# Mathematics Of Bioinformatics ((LINK))

Sergey Petoukhov, PhD, is a chief scientist of the Department of Biomechanics, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, as well as Full Professor and Grand PhD from the World Information Distributed University. He has published more than 150 research papers in biomechanics, bioinformatics, mathematical and theoretical biology, the theory of symmetries and its applications, and mathematics.

## Mathematics of Bioinformatics

Like many other biologists , I learn to program for my bioinformatics daily needs by self-study. However, because I don't have strong Math / Statistics background most of the work I do is simple I/O parsing , database quires and straightforward R script on a fancy day.

I read a small guide to Math for Physics ( , which is divided into three levels) and would like to see a similar but more detailed guide for bioinformatics (for biologists-with-weak-Math-background-and-want-to-work-in-bioinformatics to be more precise) .

Note: I expect some of the Math concepts are used frequently more than others in bioinformatics (core concepts) and some are advanced and rarely used. I'm interested in the former but I am open to all suggestions.

before I write an answer (mathophile that I am) could I ask which area of bioinformatics you mostly dabble in (sequence analysis / networks / phylogenetics / microarray analysis ... ) and whether you're also interested in system modelling / cellular biophysics. It might be a few hours before I answer.

@russH. Thank you. At the moment I am involved in CNV genotyping , NextGen sequencing and networks analysis. Not much on system modeling / cellular biophysics but definitely interested to read your take on those topics. Hopefully, enough answers on different sub-bioinformatics fields will make this page useful resource for the community.

I had to take a "contemporary mathematics" course in my second year of my college. This was a tough course that taught me many things I rarely used today such as functional analysis, measurement theory and differentiable manifold. The teacher started the course by defining many "obvious" concepts in a rigorous way. At the beginning, this process is tedious and sounds really silly because I thought it only made things overcomplicated, but after several classes, I began to learn the necessity of the math way - when you have a rigorous system, mathematics can carry you much further than what you can initially imagine. It is really like a magic. Another important fact I learned is that we should not treat mathematics purely as symbols. We should learn to visualize them in mind. At times symbols are more descriptive than words. In my naive view, solving problems with mathematics follows this route: abstract the problem with symbols, deduce using symbols, "visualize" the symbols after the deduction, and deduce even further. In the end, this "useless" contemporary mathematics course becomes the most influential course I have even taken.

I am not asking you to take such a course. Different people learn the apperception in different ways. I mainly want to point out that to make the best use of mathematics to solve real problems, you should learn to abstract problems with symbols and vividly see the meaning of symbols. Skills in deriving equations are important, too, but IMO come in the second place. I also want to emphasize that to take the full advantage of mathematics, the notation system has to be very rigorous. Everything in the system must be consistent and without ambiguity; otherwise math will stop working.

I do not have a good suggestion about how to learn the essence of math as you and I probably have very different background. Nonetheless, if you want to read a book on the mathematical aspect of bioinformatics, I would recommend Richard Durbin's "sequence analysis", the only bioinformatics book I have finished reading. Ewan Birney has recently blogged his 5 statistical things I wished I had been taught 20 years ago. It is worth reading and probably of much more practical use than my empty words here.

My last semester as an undergraduate, I took a class called "fundamentals of mathematics" or something like that. My only reason for taking the class was to get a math minor and I had no idea how it would relate to my future work in genomics and bioinformatics.

The most important parts of mathematics as far as bioinformatics is concerned is probability/statistics and discrete mathematics/combinatorics. As was stated earlier though, the value of mathemtics is more the mindset: abstracting problems, finding analogous problems for which a solution is already known. Sometimes mathematical language is the neatest way to describe a problem.

Thanks Gjain. I am aware of both Khan Academy and MIT open course. There are plenty of resources in the internet on almost any Math topic. My question is to link Math concept(s) needed to solve a common problem in bioinformatics.

Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.

The Master of Science degree programs in Mathematics provide education at the graduate level in algebra, analysis, applied mathematics, bioinformatics, and statistics. Students completing these degrees are prepared for positions in industry, government, business, college teaching, and for more advanced study in mathematics or statistics.

The M.S. degree in mathematics and statistics is offered with no concentration, or with one of the following concentrations: discrete mathematics, scientific computing, bioinformatics, statistics, biostatistics, and statistics and allied field. The concentrations in statistics are programs designed for persons who wish to prepare for careers as professional statisticians in industry, business, or government. These programs provide advanced training in applied statistics for those who are already working in areas that use statistics, as well as for those who plan to enter these areas. The programs present an optimal balance among the broad range of statistical techniques, mathematical methods, and computation. The concentrations in discrete mathematics, bioinformatics, and scientific computing are designed for students who wish to combine their study of mathematics with selected areas in statistics, computer science and biology.

The programs present an optimal balance among the broad range of statistical techniques, mathematical methods and computation. The concentrations in discrete mathematics and scientific computing are designed for students who wish to combine their study of mathematics with selected areas in discrete mathematics and computer science. There are opportunities to apply this study to related areas outside the department.

The Ph.D. program in the Department of Mathematics and Statistics is firmly committed to the twin goals of Excellence and Distinctiveness set forth in the University's Strategic Plan. The Mission of the Department is: Mathematics (including statistics) is one of the great unifying themes in our modern culture. It is a language, a science, an art form, and a tool of tremendous power. The Department of Mathematics and Statistics, in its courses for both majors and non-majors, seeks to introduce students to this vast area of knowledge and to show them how mathematics and statistics can be used to solve problems. Mathematics and Statistics doctoral students are trained in research, teaching, and public outreach via a variety of mechanisms.

The objective of the degree program is to provide comprehensive training in mathematics and statistics professional development. This training is meant to prepare students, including those from diverse backgrounds and underrepresented groups, for a variety of career paths involving research, teaching, and/or science advocacy, which include jobs in academia, government, and industry. The Ph.D. program includes concentrations in mathematics, bioinformatics and biostatistics. These concentrations address the critical need for mathematics faculty as well as the need for highly trained researchers in mathematics and statistics.

To some extent I feel like being able to do research is on my life goals bucket list. Diving into unexplored territory definitely excites me. So I somewhat feel I need to take advantage of the broad spectrum of fields I have knowledge of, although almost insignificant, it is still there. I thought maybe bioinformatics mixed with some data science algorithm research would be a good path to pursue. Would my prior experience in Biology give me an advantage? For example the ability to pick up technical biology concepts quicker?

A final word of warning - biology still very much has a culture that the reason to do a PhD is to spend your life in that field. Not necessarily stay in academia (although some of the older faculty might still be reluctant to take on someone who doesn't want an academic career), but at least start with a desire to stay in some sort of bioinformatics. I'm not saying its a good thing, but it is a thing.

No, not relative to most applicants for a PhD program in bioinformatics. There will be others who studied a quantitative field more related to biology than your math/CS pairing. Modern approaches to every area of biology involve increasingly quantitative methods. Graduates with undergraduate degrees in molecular biology, neuroscience, ecology, biochemistry, etc, are all potential candidates for bioinformatics PhD research, and they've all had an entire undergraduate education in biology beyond highschool. There will be students who initially pursued a medical/health profession and have taken courses in physiology. There will also be CS and stats undergrads who worked on biological or medical problems in their undergraduate research, people who primarily studied biology but with a minor in statistics/data science/bioinformatics, etc. High school biology, even "advanced" high school biology, will have you below the par for biology expertise in a bioinformatics field. 041b061a72