This page contains a review of Basic Mathematics for Biochemists by John Lydon published in Biochem. Molec. Biol. Educ. 29, 214–216 (2001)
As we all know, maths is all too often viewed by trainee biochemists with horror. something to be avoided if possible. Nevertheless, much of biochemistry is quantitative and on the whole biochemists need to get to grips with the subject. This book aims to help them, and since it has gone to a second edition, it must have found favour with at least some of them. There is a serious effort to justify each of the mathematical topics chosen in terms of its relevance to biochemistry and the book is packed with discussions and examples involving real biochemistry. The great strength of the book is its singleminded approach. As the author points out in the introduction, it is maths for biochemists, not maths for scientists in general, or even maths for biologists. It presupposes some familiarity with biochemistry and a desire to get to grips with the basic biochemical concepts.
The book begins with a useful review of the basic
concepts of mathematics, manipulation of fractions,
functions, plotting graphs etc. — the sort of things which
science undergraduates could handle as a matter of course
15 years ago, but, which I am assured, even some
mathematics students now find difficult because they have
had so little practice at school. The remainder of the book
is more or less A-level (high school) standard — sometimes a
little higher. The major topics are exponents and
logarithms, differentiation and integration, partial
differentiation, equation solving (linear, simultaneous,
quadratic and higher orders). A final chapter covers the
basic concepts of statistics. In my opinion, the author has
wisely avoided the let’s do the maths first and then
apply it to biochemistry at the end of the book
approach. We are into biochemical concepts from the start,
with discussions of the Michaelis–Menten equation and the
Henderson–Hasselbalch equations coming at an early stage.
As one might expect, most of the examples given concern the
areas where physical chemistry touches biochemistry —
diffusion, equilibrium constants, pH, redox reactions, etc.
—
but there are plenty of unexpected exceptions. There is for
example, an interesting discussion in the section on
permutations, of the number of possible alternative
sequences for the stages in glycolysis.
This is the second edition of a widely used 20 year-old book. I share the opinion of the author that the reviewer of the first edition who commented that the book was written at too basic a level, must have been living on a different planet and I am sure it was the correct decision to put in more basic, explanatory material rather than extending the difficulty of the text. My impression is that many of the additions are the result of feedback from the chalkface. They answer points of confusion actually experienced by students, even down to irritating trivia like the different conventions for decimal points or multiplication signs.
Of necessity, the book is inhomogeneous: any student who needs reminding that –(–4) = +4, is hardly likely to find the section on partial differentials very straightforward and some of the discussions rapidly get into deep water. For example, the dimensional analysis of an innocent-looking equation such as pH = –log [H+] rapidly lands us in discussions of the role of standard states in physical chemistry. However, that is the nature of the subject. It is a fact that some of the most central concepts in biochemistry involve subtle physical chemistry, and there is no way to avoid it.
In places, the book is refreshingly idiosyncratic. There
is a delightful footnote to the section Having a rough
idea of the answer, beginning, If you really want
to know whether 3000 lek would be enough to buy a house in
Albania ... ?
The comments are all sensibly pragmatic (for example,
why it is wise to write 5 l but 5 ml) and only
a real biochemist could have pointed out that if a solution
has a concentration > 5 M it can be nothing except urea,
guanidine HCl and water
. I especially like the couple of
pages of comment on modern, commercial graph-drawing
packages which make it only too easy to produce
perfectly horrible graphs exhibiting faults that no one
would have thought of 20 years ago
.
In some circles it might not be considered appropriate to use a book intended for undergraduate use as a soapbox, but is certainly refreshing to read the occasional opinionated comment (especially when it coincides with one’s own prejudices). The author clearly does not like the concept of pH. (I would imagine that years of trying to help one generation of undergraduates after another to cope with the calculations involving pH in the Henderson–Hasselbalch equation must have brought him close to despair):
For the ludicrously trivial advantage of having a range of positive numbers around +7 rather than negative numbers around –7, chemists have paid the excessive price of discarding a scale of obvious meaning in favour of one that generates endless confusion. Other usages such as pKM are less common: I trust they will remain so. We are fortunate that at least some extensions of the pH idea such as the rH scale for application to redox potentials have virtually disappeared. (p. 73)
The book ends with a glossary. In general, I like
glossaries. Short, to-the-point, stand-alone definitions
and explanations are useful things to steal for lecture
handouts and module manuals. Here the entries are mostly
clear and valuable - but occasionally one gets the feeling
that the author has run out of inspiration. I looked for
the old favourite —
a parameter is a variable constant
. It is not there
(but the definition of a constant makes up for its absence)
A constant: A number that does not change over the range of conditions being considered. Mathematically it is a number that does not change at all — but in scientific uses one cannot always be so rigid.
You know what he means — but as definitions go, it is hardly stunning in its incisiveness — and not of much relevance either, if one is being pedantic, when talking about the variation of equilibrium constant with temperature for example. Similarly the definition of a differential:
As an adjective this refers to the differential calculus, which is concerned with the limiting values of rates of change when the changes concerned are made indefinitely small. As a noun it refers to the limit of an actual change and is not the same as a derivative [see Chapter 4, section 7.2].
— does not immediately ring bells in the grey matter, although, to be fair, the references to the text did eventually help to show what point the author is trying to make.
Incidentally, this is the first book I have come across where a web site has been allocated to hold errata discovered after the book had been printed [ http://ir2lcb.cnrs-mrs.fr/~athel/basmaths.htm]. This is obviously a sensible idea which I am sure will soon become standard procedure. When I checked, there was a handful of corrections (of errors which I had not noticed). I doubt whether there will be many more; this has the feel of a carefully edited book.
To make a maths-for-biologists text appear interesting and relevant is an uphill task for any writer. How well this book succeeds depends, of course, on the criteria one adopts. This is scarcely likely to become anyone’s favourite textbook and I doubt whether it will inspire many students to desert biochemistry for mathematics. On the other hand, it is a reasonably priced, clear, earnest attempt to cover the maths essential for biochemists who want to understand their subject properly and I would consider that every part of the book will be useful at some point in most undergraduate biochemistry courses. There is Just enough of the personality of the author showing to add a personal touch, which makes the work readable. In the terms which it sets out for itself — this is a fine book. To echo the footnote about Albanian house prices — if you really want to know, here is an author who really wants to tell you.