id: 06151580
dt: b
an: 2015b.00905
au: Ledder, Glenn
ti: Mathematics for the life sciences. Calculus, modeling, probability, and
dynamical systems.
so: Springer Undergraduate Texts in Mathematics and Technology. New York, NY:
Springer (ISBN 978-1-4614-7275-9/hbk; 978-1-4614-7276-6/ebook). xx,
431~p. (2013).
py: 2013
pu: New York, NY: Springer
la: EN
cc: M65 I95
ut: life sciences; calculus; mathematical modeling; probability; discrete
dynamical systems; continuous dynamical systems
ci:
li: doi:10.1007/978-1-4614-7276-6
ab: There are several good reasons for the reviewer to warmly recommend this
text. First of all, because of the author’s idea that “the basic
premise of this book is that there is a lot of mathematics that is
useful in some life science context and can be understood by people
with a limited background in calculus, provided it is presented at an
appropriate level and connected to life science ideas." Secondly,
because we all agree that there is a need to close the gap between
several outstanding texts in mathematical biology at the advanced and
beginning graduate level and the knowledge of mathematics most biology
students have ‒ the book has been designed with this intention in
mind. Thirdly, because reducing the prerequisites for a reader to a
bare minimum of the first calculus course, Professor Ledder skillfully
blends mathematical ideas and biological context in applications and
presents material at the level of rigor appropriate for biology
students. “It is my aim to provide a balanced approach to
mathematical precision. Conclusions should be backed by solid evidence
and methods should be supported by an understanding of why they work,
but that evidence and methods need not have the rigor of a mathematical
proof." Arguing about technology that might be used for teaching, the
author motivates his choice as follows. “Rather than trying to find
the very best tool for each individual task, my preference is to work
with one tool that is reasonably good for any task (save symbolic
computation) and is readily available. By these criteria, my choice is
R, which runs smoothly in any standard operating system and is popular
among biologists." A collection of R scripts for various algorithms
presented in the text is available at the publisher’s link. Professor
Ledder emphasizes that “these scripts are designed to be simple
rather than robust; that is, compared to professionally written
programs, they are easier to understand but less efficient and they
lack error detection machinery. Their presence allows students to
replace the difficulty of having to learn R from scratch with the much
lesser difficulty of having to be able to read an R program and make
minor modifications." The material in the book is organized into three
parts, the last two could easily have been reversed. Two chapters in
the preparatory Part I provide a brief summary of calculus with a
special attention only to “those aspects of calculus that provide the
necessary background for the modeling, probability, and dynamical
systems that make up the rest of the book" and a chapter on
mathematical modeling featuring the role mathematics plays in biology,
basic concepts of modeling, and a wealth of material on empirical and
mechanistic modeling. Chapters 3 and 4 constitute Part II of the book
where the fundamental ideas and some applications of probability are
discussed. The distinctive feature of this part is best explained by
the author himself. “My colleagues in biology helped me appreciate
that the central topic of probability for scientists is that of
probability distribution, and this topic is best approached informally
by thinking of a probability distribution as a mathematical model of a
data set. My aim has been to get to probability distributions as
quickly as possible while saving other topics, such as conditional
probability, for later." The final three chapters in Part III introduce
the basic ideas of the theory of dynamical systems, starting with the
dynamics of a single species which is used to demonstrate main
techniques of mathematical analysis (cobweb analysis, phase line
analysis, linearized stability). Then the exposition proceeds to the
study of multivariable discrete systems and concludes with the
discussion of multivariable continuous dynamical systems. Additional
topics in discrete dynamical systems are addressed in Appendix A,
whereas brief information on the definite integral via Riemann sums and
a Runge-Kutta method of solution for differential equations can be
found in Appendices B and C. The exposition is very clear and detailed
with a large number of carefully selected examples and exercises based
on the material familiar to biologists. An excellent choice for the
lecturer interested in designing a 2-course sequence of 4-credit
courses covering almost the entire book, a 2-course sequence of
3-credit calculus-for-biology courses for students with no calculus
background, or a 3-credit calculus-for-biology course with selected
material.
rv: Svitlana P. Rogovchenko (Kristiansand)