sure if I should let things sit as they are right now, and go through some math and physics classes before making my decision. or exactly what I should do.

I plan on talking to one of the professor I was referring to soon, but I wanted to gather at least a little information, and possibly make sense out of what I'm trying to get across, before I do so.

So basically, any help you guys can give with sorting this out, telling me how the fields work, or anything, would be a great deal of help. I'm doing a lot of research on my own, but I'm not 100% sure where to look, and I feel like I just need someone in the field to talk with.


Thanks guys.

 

[Jake4]

After rereading, and really thinking, I think a major issue of mine is that I have NO idea what I will want to focus on as far as research, and I don't want to limit myself either way.

I see math research, and even the math CLUB at my university, and feel so behind, that I feel to really get into that, I have to put my all into it..

 

[Jake4]

nothing aye?

 

[lisab]

Well your passion and enthusiasm definitely show!

Now, you're in calc 1, and that's good news for someone in your predicament because it means you have the luxury of time. You should continue taking math and physics, to see which one really does it for you. I think after several classes of each, you'll know better what direction you want to go.

Is a double major out of the question?

 

[Kevin_Axion]

To tell the truth current research topics in Physics rely on the Mathematics you have just listed including topology. Research programs such as Superstring Theory/M-Theory, Loop Quantum Gravity, Group Field Theory, Quantum Field Theory and Cosmology are very mathematical and one would say a physicist is a mathematician but the physicist uses mathematical to understand the universe. Look on http://arxiv.org/ and you'll see the different types of ideas being researched and mathematics being used.

 

[nlsherrill]

Fortunately for most physics programs, the math requirements are probably nearly identical up until the end of sophomore year. However if you were to do math, you would probably only have to take (1-2) physics courses as part of your major(at least this is how it is at my school). I think once you have taken introductory calculus based mechanics and E&M, you will know if you want to continue in the physics direction.

I have been in the same boat as you are with deciding between physics, or physics/math double major. I currently am in Calc 3, and University Physics I(calc based mechanics), and to my surprise they go pretty well together. Lots of vectors/crossproducts/dot products/calculus(clearly) in both courses. Both of these courses are very interesting to me, but the physics course is much more difficult. This isn't just my opinion either, its the general consensus among the students enrolled in both courses. If you want an idea of what I'm talking about, we had to do problems involving partial derivatives and double integrals in physics before calculus 3(where you are supposed to learn them), so this just made the physics problems even more difficult. I guess it could depend on the school, but University physics 1,2,3 at my school are restricted for physics majors only(unless you get special permission from the undergraduate coordinator). With that being said they intentionally make this course harder than the other intro physics courses to weed out the people who aren't willing to spend 5 hours staring at a problem until they figure it out.

In all, just take the first few courses that you can "double dip" in both majors, and by the end of those you will certainly have a better idea of your interests. Good luck.

 

[Jake4]

Yea, if I do a Physics major, I do a good deal of the math courses I would be doing in a math major.

Also in my school both majors require a minor, so I would just be doing the other as a minor.

I've done a little more research, and I'm thinking I want to go the mathematical physics route, or something similar. For now, I'm just letting it sit, as I'm only in calc 1 (tearing my hair out with how slow the class is going though) and am going to be going into calc based physics next semester.

I may or may not be taking Discrete mathematics along with physics and calc 2, as I have finished most of my liberal arts and am mainly just doing my major classes at this point.

Would that be a ridiculous workload? As far as math, I am pretty good with it, and even though I have no knowledge of discrete math, the university sort of lumps calc 2 and that class together, which makes me think they may work out together.


As of right now, I'm leaning towards switching to Math major and physics minor. I would get a lot more of the math based support I need from this school as a dedicated math major as well as staff tutoring jobs available only to math majors : )


I'm thinking math major/physics minor will get me fairly ready to go into grad school in either (I hope, PLEASE correct me if I'm wrong)

 

[fss]

Honestly I think you should just pick one or the other (or not, if your university allows you to hold off declaring) and not worry about it until you actually start getting into "real" math and physics. Recommending a course load or academic plan when you have done nothing difficult in either subject is a great way to set yourself up for disappointment and failure. Introductory Calculus-based Physics is hardly an indication of how much you will like higher-level physics or higher-level math.

I'm thinking math major/physics minor will get me fairly ready to go into grad school in either (I hope, PLEASE correct me if I'm wrong)

If you want to go to graduate school for either (not really sure how it works on the mathematics side, but certainly for physics), you should start thinking about getting into research of some kind over the summer. Starting research early looks very good when it comes time to applying for graduate school, and if you do a good job it will also probably give you a great reference letter or two.

 

[Ryker]

I may or may not be taking Discrete mathematics along with physics and calc 2, as I have finished most of my liberal arts and am mainly just doing my major classes at this point.

Would that be a ridiculous workload?

Nah, man, it's going to be a breeze for you. I mean, you are pulling your hair out due to the slow pace of your Calculus I class after all, right?

 

[hadsed]

I'm taking calc. 2 and discrete math concurrently this semester. I wouldn't say it has a huge amount of overlap (or maybe I haven't gotten to that part yet). Regardless, I find discrete math intensely interesting and in a much more abstract and different way than I see calculus. I love all kinds of math (so far at least), and you love math, so you should be okay. I'm a double major in math and physics and I too want to do mathematical physics research in the future, though I always feel like I like math more than physics sometimes. I think really it's probably because intro physics classes are.. kind of bland.

 

[Jake4]

I'm taking calc. 2 and discrete math concurrently this semester. I wouldn't say it has a huge amount of overlap (or maybe I haven't gotten to that part yet). Regardless, I find discrete math intensely interesting and in a much more abstract and different way than I see calculus. I love all kinds of math (so far at least), and you love math, so you should be okay. I'm a double major in math and physics and I too want to do mathematical physics research in the future, though I always feel like I like math more than physics sometimes. I think really it's probably because intro physics classes are.. kind of bland.

Alright sweet, that makes me feel better.

And yes, I think that's just it. I'm very interested and intrigued by mathematics, so even calculus 1 is fun and interesting to me.

and fss, I was actually thinking about it, I think this summer might be a little too early, but next summer I hope to get some research experience since I am now getting in with the math department faculty.

Went to a colloquium presented by my calc 1 professor on a topic in algebraic topology and though I could understand nothing, it was really cool to see. My school has those just about every week, so I plan to continue to go. I may be incorrect, but it seems as if there aren't very man serious math majors at my school. I'm trying to show my colours early on so that when I try to get into some research, they'll have the knowledge that I've been active in the department for a while.

I'm officially filling out the paperwork tomorrow to switch to math major/physics minor. I'm very excited.


And one last thing, does anyone have any book suggestions for calculus? The book we have now, "University Calculus" by Hass, Weir, and Thomas, is fine, but I feel like I would like a supplemental text just for my own studies.


thanks so much for the input guys.

 

[hadsed]

Michael Spivak's Calculus would probably be valuable [and enjoyable] to you.

 

[deluks917]

Two calculus textbooks i like a lot are by Gilbert Strang and Serge Lang. They have a good mix of theory and application and are written for good students. I'd especially recommend Strang's book.

If you want a very very proof based approach to calculus there is always Spivak/Apostal. Both wrote "Calculus" textbooks that are very rigourous. Those two books are definitely worth reading but are a lot of work and cover much of what is traditionally covered in "Real Analysis" class. Still I really loved Spivak.

A final option is to just read the first half of a real analysis textbook. Maybe try Maxwell Rosenlicht "Introduction to Analysis" or Chrales Pugh "Real analysis" they aren't much harder to read then Spivak/Apostal and both books are very well written.

edit: I only recommended these because you said you liked math. Besides Strang none of these are really worth reading if you only want to do physics.

 

[Feldoh]

Just be aware that if you are learning math for the sake of physics that you will have to sit through a lot of math that is unrelated to physics about 70% of the time. Or at least that is what my personal experience has been.

 

[lsaldana]

I may or may not be taking Discrete mathematics along with physics and calc 2, as I have finished most of my liberal arts and am mainly just doing my major classes at this point.

Would that be a ridiculous workload? As far as math, I am pretty good with it, and even though I have no knowledge of discrete math, the university sort of lumps calc 2 and that class together, which makes me think they may work out together.

From what you've said about your skills and interest, it should be an enjoyable semester. Last spring i had 3 math classes and one physics and it was a great semester, lots of cool things to learn; got an A on all of them. Good luck.

Here's a tip: I found it pretty rewarding, and still do, to be ahead at least a semester in my math classes than in physics, this way you don't struggle or do lots of personal study on the side JUST to get caught up with any abstract mathematics physics professors are using.

 

[Monocles]

Kudos to you for figuring out that mathematical physicists tend to live in math departments so early! Since, as you noticed, most of these people tend to be in math departments, your math classes are more important than your physics classes. There are actually some people who work in mathematical physics who know almost no physics at all! For example, I'm reading a textbook right now called 'Frobenius Algebras and 2D Topological Quantum Field Theories', and even though this guy wrote an entire book on 2D TQFT, he laments in the introduction that he does not have any idea what the physics behind the math is.

As far as doing research in mathematical physics as an undergrad, that can be tricky to pull off, but you should try to get into it if you can. I'm in your shoes plus a couple years - I'm a senior (though I'm going to take an extra semester since I'm doing a double major in math/physics), and I got extremely lucky and managed to land a REU position doing mathematical physics this past summer, and we're working on a publication now. So, these positions DO exist for undergraduates - you just need to look very very hard for them.

 

[Jake4]

Kudos to you for figuring out that mathematical physicists tend to live in math departments so early! Since, as you noticed, most of these people tend to be in math departments, your math classes are more important than your physics classes. There are actually some people who work in mathematical physics who know almost no physics at all! For example, I'm reading a textbook right now called 'Frobenius Algebras and 2D Topological Quantum Field Theories', and even though this guy wrote an entire book on 2D TQFT, he laments in the introduction that he does not have any idea what the physics behind the math is.

As far as doing research in mathematical physics as an undergrad, that can be tricky to pull off, but you should try to get into it if you can. I'm in your shoes plus a couple years - I'm a senior (though I'm going to take an extra semester since I'm doing a double major in math/physics), and I got extremely lucky and managed to land a REU position doing mathematical physics this past summer, and we're working on a publication now. So, these positions DO exist for undergraduates - you just need to look very very hard for them.

Very cool man! Yea there are a couple mathematical physicists in our math department. I'm trying to get my foot in the door early on, as I was the only undergrad to go to the Colloquium last week. They were all trying to convince me to come this week, which I am.

You know what too, I kind of thought of the idea that I wouldn't really have to know the physics as well as the math. If I'm researching quantum loop theory, I really don't have to know the conceptualization of the physics, as long as I understand the mathematics. Of course it would help, but I feel like in all ways, it will be better for me to get very much immersed in mathematics.

Today I got the final signature I needed to switch majors(as I had to redo the paper because I handed it in without the signature of the physics department head) and honestly.. I feel so strongly that I made the right decision.

Realistically I feel that I'm so early in this journey, that I don't know if I'm going to get to my last semester and want to go onto mathematical research outside of physics. It's kind of too early to tell. I suppose the turning point was when I realized the part of physics I liked... was the math, so who knows where I'll end up.I'll definitely check those books out as well, thanks so much for the suggestions! I'm thinking I might pick up the Apostol anyways simply for the fact that I want to work on my proof understanding. Like any early on proof, I understand it if it's in front of me, but I'm not quite to the point of being able to figure out difficult proofs myself. However, I'm getting there. I've been trying to do math every day, even when I have no homework, and even if it's just a few problems, or playing around with an equation.

I look at it as, I'm trying to learn a new complex language. Sure I can do the homework for the class and keep along with it, but I'll really only get comfortable with it with repetition. That's part of the reason why I'd like to get one or to more calculus books.. often times (as everyone here knows) you'll be taught something multiple times.. but then something that ONE teacher, or ONE book says about it.. makes it just click in your head.
Lastly, I was just told by my teacher that we will only just begin the chapter on Integration in this class, to be picked up in calc 2. Which means, in a couple days I will have learned in my own time, everything I will learn in this class, hehe. And one other academic update, next semester I'm going to be in University physics 1(calc based physics) calc 2, and discrete math... as well as some other general ed.

 

[Monocles]

Here is some other advice that worked well for me. Sometime around freshman year, I started reading lots of Wikipedia pages on math and physics. The vast majority of them went over my head, and for a long time I don't think that I learned much of anything from it. When I did think that I learned something from it, I'd write it out and try to re-explain it to test my understanding (I have a couple hundred of these notes these now). Over time, more and more articles will make sense, and before you know it you'll be able to read articles on graduate level topics in order to get an overview of the subject even if you're missing a significant chunk of supposed pre-requisites. Doing this has been a great motivator for me to work hard, since I know about a lot of the neat stuff that lies ahead!

There are traps though! It is easy to think that you really understand something if you understand all of the jargon in a Wikipedia article - then you start to actually study the topic and realize you knew hardly anything at all! You didn't learn 'hardly anything' though - you at least got the conceptual stuff out of the way (this is what Wikipedia is good at), its the nitty gritty details that stop you from actually solving problems (this is why you still need to work through textbooks)! The details are the hard part - but I'm still recommending that you do it because, at least for me, it helped me keep track of the 'big picture' when I'm slogging through a problem set at 2 in the morning, which was always a great source of inspiration.

 

[Jake4]

Here is some other advice that worked well for me. Sometime around freshman year, I started reading lots of Wikipedia pages on math and physics. The vast majority of them went over my head, and for a long time I don't think that I learned much of anything from it. When I did think that I learned something from it, I'd write it out and try to re-explain it to test my understanding (I have a couple hundred of these notes these now). Over time, more and more articles will make sense, and before you know it you'll be able to read articles on graduate level topics in order to get an overview of the subject even if you're missing a significant chunk of supposed pre-requisites. Doing this has been a great motivator for me to work hard, since I know about a lot of the neat stuff that lies ahead!

There are traps though! It is easy to think that you really understand something if you understand all of the jargon in a Wikipedia article - then you start to actually study the topic and realize you knew hardly anything at all! You didn't learn 'hardly anything' though - you at least got the conceptual stuff out of the way (this is what Wikipedia is good at), its the nitty gritty details that stop you from actually solving problems (this is why you still need to work through textbooks)! The details are the hard part - but I'm still recommending that you do it because, at least for me, it helped me keep track of the 'big picture' when I'm slogging through a problem set at 2 in the morning, which was always a great source of inspiration.

Ahh that's awesome. Honestly, I keep mentioning it, but that's the reason I plan to continue going to these weekly colloquiums we have. I understand almost nothing.. but it's so motivational, I left that colloquium last week just thinking in my head "How awesome is it going to be when I can understand that, and just be on that level" Most definitely keeps your eye on the big picture.

I read a lot of wikipedia articles on this stuff haha, they have pretty decent overviews.

It's funny, because it's stupid little things like.. a year ago, I would have looked at limit notation, and thought, what is this nonsense.. same with sigma notation. Things that are now extremely fundamental, looked like a different language at that time. When I learned derivatives, as simple a concept it is, it just clicked in my head. It was logical; the way I thought in my head it would have to work, was exactly how the equation "worked". That moment, earlier this semester, was when I realized I wanted to switch majors.

Kinda dumb, I know hehe, but it's just cool when you realize that although you're definitely at the beginning, you're making tangible steps towards where you want to be.