Mathematics for biologists
Lecturers and Teaching Assistants
Dr. Josephine Shamash
Course Schedule and Location
Sunday, 09:15 - 11:00
Wednesday, 13:15 - 14:00
Field of Study, Course Type and Credit Points
Life Sciences: Lecture; Elective; Regular; 3.00 points
Life Sciences (Molecular and Cellular Neuroscience Track): Lecture; Elective; Regular; 3.00 points
Life Sciences (Brain Sciences: Systems, Computational and Cognitive Neuroscience Track): Lecture; Elective; Regular; 3.00 points
Life Sciences (Computational and Systems Biology Track): Lecture; Elective; Regular; 3.00 points
All courses in the first semester will be held on-line via zoom.
Attendance and participation
Scheduled date 1
Scheduled date 2
Estimated Weekly Independent Workload (in hours)
The course will introduce students who come from a non-mathematical background to basic mathematical tools that are essential for much of today's biological research: differential equations, linear algebra and linear systems theory, and a brief introduction to Fourier analysis. The intention is to provide a firm mathematical background for applications to be covered in advanced courses in Systems Biology and in Theoretical Neuroscience.
Topics to be covered:
- Introduction to differential equations.
- First-order ordinary differential equations: linear equations, separable equations, modeling with first-order equations, equilibrium solutions. Examples of applications include: RC circuits and current-integration by neurons.
- Introduction to linear algebra: Matrix and vector operations.
- Systems of linear equations.
- Linear transformations.
- Matrix diagonalization. Systems of linear differential equations, Relation of matrix diagonalization to solutions of systems of differential equations. Examples of applications include: predator-prey interactions.
- Inner product spaces.
- Orthogonal and orthonormal bases.
- Introduction to Fourier analysis. The concepts of spectrum and filtering.
Upon successful completion of the course students will be able to:
- Recognize the role of mathematics in various scientific fields.
- Integrate knowledge from diverse fields such as calculus, linear algebra, differential equations to formulate and analyze models that arise in biology , in particular, population dynamics and predator-prey interactions and chemistry.
- Calculate Fourier series, and use the tools of Fourier analysis for application in advanced course such as spectral analysis and signal processing
- Linear Algebra and its Applications, Strang G. (Harcourt Brace Jovanovich, 1988).
- Introduction to Applied Mathematics, Strang G. (Wellseley-Cambridge, 1986).
- Linear Algebra and Differential Equations with MATLAB, Golubitski M. & Dellnitz M (Brooks/Cole Publishing Company, 1998).
- Elementary differential equations and Boundary value problems, Boyce and diPrima, 7th edition.