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I am in the same boat as many bioinformaticians, where I got my degrees in biology and taught myself computer science, and that's gotten me pretty far. But unlike those lovely physicists-turned-bioinformaticians, I only took the required maths courses ten years ago and wish I'd payed more attention.

As far as I can tell it's currently for me more of a problem of concepts, and familiarity with symbols. For example with the latter, when I get to a part of a paper with equations, my eyes just gloss over... I'm not used to reading equations, so it's difficult for me to parse them or understand them in context- everything from 'what is that greek letter pronounced as?' to understanding the general form of the specific equation.

What is a good way to get up to speed on the important mathematics in my field? Most of the stuff I come across is either too high level (academic texts) or too low level (Khan Academy, for example). I feel that this lack of knowledge is really limiting the directions I could take my research and tools I could use, but I'm not sure how to go about improving it.

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    If you are a bioinformatician (i.e., working on computer science/programming/software engineering applications for biology), then academic texts should not be "too high level", no? As you are finding out, the math involved simply is advanced, so any method of coming to grips with it will involve advanced material, whether this is courses or textbooks. Mar 26 at 9:35
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    Related: How to build bridges between mathematicians, computer scientists and biologists? AND Start studying mathematical biology from basics AND Books on mathematical biology. Useful, I think, is A Mathematical Nature Walk by John Anthony Adam, but it's written for someone with roughly a 2-semester calculus background (U.S. calculus), so it doesn't get into more advanced stuff that you might want. Mar 26 at 12:51
  • There's no end to statistical analysis in bioinformatics with varying degrees of mathematical sophistication. Maybe an interesting analysis in a paper is a good place to start. What sort of mathematics underlies ANOVA? You could always work backwards. There's no replacing lots of experience, just pick a place to start and go, one thing leads to another. Mar 26 at 16:55
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    The way to learn mathematics is to do mathematics. Trying to understand by merely reading equations will get you nowhere. You've got to get out your pencil and paper and work problems.
    – Matt
    Mar 27 at 13:54
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    A key point of information missing is what do you want to learn the maths for/which subfield of mathematics do you want to know. Most of the answers here assume you want to learn statistics (or mathematical biology in the answer above), but there is a lot of different maths that can be applied to biology: do you want statistics or the biophysics of animals or statistical mechanics that underlies sub cell level behaviour, or optimisation (for conservation efforts/animal energy conservation), or even group theory. Knowing the level you are aiming for will help provide better answers for you. Mar 30 at 17:19

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I would recommend that you search the internet for courses of study in the specific field you need to catch up on - here, bioinformatics. For instance, here is a list of universities in Germany that offer programs in bioinformatics (in German).

Then check the relevant classes that are mandatory or recommended in those programs and that check your boxes - in your case, any introductory math course for this particular program.

Finally, find out whether you can audit this course if it is nearby or streamed on the internet (or recorded on YouTube). Or find out which textbook is used. If this is not indicated on the course homepage, you can always simply send an email to the instructor, you may (or may not) get an answer.

After that, you will indeed need to invest some time. Math is hard, which is why you did not pay a lot of attention that last time. Ideally, try to work your way through a few papers of the kind you are struggling with, until you understand 90% of the math. And yes, this can mean multiple days to understand just one paper. You will need practice, but it will get easier.

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    As a mathematician - I want to echo that math is hard. If I really want to understand in detail a paper in my specific area of research, I am in for 20-40 hours of reading and working to understand the paper. If you're used to spending an hour or two to understand a paper, you might be wondering what you are missing when in fact you're just used to a different concept of how much in the way of new ideas there is in a paper. Mar 26 at 18:19
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I'd echo the comment to the main question - I'd start by learning some statistiscs, and the math important to it. Everyone one has their favourite textbook, but personally I like

"Modern statistics for modern biologists" by Susan Holmes and Wolfgang Huber. Its available free online or you can buy a paper copy.

Also recommended are some online courses, such as Raffeal Izzary's EdX courses. In particular, take a look at the courses on Matrix Algebra and linear models.

Finally, if you are really committed, I recommend the Open University. You can take any number of first or second year undergraduate modules in Math or statisitcs, which is probably about the right level for someone wanting to do what you are doing. I learnt a lot of my statistics this way (I am a Bioinformatics PI and senior lecturer).

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Are you certain you aren't more interested in biostatistics than in bioinformatics? I'm just saying.

For starters that's Experimental Design, Analysis of Variance. Analysis of Covariance and Multivariate Analysis. Then there's more than that. And probably... today, Machine Learning. Biostatistics is the background a pharmaceutical statistician has to have to get drugs approved at the FDA.

A VERY GOOD read are the first two chapters of Albert Bourla's book: MOONSHOT. You'll be impressed with how much Bourla understands experimental design. Bourla might enjoy having a woke staff. But he's a hella statistician!

Read that book to get a feel of how knowledge of advanced biostatistics could result in a job in a leadership position at a pharmaceutical company.

On the other hand. You can self teach yourself all the statistics. But - since there is a lot of competition - you'll need a Masters to get in line for a dream job. As to how to teach yourself... Go to the bookstore at UCLA and peruse the shelf of biostatistics books. You might get lucky and discover the books have a "teachers edition" with answers to all the questions. Look on Ebay for that.

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I suggest you check out MIT ocw courses. Particularly check single variable and multivariable calculus. You also need probability and stats, check out Probability and Statistics 131a and 131b on youtube. Try to follow the textbook while watching the videos. I think these should give you the foundation that you need.

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