Mathematics for Biology

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

- matrix calculus, linear algebra

- qualitative theory of differential equations 

- solutions to differential equations in simple cases

- using mathematics to understand living organisms

Biomathematics Level 1