I am a mathematics teacher currently teaching at highschool level. I have taught at college level and I do have some preparation about topics such as differential equations and multiple integrals. Recently, I have been offered to teach a preparation course of "Mathematics applied to biochemistry" at a research center, to prepare some graduate students for their studies in a masters program. Since the course is a bit brief (5 weeks) I would like some recommendations about what the key mathematical topics in this matter, I do not wish to make it extremely abstract.

Hopefully, someone here has had a similar experience before and can recommend a great book to get myself into some of the most relevant concepts that are used in biochemistry, and to what extent should I teach them.

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    $\begingroup$ Don't the biochemists at the research center have quite explicit expectations regarding what you shoul teach in this course? $\endgroup$ Commented Apr 4 at 19:05
  • $\begingroup$ They kind of do. They gave me a "list" which basically included: vector calculus, ODE and descriptive statistics (hypothesis testing, ANOVA test tables) and probability. However, I sort of want to design a more "grounded" course, something that can be useful rather than just a mandatory course. $\endgroup$ Commented Apr 5 at 19:59

2 Answers 2


[Edit: if there is some moderator-approved way to cross post this to Biology Stack Exchange and/or Chemistry Stack Exchange, you might get some good additional feedback.]

It is a great question. I don't have a perfect answer, but let me give it a shot.

  1. Googling math textbook for biochemistry gives almost nothing. However, if you Google math textbook (or refresher math textbook) for biology or math textbook for chemistry, you will get a lot of choices. [I looked at each list.]

  2. This is the one I liked the best:


Click the "read sample" link on the upper left under the cover photo. Then, look at the table of contents.

Within that stuff, my advice for coverage is:

A. Skip chapters 1 (Math in Biology) and 2 (Arithmetic). Too easy. They have it as a reference.

B. DO chapters 3 (Unit conversions) and 4 (Solution dilution). These are also somewhat easy and are definitely things they've had. But this is getting them math-ing again. And is stuff from freshman chemistry that some may have forgotten or been weak on (especially those coming from biology, not from chemistry). And it's absolutely relevant and honestly is about 90% of the math they will need in future courses or even careers.

C. Skip 5 (Solid mensuration). Very unrelated to 99% of their future courses, or lab work.

D. Do Chapter 6 (logs and exponentials). Should be a refresher for all. But very relevant to fermenter growth in biotechnology or drug decay or the like.

[I wish there was just a little bit more on kinetics. NOT a hardcore chem graduate course that is heavy P-chem. But the chapter in an AP chem book that discusses two factor rate problems (which end up being quadratic equations). This is essentially what most enzyme kinetics is (substrate and reactant concentrations are the two variables, giving rise to a second order polynomial). But it's fine that it's missing. Do 80% well...not 95% poorly. And they did see this in freshman chem once.]

E. Do 7 and 8 (descriptive statistics and CIs). Your course is going to end up having a stats theme. Which is WAY better than a calculus theme! These are not engineers. Even Ph.D. students in the biological sciences at R1 unis are (in general, in general) math averse. Any thesis they do (if they do) will need at least CIs and p values. And the entire bio/pharma field is very stats suffused (despite not being very good at it), given the requirements for getting FDA New Drug Applications done.

F. Skip 9 (Probability) and 10 (Chi scores, t scores, ANOVA, etc.) The first is too foundational, but not really used in their work. The latter is nice, but a bit hard...and honest this part of a stats course always becomes a blizzard of formulas. Plus you don't have time.

G. Do chapter 11 (correlation and regression). They see this all the time in even the simplest publications, courses, etc. Heck, the world is becoming so Excel permeated that I see secretaries needing to make Rsq lines on scatter charts! I suspect the approach will not be theoretical (too hard), but descriptive and practical/practicing. Double-check that it doesn't need stuff from 9 or 10, but I doubt it based on the subheading names.

H. Maybe the one other thing that is slightly missing, would be a little unit on point groups (NOT theoretical, but descriptive...and even easier than the group theory that inorganic chemists do). "This molecule has a C2 axis. That one doesn't". That sort of thing. But again...I'd rather you have a theme, use a book, and get a victory than wedge too much stuff in. And the book doesn't have it.

Some general thoughts:

Avoid any books or having a course that is a calculus refresher or that covers ODEs. Most biologists have two semesters of calculus. Most chemists have three. ODEs are not commonly required, for them. And...they don't need it for an M.S. (or even a Ph.D.) Sure...there are people doing super hard research at R1 unis in computational protein folding. But they come from a physics or applied math or theoretical chem slant.

Your kids just need to get an M.S. so they can make a little more money...by supervising the tech on the Illumina sequencer, instead of being the tech. Or even being that tech instead of being the tech doing titrations. Whatever calculus they had...they probably don't need in the future (whether they learned it or not). Heck, most organic chemists just need to count to 4. It is a descriptive and spatial field.

And...no, absolutely NO predator/prey despite it being biological (albeit not biochemical). Yes...it's a pretty problem and "cool". But too hard. And not related to antibody protein folding. No ODEs. No systems of ODEs.

No linear algebra (you almost NEVER need a matrix in the real world or in their sort of courses...I didn't even see it in much more technical slanted chemistry and engineering). Yes...I know the mathies love it. But...NO. Let it be used by people doing theoretical stats. You don't need it for daily work in the life sciences (or even in practical biochem process engineering).

You don't need any vector calculus either. Sure the NMR has all kinds of complicated physics...but in practice, chemical intuitions (which hydrogens are equivalent) are what you use solving spectra and labeling peaks ("doublet of triplets" and all that). You don't need to know the magic angle or how the magnetic moments gyrate...just treat it as a black box.

I would not bother reviewing trigonometry (too basic AND rarely needed) either. They probably could use a refresher on the quadratic equation, but it isn't in the book. And, meh, just skip it. They are supposed to know it and can look it up if needed. They probably aren't great at algebra, given they went in this (descriptive, spatial) science slant instead of in the chem engineering track. So...just don't struggle changing that.

All in all...I would emphasize ease, positivity, and a good experience, with great student feedback forms about how they loved Mr./Ms. NotaMathematician...and how the summer was great bonding with the other students. High sugar to medicine ratio!

P.s. I don't have an M.S. in biochem, but have a BS/MS/Ph.D. in chemistry and have taken an upper undergrad course in biochemistry (enzyme/protein emphasis) AND one in molecular biology (nucleic acid emphasis). And worked for decades in/around pharma and biotech. I sorta know these people. [Also, I DID look at the required course list for the MS Biochem at Michigan and at Georgetown, what came up Googling...and I thought about what math would be needed based on the course title...which was generally close to zero!]

  • $\begingroup$ Admittedly I "only" have a chemistry BS, and "only" took biochemistry as an undergraduate, but including some basic calc ODEs for a graduate degree seems perfectly reasonable considering ODE-based kinetics are definitely a thing in biochem (I'm thinking michaelis-menten kinetics, for example). I also disagree with throwing out linear algebra entirely, but agree that it is probably the least important. $\endgroup$
    – Opal E
    Commented Apr 4 at 19:23
  • $\begingroup$ I love ODEs and went to a "trade school" where even the English majors had to take it. But...I just don't see the need in molecular biology. Look at the courses here: medschool.umich.edu/departments/biological-chemistry/education/… and here: msbiochemistry.georgetown.edu/curriculum/courses Maybe the only one that would use it would be Enzyme Kinetics at UM. And I bet that doesn't use it much (I took a grad level chem course in general reaction kinetics and it was P-chem on steroids)...but that ain't what these kids will do. $\endgroup$ Commented Apr 4 at 19:35
  • $\begingroup$ Many kids won't have even had a regular p-chem class. See here: reddit.com/r/chemistry/comments/16c643v/… $\endgroup$ Commented Apr 4 at 19:36
  • $\begingroup$ Thank you so much for sharing your experiencie in this subject. This surely gives me a lot of information on what are some of the "big topics" on biochemistry mathematics! $\endgroup$ Commented Apr 5 at 20:10
  • "Mathematical Methods in the Physical Sciences" by Mary L. Boas
  • "Biocalculus: Calculus, Probability, and Statistics for the Life Sciences" by James Stewart and Troy Day
  • "Mathematics for the Life Sciences" by Erin N. Bodine, Suzanne Lenhart, and Louis J. Gross
  • "Mathematical Models in Biology" by Leah Edelstein-Keshet
  • "An Introduction to Systems Biology: Design Principles of Biological Circuits" by Uri Alon

Hope this helps


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