**Courses in linear analysis will be brought under one thematic module**

A new project launched at the university focuses on the teaching of matrix and linear algebra as a single entity and produces content that is suitable for the needs of different academic subjects as extensively as possible.

“Despite having a common goal, teaching of the basics of linear algebra is scattered into several courses, which is not optimal from the point of view of students or learning,” University Lecturer **Janne Gröhn **from the Department of Physics and Mathematics says.

In response, the linear analysis project will implement a reform in which the whole will be viewed from a broader perspective than a single subject.

This will clarify the study of linear algebra courses, enhance university teaching and create an interesting thematic module for the market of continuous learning. Parts of the thematic module can be flexibly tailored to students of mathematics, to people involved in applied mathematics, and to professionals working with mathematical computing.

“The aim is to create a thematic module that flexibly supports different student groups who have different desired learning outcomes,” Gröhn says.

“The creation of a multidisciplinary thematic module in linear analysis is a very important project. Linear algebra plays a key role in almost every aspect of mathematics from analysis to geometry, and even to number theory. In natural sciences and technology, a concrete example of where linear algebra is needed is the modelling of natural phenomena,” Professor **Risto Korhonen **adds.

“The new project focuses on the university’s teaching of matrix and linear algebra as a single entity and produces content that is as suitable for the needs of different academic subjects as extensively as possible,” say University Lecturer **Anna Kaasinen** and University Lecturer **Päivi Ronkanen** from the Department of Applied Physics.

## For students of applied physics, mathematics is an important minor.

### Anna Kaasinen and Päivi Ronkanen

University Lecturers, Department of Applied Physics

“Matrix and linear algebra are areas of mathematics that serve as a foundation for many other courses in both mathematics and physics,” Kaasinen and Ronkanen note.

“The needs of applied physics in matrix and linear algebra are partly the same as the needs of other academic subjects, so it makes sense in terms of time and teaching resources to try to produce shared content and, where possible, to co-teach courses.”

“Students coming from different academic subjects have a very different initial level of mathematics, and the desired learning outcomes differ from one subject to another. For this reason, the needs of each subject involved in the project will be charted at first, and this information is used to determine the common sections of the thematic module.”

In addition to the common sections, each subject can plan and produce additional content that meets the specific requirements of the discipline. Built in this way, the thematic module will optimally cater to the needs of as many students as possible. For example, a software course is planned for students of applied physics alongside the broad matrix and linear algebra component. The software course will explore numerical computing using the MATLAB software.

“Thanks to new content, a large number of students in our university will have the opportunity to peek into the world of mathematics. In addition to the subject matter of the courses, students will also learn about mathematics as a discipline, and about its special features.”

“The better we know other disciplines, the more opportunities we find for collaboration in education and research alike. We can produce content that is suitable for both upper secondary school students and for courses offered as continuous learning,” Kaasinen and Ronkanen say.

## Linear algebra is the basis for many modern methods of data science, artificial intelligence and machine learning.

### Pauli Miettinen

Professor of Data Science, School of Computing

“These include neural networks and Google’s PageRank algorithm, for example,” Miettinen says.

Therefore, knowledge of the basics of linear algebra is practically a prerequisite for a good understanding of these methods and for the development of new, similar methods. It can be assumed that many future methods will also rely on linear algebra, so strong skills in linear algebra will help to understand methods to be developed in the future.

Lecturer of Statistics **Mika Hujo** adds that matrices are a key tool for many statistical methods.

“They come up all the time. Broadly used linear models and mixed linear models are presented using matrices. Estimators of ordinary least squares and generalised least squares are calculated using matrix algebra. Matrix algebra also plays an important role in multivariate methods. For example, eigen values and eigen vectors of linear maps represented by matrices are used in main component and factor analysis.”

Linear algebra is based on groups of linear equations and linear descriptions that operate between linear spaces. Linear descriptions can be presented using matrices, which makes matrix algebra a universal presentation language for linear algebra.

Funding granted by the Ministry of Education and Culture will be used to build a multidisciplinary thematic module in linear analysis, and an open online learning environment will be created for it. The selection of courses will include studies in mathematics, physics, applied physics, statistics and data science. The project is coordinated by the Department of Physics and Mathematics in Joensuu.