# Chapter 13: Further reading and bibliography

### Useful books

Cann, A. J. (2013). *Maths from **s**cratch for **b**iologists*. Wiley.

A useful and reasonably comprehensive problem-based book which start with basic manipulation of numbers, algebra and works towards a basic understanding of descriptive and inferential statistics. Though there is not an emphasis on the biomedical context, this book links, when possible, mathematical concepts to biological examples.

Foster, P. C. (1998). *Easy* *ma**thematics for **b**iologists*. CRC Press.

This is another useful problem-based book which covers many of the topics included here albeit from a non-biomedical perspective, the notable exceptions being the sections related to cell biology, clinical diagnostics and descriptive statistics. The book also includes some problems to help with fractions, decimals, percentages and ratios, which is assumed understanding here.

Bowers, D. (2019). *Medical **s**tatistics from **s**cratch: An **introduction for health professionals*. Wiley.

This book does not assume any prior knowledge of statistics. It begins with a primer on variables and types of data, includes a chapter on how to interpret graphical information and builds towards the theory behind experimental design and more complex statistical analysis. An accessible book that tries to avoid jargon and complex mathematical proofs and instead teaches using current examples from the medical literature.

Triola, M., Triola, M., & Roy, J. (2017). *Biostatistics for the **biological and health sciences* (2nd edn). Pearson.

This text will help reinforce the descriptive statistics presented here as well as help you to understand probability distributions. However, the text builds on this to describe how to use statistics to analyse authentic data using interesting examples from biology, health sciences and everyday life.

Milo, R., & Phillips R. (2015). *Cell **b**iology by the **n**umbers*. Garland Science.

This book is based on an online resource, Bionumbers (see below), developed by one of the authors, and investigates cell biology through a quantitative prism. It does this in Socratic fashion by asking questions and answering them through small mathematical vignettes. Reading this will help you understand many key concepts in cell biology and give you a lot of confidence to tackle back of the envelope calculations.

La Barbera, M. (2015). *It**’**s **a**live! The **s**cience of B-**m**ovie **m**onsters*. University of Chicago Press.

A fun exploration of the scientific plausibility of movie monsters which surprisingly contains a lot of basic biology and mathematics (particularly when discussing issues of scale, e.g. giant insects!). A useful book for learning how think ‘outside the box’.

### Useful websites

#### Bionumbers

This vast, searchable database is an incredible resource that allows you to look up numbers related to biology and in particular molecular/cell biology. Every entry has a reference, often with comments about the methods used to obtain the number or notes provided by the authors. Contains numbers from the practical, such as the number of protein molecules per cell, to the esoteric such as the rate of fingernail growth, and everything in-between!

#### Cell size and scale

A visual demonstration of biological scale. This site will help you appreciate the relative sizes of various cell types and macromolecules as well as learn unit prefixes.

#### Prepare for university – Mathematical biology

From Cambridge University, a problem-based resource on quantitative biology to help prepare students starting university. A challenging and interesting set of problems which will definitely get you thinking.

#### Biomath

The Biomath page for the University of Arizona Biology Project contains a series of quantitative biology problems as well as links to some mathematics tutorials.

#### The maths of COVID-19

A collection of articles from *Plus Magazine* about the mathematics behind COVID-19. Mathematics has played an enormous role in fighting COVID-19 and the articles here are written in an accessible and informative style.

### Useful journal articles

Altman, D. G., & Bland, J. M. (2005). Standard deviations and standard errors. *British Medical Journal**, 331*, 903. https://doi.org/10.1136/bmj.331.7521.903

An excellent article explaining the difference between standard deviation and standard error and when to use them.

Ayoub F., Sato, T., & Sakuraba A. (2021). Football and COVID-19 risk: correlation is not causation. *Clinical Microbiology and Infection: the official publication of the European Society of Clinical Microbiology and Infectious Diseases*, *27*(2), 291–292. https://doi.org/10.1016/j.cmi.2020.08.034

An excellent article explaining that observational studies which demonstrate correlations are only useful for hypothesis forming and closer examination of a situation is required to establish true causation between two variables.

Bar-On, Y. M., Flamholz, A., Phillips, R., & Milo, R. (2020). SARS-CoV-2 (COVID-19) by the numbers. *eLife*, *9**, *e57309. https://doi.org/10.7554/eLife.57309

An infographic showing the key numbers from peer-reviewed literature which describe the biology of the virus and the characteristics of infection of a single human host.

Cumming, G., Fidler, F., & Vaux, D. L. (2007). Error bars in experimental biology. Journal of Cell Biology, 177(1), 7–11. https://doi.org/10.1083/jcb.200611141

A short publication explaining how to use and interpret the error bars you see in graphical data.

Sender, R., Fuchs, S, & Milo, R. (2016). Revised estimates for the number of human and bacteria cells in the body. *PLoS** Biology*, *14*(8), e1002533. https://doi.org/10.1371/journal.pbio.1002533

An excellent example of how to use the literature to make informed estimates in quantitative biology.

Swift, A., Heale, R., & Twycross, A. (2020). What are sensitivity and specificity? *Evidence-Based Nursing*, *23*(1), 2–4. http://dx.doi.org/10.1136/ebnurs-2019-103225

An explanation of how to describe the validity of diagnostic tests. It contains a detailed sample calculation for sensitivity and specificity with a helpful visual interpretation.