Course content

Many fields within the Biological Sciences 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.

Learning outcome

Knowledge

After completing the course the student will possess knowledge of:

• Fundamental concepts in Linear Algebra, including vector spaces, bases, dimension, linear transformations, eigenvalues and eigenvectors
• The most important theorems and results in linear algebra.
• Principal Component Analysis, with a detailed understanding of its components and inner workings.

Skills

After completing the course the student will be able to:

• Carry out simple mathematical proofs and follow along with more complex ones.
• Utilize mathematical notation and language to express their ideas more precisely.
• Perform a number of calculations related to the topics of the course, such as calculating the dimension of a vector space or subspace, the inner product between vectors with an arbitrary definition of this operation, calculate eigenvalues and eigenvectors, perform a change of basis, calculate Principal Component Analysis on a dataset and more.

Competence

With this course the student will develop basic competence in:

• Understanding many of the basic elements employed in analysis techniques in the Biological Sciences, such as Principal Component Analysis, and being able to better interpret the results obtained with those methods, potentially recognizing their limits and how to go beyond them.
• Applying mathematical reasoning and logic to better judge the validity of an argument.
• Using the knowledge gained in this course to be able to approach more complex topics.

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

• Exercises

Further on evaluation

The evaluation of the course will consist on a written 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.

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

Required previous knowledge

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.

Course materials

To be announced