Mathematics: Algebra and Vector Geometry

The course addresses concepts in basic algebra in a more rigorous way and provides an introduction to linear algebra through vector geometry in two and three dimensions. The algebra section covers logic and set theory, number theory, divisibility and Euclid’s algorithm, mathematical induction, as well as complex numbers, the binomial theorem, polynomials, and algebraic equations. You will also be introduced to the axiomatic structure of the real numbers, in connection with the course Analysis in One Variable.

In vector geometry, you will learn how vectors are used to introduce bases and coordinate systems in space, as well as to describe equations for lines and planes. You will also learn to use important tools such as the scalar product, vector product, and volume product, and to perform calculations involving distances, angles, areas, and volume. The course also covers systems of linear equations, matrices, and determinants, giving you tools for further studies in linear algebra.

Throughout the course, you will develop your ability to recognise connections, formulate mathematical reasoning, and work with abstract concepts to understand and solve problems. The course is compulsory within certain specialisations of the Bachelor’s programme in Science and can also be taken as an elective or standalone course.

Course syllabus

The syllabus contains the formal and legal details of the entire course. It’s a legal document outlining the course structure and requirements, intended mainly for administrative use.

Course literature

The course literature listed may be updated up to eight weeks before the course begins.

Teaching consists of lectures, seminars, problem-solving sessions, and mentor meetings. You will solve mathematical problems both independently and together with others, and practice formulating and explaining mathematical reasoning orally and in writing. The course includes both group assignments and an individual assignment where you will practice communicating mathematics in a popular-science style.

The teaching aims to provide you with tools to work with mathematics in a structured and analytical way, and to develop your problem-solving ability using mathematical methods. Assessment consists of assignments submitted during the course (1.5 credits) and a written exam at the end of the course (6 credits). If you have a permanent disability, support and alternative examination options are available.

The course is a first step toward further studies in mathematics, physics, and other natural sciences. By working with abstract concepts and mathematical structures, you will train your analytical skills, learn to solve complex problems, and communicate clearly and precisely. The ability to think logically, structure information, and work methodically is valuable in many professional roles, whether you choose to specialise in mathematics or broaden your expertise into other fields.

Entry requirements

General requirements and studies equivalent to Swedish Upper Secondary School course Mathematics 4 (or older course Mathematics D)/Mathematics further level 2

Selection criteria

Seats are allocated according to the following: The general average (GPA) of your higher secondary school leaving certificate: 34 %, The Swedish national university aptitude test: 34 %, number of previous ECTS at application deadline (up to 165): 32 %. If students have equal credentials, seats are allocated based on their results on The Swedish National University Aptitude Test. If this too is equal, seats are allocated based on a draw.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.