Faglig innhold

Many fields within the Biological 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 biologists to basic concepts in Linear Algebra 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 knowledge of Linear Algebra is required, as we will start from the basics, namely: sets, vectors and matrices. We will then introduce the concepts of vector spaces and subspaces, while also covering linear combinations, bases, coordinates and dimensions. We will finish by discussing linear transformations, change of basis and eigendecomposition. We will integrate the acquired knowledge by introducing and discussing the technique of Principal Component Analysis.

Læringsutbytte

After completing the course the student will:

1. Have been exposed to basic constructive mathematical reasoning, including a very limited exposure to mathematical proofs.
2. Have a familiarity with fundamental and ubiquitous concepts from Linear Algebra including, but not limited to, the notion of a basis, coordinates and the dimension of a vector space, and an understanding of the concept of linear transformations, as well as eigenvalues and eigenvectors of a matrix.
3. Be able to use this newfound knowledge to better understand the foundations of many analysis techniques widely employed in the Biological Sciences, such as Principal Component Analysis.

Læringsformer og aktiviteter

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.

Obligatoriske aktiviteter

• Oppgaver

Mer om vurdering

The evaluation of the course will consist on a digital home exam, which will contain exercises similar to the ones discussed during the course. Additionally, students will be required to submit 4 short assignments throughout the course, which they will need to pass in order to be allowed to take the exam.

Spesielle vilkår

Forkunnskapskrav

Admission requirements: The student must be either enrolled in a PhD programme, be a Medical student, be enrolled in the Student Research Programme or be enrolled in a MSc programme at NTNU. Candidates enrolled in the Master in Neuroscience programme at NTNU have to be assessed individually by the course coordinator.

Kursmateriell

To be announced