# Linear Algebra and Probability (Spring 2023)

#### Official course description:

##### Course info

##### Programme

##### Staff

##### Course semester

##### Exam

##### Abstract

This is a course in mathematics covering linear algebra and basic probability theory. This course is the first course of the Algorithms and Machine Learning specialisations.##### Description

The topics covered by this course are important in various branches of computer science, in particular in algorithms and machine learning. The topics covered in the linear algebra part of the course include systems of linear equations, matrices, determinants, vector spaces, bases, dimension, and eigenvectors. The topics covered in the probability theory part include conditional probability, Bayes theorem, discrete and continuous random variables, as well as the limit theorems. The course focuses on providing a basic understanding of the mathematical concepts covered, but will also include a few illustrative examples of their use, such as least squares analysis.

##### Formal prerequisites

The course assumes that the students have taken the course Foundation of Computing: Discrete Mathematics from the BSc in Software Development or similar.Knowledge of single variable calculus, in particular differentiation and the integral is required.

##### Intended learning outcomes

After the course, the student should be able to:

- Solve systems of linear equations
- Define the basic concepts of linear algebra and probability, e.g., eigenvalues for a matrix or variance of a discrete random variable
- Compute the essential constructions of linear algebra, such as the inverse of a given matrix or the eigenvectors of a given matrix. Compute probabilities, expected values, variances and other concepts from probability theory.
- Apply the tools of linear algebra and probability to solve small mathematical problems.
- Model simple probabilistic problems using the distributions covered in the course.

##### Learning activities

Lectures and exercises.

At the exercise sessions the students will solve and present solutions to mathematical problems. The mandatory assignments are of the form of mathematical problems, but can also involve some programming. The solutions must be submitted in written form.

##### Mandatory activities

There are 6 mandatory assignments, out of which 5 must be approved for the student to qualify for the exam. The deadlines are evenly distributed over the semester (approximately one every 2 weeks), exact dates will be posted on learnit the first week of the semester. If a mandatory assignment is not approved the first time, the student will be allowed to resubmit approximately one week after the first deadline.The pedagogical purpose of the mandatory activities is to ensure that all students practice presenting mathematical arguments in writing and that they get feedback on this. Written formative feedback will be provided by teachers and TAs.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

##### Course literature

Ron Larson: *Elementary Linear Algebra*, 8th ed, metric version

Anderson, Seppäläinen and Valkó: *Introduction to
Probability*, Cambridge University Press

##### Student Activity Budget

Estimated distribution of learning activities for the typical student- Preparation for lectures and exercises: 40%
- Lectures: 20%
- Exercises: 20%
- Assignments: 20%

##### Ordinary exam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Written and printed books and notes

Pen

E-books and/or other electronic devices

- E-books on laptops and tablets.

Notes on laptops and tablets

##### reexam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Written and printed books and notes

Pen

E-books and/or other electronic devices