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Math required for physics grad school

  1. Jun 4, 2010 #1
    I'm heading into my junior year as a physics undergrad, and I'm starting to think my math skills won't be where they need to be for grad school.

    So far, I've taken calc 1-3, probability theory, and an "Intro to Mathematical Physics," which used the Boas text. That class was basically a crash course in many different subjects in math.

    By the time I graduate, I hope to also have DiffEq and Linear Algebra under my belt.

    Is that enough? Right now, my main interests are in cosmology and particle physics. Unless that changes in the next 12-15 months, those are the areas I'll be applying to grad school for.

    I won't have topology, real analysis, complex analysis, set theory, or anything else that might be required under my belt, except what I learn "on the fly" in my physics classes.

    Will this get me into trouble down the road, or are these typically picked up in grad school for a physics major?
     
  2. jcsd
  3. Jun 4, 2010 #2
    Well your experience may be different from mine. But in my experience, the only math you really need to take in a math department is calc 1 and 2, multivariable calc, and linear algebra/differential equations. Yeah, a lot more math is needed in physics, but they usually teach this to you along the way. Heck, I learned more math in physics than I learned by being a math major on the side! Often, physics departments will also have their first year grad students take a mathematical methods course to cover any gaps in their mathematical understanding.

    All that other stuff you're taking is fun in its own right. But I've never needed any of it in the course of my (so far short) career as an experimental physicist. Unless you're doing some crazy string theory or loop quantum gravity stuff, I doubt you'll ever need to take an advanced math course.
     
  4. Jun 4, 2010 #3
    Pick up courses in complex analysis and differential geometry if you can.
     
  5. Jun 4, 2010 #4
    If you want to do theory, you should take as much as possible. You'd be surprised what pops up where. For example, I work in condensed matter, and I run into everything from various cohomology theories to characteristic classes on a regular basis, both of which are fairly high-level topics in mathematics.
     
  6. Jun 4, 2010 #5
    Taking "as much as possible" limits me to what I've already mentioned.

    In the next 4 semesters, I need to take:

    Mechanics (upper level version)
    E&M
    Modern Physics 1
    Modern Physics 2
    Intermediate Lab Physics 1
    Intermediate Lab Physics 2
    Thermodynamics
    Solid State Physics
    Quantum Mechanics
    General Chemistry 1
    General Chemistry 2
    Capstone Research Project

    Adding in DiffEq and Linear Algebra, plus my one gen ed I need to get out of the way, my schedule is booked. That's 15 classes, many of which are 4 credits, in 4 semesters.
    I might be able to squeeze in one more math class, but I don't have the pre-reqs in place for some of the upper level math suggested.

    That's why I was asking about grad school math classes.

    Thanks for the replies so far.
     
  7. Jun 4, 2010 #6
    Postpone your graduation a year to fit more in
     
  8. Jun 4, 2010 #7
    I don't have the money to go an extra year. I have a mortgage to pay, and I can't work my whole 52 hours a week I'd like to while going to school. I'll be down to 31 hours a week this fall, for example.

    I've timed it such that I go completely broke at the end of my senior year. :-p
     
  9. Jun 4, 2010 #8
    I think an important distinction needs to be made here:

    Do you want to do theoretical physics or experimental physics?

    If you're just going to be doing experimental physics, what you have is more than sufficient. If you want to do theoretical physics, however, do what a few others said, and pick up a complex analysis and differential geometry (This will teach you a little topology) course. It's not necessary, but it would be good.

    I'm looking into grad schools myself, but from what I've read in my books, these courses are very important for theoretical physics, although it depends. Some schools, like Imperial College, will give you a course in differential geometry if you decide to go into theoretical physics. Most schools, I think, have mathematical physics courses that teach you the necessary mathematical acumen required for your field. However, I find that physics teachers have a tendency to be damned poor math teachers.
     
  10. Jun 4, 2010 #9
    I'm more interested in theory at the moment, but it could go either way.

    It sounds to me like I should be able to pick up just a couple of courses in grad school if needed. I was mainly worried about an overwhelming response of "you're not prepared!"

    It seems to be about 50/50, and I'm pretty ok with that.

    For what it's worth, I did some financial calculations with expenses and incomes, assuming a Gaussian distribution of each.

    In 2 years, I only run approximately a 20% chance of financial ruin. At 3 years (adding an extra year of undergrad,) the number is around 40%. Of course, this includes a lot of assumptions and idealizations, so the numbers include some uncertainty. Adding an extra year of undergrad is cutting it too close for comfort.
     
  11. Jun 4, 2010 #10
    Jack, I'm guessing Tenparsecs was joking (but correct me if I'm wrong).

    I don't know how Harvard or MIT work, but your average state school isn't going to reject your application just because you didn't take advanced math. Heck, at my school they sometimes accept a few people who haven't even taken senior quantum or stat mech. These people just use their first year to fill in the gaps in their undergrad. If they're that tolerant with gaps in physics coursework, they will be much more generous with math classes. After all, at the end of the day physics isn't math. Furthermore, first year students aren't expected to have a specific research interest yet. When you apply, they don't know what you want to do for your thesis research. So they're not going to sit down and say "this guy wants to do theory, but he doesn't have enough math, so let's reject him." Really they just care that you have good grades and decent research experience.

    If you need to know a certain level of math for your theoretical physics research, there's a good chance you can just take the appropriate math classes in grad school. Actually, most of the theory guys at my department just have their grad students do a lot of reading their first summer in order to get mathematically acquainted with the topic. As you said, delaying graduation costs you money. Getting into grad school on time will have the opposite effect, because grad school is free. Not only that, but they even pay you a small stipend. It's not much. But the time derivative of your bank account balance is always positive (if you're not a spendaholic), you can put your student loans on hold, and best of all, you're not paying through your *** (i.e. $10,000+ per year) on your education.

    Obviously do your own research. I'm just a grad student, so it's not like I have some secret knowledge or anything. But do keep all this in mind.
     
  12. Jun 4, 2010 #11
    I find math vary easy. No mystery's or anything. Just follow the formula o_O
     
  13. Jun 4, 2010 #12
    @OP: At my liberal arts college, it seems that many physics students who will not go heavily into theoretical physics do not take much beyond linear algebra and multivariable calculus. However, the students I'm referring to are also doing research, and most have been for at least a year.

    This does not address anything from the OP. Besides, we need context. What mathematics are you referring to?
    Edit: You're 14. The mathematics you're learning now isn't anything like university mathematics.
     
  14. Jun 4, 2010 #13
    About extending graduation for another year? No, that wasn't a joke. One of the biggest mistakes people make is rushing to graduate. They miss out on courses they should have taken, they miss out on a chance to pick up a second major or a minor, or most commonly they take too many courses at one time and let their grades suffer. I've seen students overload on hours and finish a semester with a 2.5 only to go and do the exact same thing all over again expecting different results.

    Now, if money won't allow extra time, then you just have to operate within your means. But most of the time, money isn't the real issue... at least not to the extent that it's truly a debilitating factor.
     
  15. Jun 4, 2010 #14
    I started college in the spring 2010 semester so I would typically graduate by fall 2013. I figure since I started college a semester late anyway, would there be anything wrong with me graduating in spring 2015? I plan to do a double major in math and physics and based on what I've heard and read, I think an extra three semesters(11 as opposed to the typical 8) would give me time to self-study and take as many courses as I feel necessary. It would also give me time to do research and prepare for the GREs.

    What are the disadvantages of spending 11 semesters in undergrad vs. 8 semesters?
     
  16. Jun 4, 2010 #15
    Few. The pain of the trial of patience? Even if a person had to borrow student loans for an extra year, it's almost always worth it in the long run. Taking your time means higher quality end results which is something that will pay off throughout your life.

    I recall one kid that took 17-18 hours every semester of his junior and senior years because he was desperate to finish--he didn't want to take out extra loans. His GPA ended up atrocious and he got accepted to no grad schools. Last I heard, he was working some menial job in tech support. Not that there's anything wrong with tech support--unless your goal to start with was to be a research scientist at FermiLab.

    I sometimes wonder if he ever compared in his mind the money he saved by not taking out an extra $10,000-$20,000 in loans vs. what he potentially lost for the rest of his life for not achieving his goals. I would bet that five figure savings will have cost him seven figures when it's all said and done.
     
  17. Jun 4, 2010 #16
    you need at least pdes and complex analysis on top of what you've mentioned. you also need to know how to do numerical things like solving pdes/integrating/monte carlo in code (read: you need to know how to program and numerical methods).
     
  18. Jun 4, 2010 #17
    Yes university math is harder then the math im taking right now, but it would be easy for me anyway if i keep up the good work im doing. Math Only gets hard when you weren't paying attention or just lazy. All of this is just my ''point of view'' on things. By the way, I was referring to ANY kind of math. Work hard and its not a big deal. Start good, keep it up, and you will find math easy, or at least okay. (Its harder then it sounds, but its possible and a number of people have done it. For e.g. My dad.)
     
  19. Jun 4, 2010 #18
    You mean "plug and chug" math.
    Let me clarify. Assuming all finances are covered, are there any disadvantages to spending an extra 3 semesters in undergrad? I will finish my undergrad at a college that is 15 minutes away from where I live(my parent's house) and my parents are covering all expenses.

    As of right now, my mind is on going to grad school for either pure math or theoretical physics, and although I haven't formally taken advanced classes yet, I'm self-studying as much as possible so I'm able to apply for REUs. I find that doing math, particularly proofs in set theory, can be very satisfying(like completing a puzzle, painting, schematic, etc.) while with physics I'm preoccupied with understanding the universe on a deeper level. I'm aware that the theoretical side of fields within physics and pure mathematics are nothing like the overgeneralized sensationalist garbage you would come across in popular books, but I say thank Zeus for that.

    My tuition for grad school will also be covered by my parents, regardless of how expensive it is. I'm financially secure even without a job thanks to my parents so my main focus is on getting the education I want, and I'm also a low maintenance person(for example my parents bought me a Mercedes, but I never bothered to learn how to drive) so I'm not too worried about job prospects after I get my terminal degree. I just want to know if there are any circumstances where I would suffer from spending an extra 3 semesters in undergrad since I don't see how taking more math and physics courses, and having more time to do research would be detrimental in terms of getting admitted to graduate schools.
     
    Last edited: Jun 4, 2010
  20. Jun 4, 2010 #19
    I have no intention of loading up on hours unnecessarily. I'll graduate on time at 15 credits per semester, maybe slightly less during my senior research project. Based on the comments so far in this thread, I'll pick up a few of the math courses in grad school.

    My problem is I got a late start. I'm 27 years old with a mortgage that I'm kinda stuck with. I bought the house 4 years ago, near the top of the housing bubble, so it's unclear at the moment if I could sell the house for enough to cover my mortgage plus home equity loan that I took out in order to go back to school. My schedule for the past two years, and the next two years, has been any day I'm not scheduled for class, I'm scheduled to work 11 hours (8 on Sunday).

    Last semester, I worked 41 hours a week while taking 15 credits, and that's about the break-even point for my bills. I won't be able to do that in the fall, I'll be down to 30 hours. I'd like to think that in my case, money is an actual limiting factor.

    More likely, you'll get an assistantship, so they won't need to pay any tuition.
     
  21. Jun 4, 2010 #20
    You might want to consider completely rethinking how you are living your life.
     
  22. Jun 5, 2010 #21

    Vanadium 50

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    For some reason, this thread has attracted a lot of advice from people who haven't completed (or attended!) graduate school itself.

    You can get an idea of what graduate schools expect by looking at their own undergraduates' degree requirements. Typically it's calculus, one class in differential equations, one class in linear algebra, and one or two others (often electives). Beyond that, the graduate program will teach you what they think you need to know, usually in a class called "math methods".

    Will it be useful to have seen the material in math methods before? Absolutely. Is it necessary? No.

    I'm shocked at the number of people who say undergraduate differential geometry is required. (But then I read my first paragraph again). If you aren't doing GR, you're unlikely to ever see it. I have never taken a class in it, and my PhD (and my career) are doing just fine. Indeed, at many colleges, you'll have a hard time taking it as an undergraduate majoring in something else.

    The one thing that I do see entering graduate students extremely deficient in and something seldom taught in math methods is probability/statistics.
     
  23. Jun 5, 2010 #22
    Thanks for the reply, V50. That really puts my mind at ease. Luckily, I've already taken probability theory, so I feel better about my preparation.
     
  24. Jun 5, 2010 #23
    I assure you that I currently do not have trouble with my mathematics classes, and that my mathematics skills are among the best among people I know for my level of prior training. Anyway, you dodged the issue; one cannot just 'memorize the formulas' for college level and some high school level math.

    @Vanadium 50: How much probability/statistics do you think is enough for physics graduate students? Also, could you give a ranking of the importance of probability/statistics for some of the major science fields?
     
  25. Jun 5, 2010 #24
    For some of the classes recommended, did you guys mean Applied or Pure Math classes? For instance, Complex Variables?
     
  26. Jun 6, 2010 #25
    Heh, I'm not sure I'd even go so far as to call my previous comments "advice." Really it's mostly just my observations based on my experiences thus far. But in addition to my previous disclaimer, I should add that since I do experimental physics, I almost never do any mathematical calculations at all. So I'm sure that someone who's doing theory will need a lot more math than me.

    It's funny you mention that. I actually took differential geometry in undergrad. For me it wasn't so weird, since I was a math major too. I don't think I've ever used it. Heck, even when I took undergrad cosmology later on (which has a pretty huge GR component), I never actually approached the material in the same way as we did in differential geometry. Differential geometry is a lot of fun from a math perspective. But it didn't really do anything for me physics-wise.

    I can definitely attest to that. Since I do high energy astrophysics (which is basically just regular HEP with un-cool protons and electrons instead of exotic particles), pretty much everything I do is statistics. It's sort of annoying that I don't know where the formulas for detection significance, excess counts, etc. come from, or how our monte carlo methods work. In undergrad and first year grad school you spend a lot of time learning about calculating cross-sections and spin eigenstates, but not so much time learning how to analyze experimental data.
     
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