Course content

Many fields within the Life Science are becoming increasingly quantitative and interdisciplinary. This poses the double challenge of having a good understanding of the biological aspects of the problem under study, as well as of the mathematics used to analyze the acquired data and to develop models for it. The goal of this course is to introduce PhD students in the Life Sciences to concepts in Calculus and Probability Theory that they will encounter in most of the analysis techniques and models they will employ in their research. The course will smoothly introduce the language of mathematics, with the aim of easing interdisciplinary communication. No previous mathematical knowledge is required, as we will start from the basics, namely: sets and functions. We will then introduce the concepts of limits and continuity of a function and build up from there to the concept of derivatives. We will see how to apply derivatives to solve optimization problems and to perform linear and higher order approximations of a function. We will then introduce the notion of (Riemann) integrals and connect them with the idea of derivatives via the Fundamental Theorem of Calculus. We will comment on how to extend these concepts to multivariate calculus, introducing the idea of gradients, and also on the application to differential equations. Finally, we will provide a short introduction to Probability Theory from the Bayesian perspective.

Learning outcome

After completing the course the student will:

• Have been exposed to basic constructive mathematical reasoning, including a very limited exposure to mathematical proofs.
• Have a familiarity with fundamental and ubiquitous concepts from Calculus including, but not limited to, the notion of functions, limits, continuity, derivatives and integrals.
• Have a basic understanding of how these concepts are applied to the resolution of problems involving minimization or maximization of a function and to the resolution of differential equations.
• Have a familiarity with basic ideas and concepts from Probability Theory.
• Be able to use this newfound knowledge to better understand the foundations of many analysis techniques widely employed in the Life Sciences.

Learning methods and activities

Each class will be divided into a lecture and a practical session. The practical sessions will consist on solving exercises in order to assimilate the concepts introduced during the lectures. We will use the practical sessions to monitor the progress that the students make with the exercises. At the end of the course, and right before the exam, there will be a recap reserved for further discussion.

Compulsory assignments

• Assignments

Further on evaluation

The evaluation of the course will be a written exam, which will contain exercises similar to the ones discussed during the course. The evaluation will be graded with pass/fail.

The students will be required to hand in 4 written assignments. The assignments will be evaluated as approved/not approved.

Compulsory activities from previous semester may be approved by the department.

Recommended previous knowledge

Having passed "Math for Biologists I: Linear Algebra" (NEVR8012) is beneficial but not mandatory for taking this course.

No background in Mathematics is assumed.

Required previous knowledge

The course is meant for PhD students working in the Life Sciences.

Course materials

To be announced