B03
Mathematics I
Course Coordinator: 
Robert Sinclair
Description: 

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.

Aim: 
Survey of basic mathematics for application to life/environmental sciences.
Detailed Syllabus: 
  1. History of mathematics and relation to natural sciences.
  2. Geometry: Distance, Euclidean and other spaces.
  3. Geometry: Vectors, dot and cross products.
  4. Geometry: Computation of angles and distance from a point to a line segment and a plane.
  5. Geometry: Volume of a tetrahedron. Application to concept of rank.
  6. Probability: Concepts (frequentist and Bayesian), independence, conditional probability, Bayes’ Theorem.
  7. Probability: Random walk, Bernoulli processes, Stirling’s formula, normal distribution.
  8. Probability: Nearest-neighbour distance distribution for randomly distributed points in a plane.
  9. Calculus: Concepts of limit and slope. Application to biology.
  10. Calculus: Taylor expansions. Exponential decay.
  11. Calculus: Harmonic oscillator. Diffusion.
  12. Numerical Methods: Roots of a quadratic polynomial.
  13. Numerical Methods: Least squares curve fitting. Bisection.
  14. Numerical Methods: Approximation of functions by polynomials.
  15. Student presentations.
Course Type: 
Elective
Credits: 
2
Assessment: 
Weekly written exercises, Student presentation in final week.