Basic Mathematics for Biochemists
Published by Oxford University Press
paperback (ISBN 0 19 850216 8) £21.99 or $34.50.
The prices were last checked on 23rd November 2004 but may change without notice.
The hardback edition (ISBN 0 19 850217 6) is no longer available.
An order form can be obtained from the publisher in
This is a new edition of the book published under the same title by Chapman and Hall in 1981.
Two chapters (the first and the last) are completely new, and the remainder have been thoroughly
revised to make the treatment more suitable for modern students of biochemistry.
This book is available from
Chapter and Section Titles
- Basic Ideas
- Manipulating algebraic expressions
- Converting between fractions and decimals
- Relating numbers to powers of ten
- Operations that leave expressions unchanged
- Simplifying fractions
- Probability as a mathematical concept
- Permutations and combinations
- Having a rough idea of the answer
- Appendix: notes and solutions to the problems in Box 1.1
- The Language of Mathematics
- Priority rules for operators
- The summation sign
- Constants, variables and parameters
- Dimensional analysis
- Plotting graphs
- Exponents and Logarithms
- Integer powers
- Fractional exponents
- Addition and subtraction of exponents
- Common logarithms
- Negative numbers have no logarithms
- Natural logarithms
- Logarithms to base 2
- Exponential decay
- Logarithms as a method of scaling
- Products of equilibrium constants
- Logarithms of dimensioned quantities?
- Metabolic "efficiency"
- Redox potentials
- Standard states
- Dependence of redox potentials on pH
- Differential Calculus
- Coordinate geometry
- Slope of a curve
- Rapid differentiation
- Derivatives of sums and products
- Derivative of a "function of a function"
- Derivative of a ratio
- Higher derivatives
- A note on terminology
- Points of inflection
- Sketching curves
- Integral Calculus
- Increases in area
- Definite and indefinite integrals
- Simple integrals
- Other common integrals
- Integral of 1/x
- Differential equations
- Numerical integration: evaluating the area under a curve
- Solving Equations
- Linear equations in one unknown
- Rearranging equations
- Simultaneous linear equations
- Quadratic equations
- Graphical solution of equations
- Newton’s method
- Approximate methods
- Partial Differentiation
- The meaning of a partial derivative
- Exact and inexact differentials
- Least-squares fitting of the Michaelis–Menten equation
- Ideas of Statistics
- Measures of dispersion
- The idea of a population
- Continuous distributions
- Thinking statistically
- Notes and Solutions to Problems
Errors in the book as printed
p.6, expression after line 4, and equation following it:
- –6ab in the numerator should be –12ab
p. 7, first displayed expression in Section 1.3
- The third fraction in the expression should be 3/10 (instead of 3/100)
p.8, equation after line 5, and the next equation three lines down
- In the first equation, (2 – 6)/(15 – 6) – (1 – 15)/(6 – 15) should be
(2 × 6)/(15 × 6) - (1 × 15)/(6 × 15),
i.e. four out of the five minus signs in the expression should be multiplication signs. A very similar error occurs in the next equation,
where (2 – 2)/(15 – 2) – (1 – 5)/(6 – 5) should be
(2 × 2)/(15 × 2) – (1 × 5)/(6 × 5)
p. 26, answer 2
- Delete the second
this (at the beginning of the last line).
- p. 28, problem 1.3(e)
- The expression given has no rational factors; to give the solution shown on p. 201 it should be 9x2 + 12xy + 4y2.
p. 34, Box 2.3, part B
- The decimal point in 8.7 should be written above the line. This may be difficult to show correctly on the web
as not all browsers understand the code, but in principle this should be correct: 8·7
p. 37, Box 2.5: line starting with 12/2/3
- 6/32 should be 6/3=2
- p. 35, Box 2.4
- Line 3 of the right-hand column should read NOT 152 = 225. Being a negative statement the form actually given is not wrong, but there is no logical reason to give it rather than any other negative statement.
p. 49, Fig. 2.7 legend (a)
p. 56 Problem 2.1(e)
- See correction to solution (p. 202) below.
p. 67, line 6 from the bottom
- The word
No is missing from the beginning of the line. The sentence should read
No corresponding formula exists for calculating logarithms to any other base....
p. 73, line 13 of 2nd paragraph
Similarly Ka means read
Similarly pKa means (add
p. 77, line 2 of 2nd paragraph
Suppose that *gkcapdeltaG0 =
Suppose that *gkcapdeltaG01 =
(add subscript 1)
p. 77, last line of 2nd paragraph
E ln K1 = K2
E ln K1 = ln K2
p. 78, line 4
- The value of the Faraday constant is 96485 coulomb mol–1.
p. 78, first displayed equation on the page
0.77 in the middle expression. The unit written at the end of the line was intended to refer to both terms, but to be 100% clear it might be better to write "volt" after the second
0.77 as well.
p. 84, second displayed equation
- This should read *gkcapdeltaE0' = *gkcapdeltaG0'/nF
p. 87, line 1
any product read
a product or ratio
p. 87, Series of equations near the bottom of the page
- The third line should read –0.11 + 0.03pKa – 0.09pH (i.e. the second minus should be plus).
p. 88, Fig 3.2
- The equation in the upper text of the graph should read Eo =
+0.03 – 0.09pH instead of
Eo = –0.03 – 0.09pH
- p. 90, Problem 3.1(i)
- See correction to p. 203 below.
p. 93, line 16
- x = –b/a should read x = –a/b
p. 103, 4th displayed equation
- The approximately equal sign should be an ordinary = sign.
p. 115, 5th displayed equation
- This is identical to the equation above it, and should be deleted.
p. 115, last displayed equation
- Insert = before the second pKa
p. 117, 2nd line of 1st displayed equation
exp before the open curly bracket.
p. 118, Problem 4.6
- The y in
and y is a constant should have a tilde.
p. 122, Example 5.1
- The function should be y = 6x2 – 2x + 5 instead of
y = 4x2 – 2x + 5 in order to give the integral shown.
p. 124, line 5
will produce in a should read:
will produce ln a.
p. 127, first displayed equation
- The numerator of the second term on the right-hand side should be A2.
p. 127, Example 5.3 line for from the end
so P + Q read
so P = Q (replace plus by equals).
p. 134, Mechanism in the middle of the page
- The second step should be shown as reversible, with a rate constant k–2 for the reverse reaction.
p. 136, penultimate line of text
- The first (y1 + y2)h/2 should be (y0 + y1)h/2. (The second time this expression occurs in the line it is correct).
p. 137, penultimate equation
- The equation should read ch2 = (y2 - 2y1 + y0)/2
p. 138, first equation
- The expression in square brackets at the right-hand side should be
ax + (1/2)bx2 + (1/3)cx3, i.e. the fraction (1/2) should be moved to the other side of the + sign.
p. 139 Problem 5.1(e)
- The denominator of the expression to be integrated should be 2 – x (minus, not plus), to give the solution shown on p. 205.
p. 140 Problem 5.8
- The last symbol in the first displayed equation should be c not C. Three lines down, the L in g/L should not be italic.
p. 163, fourth equation (expression for [G2–])
- The coefficient 5 × 10–10 should be 2 × 10–10
p. 165, second equation
- Delete the superscript 2 at the end of the equation. Note.When this error was first reported on this web page the page number was wrongly given as p. 163. There is a different correction to be made on p. 163.
p. 167, Problem 6.2
- The symbol V1 near the end of the first line should be
p. 167, problem 6.3(a)
- See the correction to the solution on p. 207.
p. 170, first equation
- The middle expression should be R/p instead of R/Tp
p. 171, last sentence of last complete paragraph
if we recall the expression for the derivative of a ratio (Section 4.6) read
if we recall the expression for the derivative of a product (Section 4.4).
p. 185, Box 8.3, line 9
equal to ...
- The summation should be *gkcapsigmax not *gkcapsigman.
p. 193, Box 8.3 continued, table in the middle of the page
- The value of 9.64 shown in line 3 as the squared of 3.1 should be 9.91, and the sum shown below it should be 39.14.
In consequence the value of s2 shown in the first line of text after the table should be 2.807, not 2.817. However, the value s = 1.675 is correct.
p. 192, legend to Fig. 8.1, line 2
superimposed on panel (c) read
superimposed on panel (e).
p. 192, line 6 from the bottom
and a sample mean close to the population standard deviation read
and a sample standard deviation close to the population standard deviation.
p. 196, Table 8.1
- The value in the Probability corresponding to 4 in the first column should be 0.1730, not 0.0976.
This error affects all of the later entries in the Cumulative probability column, which should be 0.4115, 0.5918, 0.7468, 0.8598, 0.9312, 0.9709, 0.9905,
replacing 0.3360, 0.5163 ..., and also requires correction of the text on p. 197 (see below).
p. 197, line 2 (effect of error in Table 8.1: see above)
This means there is chance of 1 – 0.8557, i.e. 0.1443, or about 14% of observing at least nine read
This means there is a chance of 1 – 0.9312, i.e. 0.0688, or about 7% of observing at least nine.
p 192, line 13
- The end of the sentence should read
and a sample standard deviation close to the population standard deviation.
- p. 201, Problem 1.3(e)
- See correction to p. 28 above.
p. 202, Problem 2.1(e)
- The solution should be 3.617. (The solution given would be correct for summation from i = 1 to 6).
- p. 203, Solution to problem 3.1(i)
- 4 × 3 × 2 × 1 = 24 (not 120, which is 5!).
p. 205, Solution to problem 5.1(e)
- See the correction to the problem (p. 139, above).
p. 207, Solution to problem 6.3(a)
- The value of x should be 1, not –1.
p. 207, Solution to problems 6.3(e–f)
- The solution given for problem 6.3(e) is actually the solution to problem 6.3(f); the solution to problem 6.3(e) is missing. (It will be added here after checking)
p. 207, Solution to problem 6.6(c)
- The value should be 41, not 51.
p. 208, Fourth line of page (remarks following solutions to problem 6.6)
This is normal is scientific problems read
This is normal in scientific problems.
p. 208, Solution to problems 6.11-12
- The solution given for problem 6.11 is actually the solution to problem 6.12; the solution to problem 6.11 is missing. (It will be added here after checking)
p. 209, Solution to problem 8.6(c)
- 1.48/70.5 = 0.56 (not 0.60).
p. 216, the definition of point of inflection is not quite correct (though it is correct for the sort of functions normally
encountered in elementary biochemistry). Rather than stating that the second derivative is zero it would be better to say that it is
normally zero, though it may also be undefined, in certain cases beyond the scope of the book.
This list was last updated on 22nd December 2006.
If you notice any other errors, please let me know. I thank the following correspondents for drawing my attention to most of those noted:
- David M. Behrman (Somerset, Kentucky)
- Fred Boogerd (Amsterdam)
- Isadora Cornish-Bowden (Marseilles)
- Simon Harrison (Bristol)
- Y. F. Leung (Hong Kong)
- Shu-Kun Lin (Basle)
- Bernd Müller-Fembeck (Austria)