This course introduces necessary background and fundamental mathematics for graduate biologists. The course emphasizes relevant topics in calculus, probability, and numerical methods with their applications in biology.
Survey of basic mathematics for application to life/environmental sciences.
- History of mathematics and relation to natural sciences.
- Geometry: Distance, Euclidean and other spaces.
- Geometry: Vectors, dot and cross products.
- Geometry: Computation of angles and distance from a point to a line segment and a plane.
- Geometry: Volume of a tetrahedron. Application to concept of rank.
- Probability: Concepts (frequentist and Bayesian), independence, conditional probability, Bayes’ Theorem.
- Probability: Random walk, Bernoulli processes, Stirling’s formula, normal distribution.
- Probability: Nearest-neighbour distance distribution for randomly distributed points in a plane.
- Calculus: Concepts of limit and slope. Application to biology.
- Calculus: Taylor expansions. Exponential decay.
- Calculus: Harmonic oscillator. Diffusion.
- Numerical Methods: Roots of a quadratic polynomial.
- Numerical Methods: Least squares curve fitting. Bisection.
- Numerical Methods: Approximation of functions by polynomials.
- Student presentations.
Weekly written exercises, Student presentation in final week.