Calculus: Idea of functions using examples from biology (Eg. Concentrations of proteins as a function of space and time. Circadian oscillations)
Differentiation. Plotting functions. Integration. Calculus of growth and decay processes. Differential equations.
Vectors, Co-ordinate systems: Scalars and vectors. Spherical polar coordinates, Cylindrical coordinates. Use of these coordinate systems (Eg. 3-dimensional configuration of proteins )
Probability and Statistics: Relevance of stochasticity in biology. Need of using statistical methods.
Mean, variance, standard deviation, Errors, fitting a function to an experimental data set — linear and non-linear fits.
Introduction to probability, Probability distributions, Moments, Binomial distribution , Normal distribution , Poisson distribution, Examples from biology. (Eg. Knudson’s two-hit hypothesis, Luria-Delbruck fluctuation test, Wright-Fisher model)
Fourier transformation and its application in biology (eg. crystallography, optics)
- Mathematics for Biological Scientists, M. Aitken, B. Broadhursts, S. Haldky, Garland Science (2009).
- Introduction to Mathematics for Life Scientists, E. Batschelet, Springer Verlag, 3rd edition (2003).
- Calculus for Life Sciences, R. De Sapio, W. H. Freeman and Co. (1976).
- Physical Biology of the Cell, R Phillips, J Kondev, J. Theriot, Garland Science (2009).
- Random Walks in Biology, H. C. Berg, Princeton university press (1993).