Biomathematics/Mathematical Biology

[altcmdesc]

I'm a freshman who's about to enter the U of MN Twin Cities Campus this fall. My college offers a UG degree in "Mathematical Biology" that really is drawing my attention. What sort of work would be done with this? How marketable is the degree? I'm planning on going to graduate school, by the way.

What I would like to do is use mathematics to model and analyze biological systems, would this get me there?

Would it be advisable to get a UG degree in, say, Biomedical Engineering, as a fall-back career and then go to graduate school for Mathematical Biology?

 

[cmos]

For future reference, it would be helpful to supply a link for posts like these; e.g. http://www.math.umn.edu/undergrad/degree_requirements/#tracks

Anyway, it looks like this program is applied mathematics with several classes that the average math major would usually not take. Note that it's a specialization within the math major and not a separate degree program. With that said, it all depends on what you want to do with your life. Bioengineering is generally about applying engineering methodology to biomedical problems. This mathematical biology program seems like it supplies a mathematician with the necessary biological knowledge so that he/she may solve mathematical problems in biology.

 

[altcmdesc]

What are the career possibilities for that track after graduate school? Bioinformatics seems way too computer science-y for my liking and doesn't seem to involve much hard mathematics.

I'm really having an issue right now between pursuing my ideal degree in a theoretical math/science program or settling for a practical degree in engineering.

 

[cmos]

Ah, yes, the ever elusive question of pure or applied science. From my understanding, bioinformatics is more about data mining than anything else. It all depends on what you're interested in. Also it depends if you think you will want to go to graduate school or not. Definitely consider than in choosing a field.

 

[altcmdesc]

Yeah, bioinformatics doesn't seem interesting at all. It's more suited towards a CS major than a Math major as far as I know.

I will most likely be going to graduate school, and if finances permit, going for a Ph.D. I've seen research in biomathematics that deals with constructing mathematical models of biological processes such as scar tissue formation, enzyme activity, tissue mechanics, etc. The classic example that I saw were the classic logistic population curve and the predator-pray differential equations. It seems like a very interesting field.

Does anyone have any experience, direct or indirect, with the field? I'd really love to find out about the job search, research positions, day-to-day life, etc.

 

[altcmdesc]

Also, what pure mathematics courses would be useful for me to take? I plan on taking Topology since it seems to be something that ought to be in any mathematics major's curriculum.

 

[Andy Resnick]

I'm a freshman who's about to enter the U of MN Twin Cities Campus this fall. My college offers a UG degree in "Mathematical Biology" that really is drawing my attention. What sort of work would be done with this? How marketable is the degree? I'm planning on going to graduate school, by the way.

What I would like to do is use mathematics to model and analyze biological systems, would this get me there?

Would it be advisable to get a UG degree in, say, Biomedical Engineering, as a fall-back career and then go to graduate school for Mathematical Biology?

Currently, mathematical models of cells, organs, and organisms are generally systems of linear ODEs- and those are the sophisticated ones. Other than that, there is a lot of statistical analysis for drug tests and patient outcomes and epidemiology type analysis. There is also a nice subset of work regarding image analysis- imaging, but also crystallography.

It's not clear to me what the UG degree will prepare you for, but that shouldn't stop you if you enjoy the field. Make sure you take some real bio and biochem classes to complement the theoretical stuff.

 

[The|M|onster]

From looking at the link provided, that seems to be a pretty standard applied mathematics curriculum with an emphasis in biology. The Twin Cities is pretty solid in applied mathematics, so if that's what you want to do then you picked a pretty good school.

If you want to include some pure mathematics, the most important classes are probably abstract algebra, real analysis, and topology. But you'll probably want a class in complex analysis and an advanced linear algebra course geared towards theory.

 

[altcmdesc]

As part of the curriculum, the school makes you take

"Intro to Modern Algebra" - Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields.

"Applied Linear Algebra" - Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications.

I'm not sure if this is the "advanced linear algebra course geared towards theory" you're talking about. I have to take a Linear Algebra course before this as a part of Calc IV: Linear Algebra & Differential Equations

In terms of real analysis, the course every math major must take in order to get into upper division is

"Sequences, Series and Foundations" - Introduction to reasoning used in advanced mathematics courses. Logic, mathematical induction, real number system, general/monotone/recursively defined sequences, convergence of infinite series/sequences, Taylor's series, power series with applications to differential equations, Newton's method. Writing-intensive component.

which I assume is "half" of real analysis. The other half seems to be

"Advanced Calculus" - Axioms for the real numbers. Techniques of proof for limit theorems, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-/multi-variable functions.

Is the "Advanced Calculus" course something I should take? Or is it just overkill? And is the "Intro to Modern Algebra" course all of the abstract algebra I should be exposed to?

Thanks for the suggestions, I'll try to fit in Topology and Complex Analysis.

 

[Cincinnatus]

Currently, mathematical models of cells, organs, and organisms are generally systems of linear ODEs- and those are the sophisticated ones. Other than that, there is a lot of statistical analysis for drug tests and patient outcomes and epidemiology type analysis.

I am a graduate student in theoretical biology. We use much more sophisticated mathematics than your comment implies.

I'll go even farther and say that I know many people who think it's just a matter of time before biology really influences mathematics, as physics always has. Here is an interesting article claiming that this is already going on: http://www.claymath.org/library/05report_featurearticle.pdf

 

[Andy Resnick]

That's a very nice article- thanks for bringing it to my attention! I'd say you are correct- and it's nice to see.

So, my question is- and I'm asking because I've dealt with this- how do you get the biologists interested in your work (or the ideas in that article)? I've had to really struggle to make 'traditional biologists' understand why physics is relevant to biomedical research (besides instrument development).

 

[altcmdesc]

Very cool article.

I have a question - What is the difference between Mathematical Biology and Biophysics?

 

[Cincinnatus]

So, my question is- and I'm asking because I've dealt with this- how do you get the biologists interested in your work (or the ideas in that article)? I've had to really struggle to make 'traditional biologists' understand why physics is relevant to biomedical research (besides instrument development).

I'm not sure it's much harder to get biologists interested in what I do than it is for any "traditional" biologist to get another one working in a different area of biology interested.

I have a question - What is the difference between Mathematical Biology and Biophysics?

Sometimes no difference, sometimes a huge difference. It depends who you ask, these fields are pretty ill-defined and interdisciplinary anyway. I'd say that mathematical biology is almost always theoretical whereas biophysics could refer to either theoretical or experimental work.