Mathematics for Biology

This course provides a concise overview of the concepts necessary for mathematical modeling in biology. The focus is on linear and nonlinear dynamical systems in one and two dimensions. The course begins with essential concepts in linear algebra: matrices, systems of linear equations, and the geometric interpretation of the solutions to these systems as vectors and subspaces (lines, planes, etc.). The theory of vectors and eigenvalues of matrices is introduced in relation to linear dynamical systems. For nonlinear dynamical systems, the qualitative theory of differential equations (attractors, phase portraits, zero-level isoclines) is presented as an alternative to the often complicated calculation of solutions. The tutorial covers a wide range of biological models used in ecology, epidemiology, oncology, and systems biology.

- matrix algebra, linear algebra

- Qualitative theory of differential equations 

- Solutions to differential equations in simple cases

- using mathematics to understand living organisms

Biomathematics, First-Year Level