Topics In Higher-Level Mathematics Used Frequently In Your Research.

Question

[Burlappsack]

Hello, My formal training is in biology, but my field of study bioinformatics. I have been desperately trying to increase my skills in areas which I had little exposure to as an undergraduate, computer science and mathematics. Now, I am trying to figure out what areas of mathematics I should focus on learning to open a breadth of possible areas of interest in graduate school. So my question is this: What areas of high-level mathematics do you use in your research, and what is that area of research?
Thank you very much!

Answer 1

[David Quigley]

I usually associate "high-level mathematics" with topics like abstract algebra. My work in quantitative genetics (e.g. association studies and linkage analysis, as opposed to molecular genetics) uses primarily applied statistics. I'll assume this counts for the purpose of your question. Most of what I work with every day is very elementary probability and statistics. Linear models, common distributions, survival analysis, non-parametric statistics, student's t test, the Fisher exact test, analysis of variance. Some machine learning as well, mostly straightforward application of classifiers. To prove properties of estimators or code an support vector machine yourself you'll need calculus and linear algebra, though you can work in the field quite happily without ever doing that. If you intend to develop new methods in statistics you'll need a proper grounding, but that doesn't sound like your intention.

I would claim that a working understanding of biostatistics is crucial to work in any area of biology, particularly inherently quantitative work such as bioinformatics.

Answer 2

[Qdjm]

David's right, applied statistics is what you need for most bioinformatics. You should learn R, most of what you need is already coded therein. After that the next most important fields are (elementary) linear algebra and graph theory. Modern biological network analysis relies heavily on graph theory and understanding matrix diagonalization will help you understand principal component analysis, singular value decomposition and multivariate linear models.

My lab develops machine learning methodology for computational biology; we primarily work with functional genomic data. In my field, in addition to the linear algebra and vector calculus, you also need to know convex optimization (and a little bit about non-convex optimization) and advanced applied statistics, esp. Markov Chain Monte Carlo methods, the expectation-maximization algorithm, exponential family models, and Bayesian inference. Information theory is also very helpful and we end up using a lot of graph theory.

[Burlappsack]

thanks! I already use R for exploratory data analysis. I'm taking a course that covers graph theory, and have picked up Matricies and Transformation by Pettofrezo a few days ago for a quick intro to linear algebra.