Which Graduate Program Should I Consider: Math or Chemistry?

[hebrewBAMmer]

Hi everyone (hopefully I posted this in the right section),

I know very little about graduate schools since I was pre-med for a long time, but only a few months ago realized I'd rather go to graduate school. I was hoping someone could help me figure out which programs in graduate schools to look at. Ideally, I'd like to be able to apply abstract algebra to biological/chemical systems like in these two papers (moreso the first one as the second one is more macroscopic)

http://bioinfo.uib.es/recercagrup/magarshak.pdf
http://www.tbiomed.com/content/pdf/1742-4682-8-21.pdf

Anyways, here's a bit about me:

Just graduated from college, currently doing a medicinal chemistry internship.

Math/Chemistry double major (Chemistry w/ honors)

Overall GPA: 3.674
Math GPA: 3.749
Chemistry GPA: 3.745

Math Courses taken: Calculus II, Linear Algebra, Combinatorics, Analysis, Abstract Algebra, Topology, Number Theory, and Applied Statistics

Chemistry Courses taken: General Chemistry I, Analytical/Inorganic Chemistry, Organic I, Organic II, Advanced Organic, Advanced Inorganic, Physical Chemistry I, and Biochemistry

I've done two summers of research in proteomic mass spectrometry (one summer was more biophysical chem and one was more biochem). During my school years, I was a math tutor for 2 semesters, Organic Chemistry class TA for 3 semesters, and an Organic Chemistry lab TA for 1 semester.


Anyways, after talking to some professors from my college, they said that I would have a much easier time getting into chemistry graduate school and would have a harder time doing math graduate school (also because of lack of really doing anything with math besides the chemistry research where it was involved). Unfortunately, I haven't found any chemistry graduate school research groups/programs that use a lot of abstract algebra (I know group theory plays a major role in crystallography, but I talked to a crystallographer who told me that he uses very little math). So I started looking at applied math graduate school programs, but I'm not sure with my math stats and courses if I could even get into to math graduate school to do applied math. Any help from anyone would be most appreciated!

 

[Mike H]

So, the obvious questions: did you see who cited and who was cited in those papers and gotten an idea of potentially good programs to apply to as a prospective grad student? What about actually just inquiring about graduate programs where those authors are located? Have you checked out the http://www.springer.com/chemistry/physical+chemistry/journal/10910" to get ideas as to possible future graduate mentors?

General suggestions -

1.) You may want to also consider biophysics and/or chemical physics graduate programs, in addition to possibly even systems biology/integrative bioscience/"other trendy phrasing" programs. It really depends on just how badly you want to stay in the company of (mostly) chemists. ;)

2.) One thing to always keep in mind is that if you can get yourself a graduate fellowship of some type (so you will not be a drain on a hypothetical advisor's grants), you can likely have more leeway to do what you'd like.

3.) This is very general graduate school advice - try and pick a program with adequate "critical mass" in case of unforeseen complications or interpersonal conflicts. If you can really only see yourself working with a single faculty member at a program, I have anecdotally found that people in such situations can find themselves in proportionally less pleasant straits should things go south.

 

[hebrewBAMmer]

I didn't really see any references on the first paper, but I haven't gone through all of them on the second. I did try emailing the authors a few days ago to see if they know anyone in the US studying this, but I have yet to hear back. Unfortunately, one paper is from authors in Spain and the other is Canada, whereas I am here in the US (and I would prefer to stay in the US if possible.)

I did take a look at that Journal (at least what I am able to access), but it seems a lot of the math used is more computational/calculation based rather than abstract algebra based. I'll take a look into some biophysics, but hopeflly I can find one that uses a bit of abstract algebra (I think I generally prefer theoretical stuff instead of experimental stuff -- my medicinal chemistry internship has shown me that I don't want to be at a lab bench nonstop).

Thank you for your advice btw. It seems that a majority of the chemists out there only borrow from math a little bit, whereas I really want to use it and apply it on a theoretical level.

 

[cgk]

I'm in chemical physics/quantum chemistry, which is probably the most mathematical of the chemical fields. But I don't think I've ever seen any use for abstract algebra in this field, apart from some group theory and some Lie algebra stuff (which, however, is all well known).
The fields of mathematics which are most often used are primarily large scale numerics of all kinds (widely used methods like Davidson diagonalization or very powerful Krylov subspace convergence accellerators (DIIS and co) were invented in chemical physics), methods for partial differential equations, and some analysis. I'm afraid apart from numerics I don't see very much potential to do mathematical reasearch which would be beneficial for chemistry.

That being said, you could check out what the groups at the Max Planck institute for mathematics in the natural sciences (in Leipzig) are doing to get some ideas.

 

[hebrewBAMmer]

All the group theory I have seen (which has primarily been crystallography) does seem already fully developed, which is one of the reasons I was looking into applied mathematics (seemingly "mathematical biology" as that looks to be the closest way to combine higher level mathematics with something as chemically related as possible). The problem is... I have no idea what my chances would be of getting into a program, especially without the math subject GRE (I've already signed up for the chemistry one, but I didn't see the point of registering for the math GRE unless I had a good chance of getting accepted).

I'll take a look at the Institute, especially since I have never heard of it. Thanks!

 

[Mike H]

The main reason I suggested systems biology graduate programs is that you are likely to find mathematicians among the faculty who have developed an interest in biological problems. Of course, the potential downside from your POV (from what I can tell) is that some of them are more interested in evolutionary dynamics and related topics - which while they use algebraic methods (including graph theory) and game theory in such pursuits, it's quite macroscopic in nature, certainly when compared to what people would be more inclined to look at in a chemistry or biochemistry department. You would really need to investigate what each program is like (at least on paper).

I don't know enough about applied mathematics graduate programs to offer any substantive wisdom, except to say that I remember the applied math department at my graduate alma mater had all kinds of people running around with a wide range of backgrounds. I imagine the environment would be different in comparison to a proper mathematics department, as well as in their expectations of incoming graduate students.

 

[hebrewBAMmer]

You guys have been very helpful to me. Thank you :). I also heard back from a math professor at my college I emailed a few days ago about Applied mathematics/mathematical b iology graduate school versus chemistry graduate school. This was his response.

Mathematical Biology does seem to be riding quite a wave these days, but it's not something that's going to relate closely to abstract algebra, so I don't see how this helps you. As far as I can tell, algebra relates to chemistry primarily through the study of symmetry. I know that Serre wrote the first part of "Linear Representations of Finite Groups" specifically for quantum chemists. I also have a book called "Symmetry in Chemistry" that goes into applications of group theory to chemistry. These are older books (published in 1977 and 1965 respectively), so I don't know if there is active research going on in the topic.

My advice would be to go to chemistry graduate school, keeping your eyes out for places that have connections with a physics program. That is, look for people who have the word "quantum" as a word appearing in their list of interests. That's where representation theory is going to arise most in chemistry, and representation theory is, in some ways, simply advanced abstract algebra.

Again, my tentative thinking is that Mathematical Biology isn't for you -- it's generally going to be far more related to the statistical side of mathematics. I suspect there is mathematical chemistry out there, and not just the computational sort -- you might need to look a little harder to find it.

 

[Mike H]

Most of the theoretical chemistry groups that I'm familiar with do have room for people doing both theory/methods development (although perhaps not as elegant as you have in mind) as well as applications, so I suppose it's really just a matter of finding a good fit with a flexible enough advisor. Of course, there are plenty of potential projects that bridge the gap, although I'm not sure about how much computational work could be avoided in the long-term if you actually wanted to tie it to experimental data. I would, of course, strongly suggest that you start perusing the journals to get an idea of the lay of the land, as well as certainly more focused lit searches.

Also, a point of curiosity - when you said you took "Physical Chemistry I" did you mean that you just took the standard physical chemistry sequence (the standard upper division - typically junior year - mix of thermo, kinetics, quantum, and dashes of other material that you get in most US universities) or that you just took one semester/quarter class of a full-year sequence? My impression is that most if not all US chemistry graduate programs do expect you to have a full physical chemistry sequence under your belt (unless you came in with equivalent coursework in physics or some such).

 

[hebrewBAMmer]

Sorry for such a late response! Last weekend was the GRE and between work and whatnot, I've been super busy.

According to our course catalog, this is their description of Physical Chemistry I:

"An introduction to physical chemistry that emphasizes experimental and theoretical aspects of chemical thermodynamics, chemical and physical equilibrium, and kinetics. Three classes, one laboratory each week."

Technically we have a Physical Chemistry II class even though it wasn't required for the major (in fact one year I couldn't take it because it conflicted with Number Theory, and the second year I could have but took Biochemistry instead).

In trying to find chemistry groups, I did manage to come across this one that looks semi-promising:

http://www.chem.yale.edu/faculty/iachello.html

Not sure of how much pure math I would use, but also looks to be one of the most mathematical groups I have found thus far.

 

[Mike H]

No worries about the lag.

So, just as a representative example of what I was talking about, it took me about three minutes to find this given your link -

http://www.yale.edu/printer/bulleti...nting-departments-and-programs.html#chemistry

Applicants are expected to have completed or be completing a standard undergraduate chemistry major including a year of elementary organic chemistry, with laboratory, and a year of elementary physical chemistry. Other majors are acceptable if the above requirements are met.

It sounds that you missed out on standard full physical chemistry sequence that covers elementary quantum mechanics/electronic structure/spectroscopy in the second half. This might be problematic, although the fact you were a math major should strongly suggest to any admissions committee that you are not terrified of the mathematics that would be involved, although you might find it boring to tedious depending on your temperament. (To wit: my one past roommate - a mathematics grad student - once said when he saw me doing a problem set, "I would have gotten bored as snot after proving the validity of part A and never done the calculations in B, C, and D.") I would definitely speak to any and all of your professors from your undergrad institution about this issue sooner rather than later.

Your situation in terms of stated interests is leaving me at a bit of a loss in terms of specific advice (I am one of those degenerates who mostly does experimental (bio)physical chemistry), but I would really think through whether you could see yourself doing theoretical chemistry in general (even if you can't apply your pet areas of mathematics) and even some computational methods on occasion.

 

[hebrewBAMmer]

I see what you're saying. I would assume most universities who have a chemistry major generally require a year of physical chemistry to complete the major, so maybe that is where it is coming from? My school only required 1 semester of it, so Yale might be unconcerned as long as I completed the major (I will contact my professors and find out for sure). I know a number of people who went to graduate school in chemistry without taking Physical Chemistry II, though none of them were at Yale.

It almost seems like what I am looking for is along the lines of chemical physics. If I can't really use the math I've developed, I can't say I'm that interested in theoretical chemistry (in fact, I would probably do organic since that was the other area of chemistry I enjoyed). Perhaps I don't actually fully understand what theoretical chemists do besides either using a ton of mathematics or using a lot of computers to do some computational stuff (which is probably one of the reasons I liked this Yale group -- they were actually using the mathematics directly.)

 

[Mike H]

At the schools I attended, chemistry (and even biochemistry) majors did a full year of physical chemistry. My impression from classmates in graduate school and coworkers since then is that is fairly standard, although certainly other coursework requirements are far more flexible (e.g., I had a negligible background in inorganic chemistry; on the other hand, a few classmates had rather broad coursework requirements as undergrads). Anyway, I am sure that as you did complete a chemistry degree at an accredited institution of higher learning it wouldn’t be a dealbreaker, although you’d probably be expected to demonstrate some minimum level of competence in elementary quantum and atomic/molecular structure & spectroscopy. I am not sure that a chemical physics graduate program would be that much more suitable, as such programs tend to be essentially the physical & theoretical chemists joining forces with physicists with appropriate interests in atomic/molecular and condensed matter physics.

Certainly, theoretical chemists tend to be the least math-phobic of all chemists, and I would be lying if I didn’t mention that a number of them are more towards the computational side of things. When I generally think of theoretical chemistry as a field on the whole, my view is more in line with the sorts of things mentioned and described on this site:

http://simons.hec.utah.edu/TheoryPage/

I would definitely go through that site and get a very general “lay of the land” insofar as is possible via a website.

I really do think there is plenty of room for someone with a broad and strong mathematical background to make contributions to chemistry & biochemistry. What I am not so sure of is whether that person will be able to just take a part of what they know mathematically and focus on that (e.g., abstract algebra), or if nature will be extremely annoying and demand that they apply all they know, since it refuses to be that easy (all of your mathematical background). Of course, the issue is that since you have no upper-level or graduate coursework in quantum mechanics/chemistry, this is all a bit premature. You may find that after you take such a course, your interest is piqued enough – and find the material adequately stimulating – to carry on with it in some manner, and even melding it with your interests at the present.

 

[hebrewBAMmer]

As an update, I heard back from a physical chemist at my college about the only taking Pchem I thing, and this was her response:

"As such, the emphasis on biology/biochemistry on your transcript and the absence of physical chemistry II and the choices that lead to that is not going to make a lot of sense to readers of your application. I think students who want to do organic/biochemistry MAY be able to get away with not having had both semesters of pchem, but that is more difficult if you want to enter phys chem/chem phys programs at any school (I did not realize you had not taken it). So two things I might suggest—emphasizing the impact of other related chem coursework (what electives did you take? instrumental? Biophys?). And, considering if there is somewhere near you where you might take that course next semester (one of the California universities or state schools). For purposes of having it on your transcript it would not matter if it did not have a lab."

I did some research, and UCSD's p-chem II is in the spring term (i.e. not until april which is way past admission committee decisions).

In terms of the link, a lot of the theoretical chemistry I'm thinking of is involved in that too.. perhaps the way I am looking at it is more that there are chemists who do the computations of chemistry, but to do that computationd of chemistry, there must be some fancy math/physics that goes into figuring out all the math and formulas that goes into the computer. That math/physics is what I would like to work with (I'm sure there will be no way out of doing computational stuff, and some of it I am fine with, but I'd hate it if that's the only thing I'd be doing -- hence the Yale research group that looked more appealing.) The other option is to try for math grad school in applied math, but my chances of getting into a decent one are probably not that high

 

[Mike H]

So, obligatory disclaimer in case it wasn’t previously obvious – I’m not a faculty member anywhere, so I don’t have any inside track on what goes on in the minds of admissions committees.

I think it’s reasonable to say that if you want to go to grad school for physical/theoretical chemistry, not having the full p.chem. sequence under your belt is likely to be an obstacle to some extent. I would suspect that your application would be stronger if you were to apply next fall after getting the class under your belt, not least since you’d have a better idea of what is actually involved. Of course, I’m not sure how practical that might be for you.

General advice is hard to give, as the nature and direction of graduate research can never be fully predicted. You’ll want to look for groups that have strengths on the theory and method development side. Although, of course, that often leads to researchers wanting to apply those cutting-edge developments to questions where computations/simulations are essential. Sometimes, it’s by trying to figure out how to make computational methods more efficient to treat these larger and more complicated systems that you are really forced to focus on the essential physics and mathematical formalisms. But I would also give some thought as to what problems in chemistry/physical chemistry interest you, as that will govern what kinds of things you will probably spend most of your time thinking about, all in all. For example, there are plenty of groups out there with interests in computational organic chemistry and biochemistry.