MATA32 Algebra and Vector Geometry, 7.5 credits, is a compulsory course for a Bachelor of Science degree in mathematics and physics. The course can be taken as a stand-alone course. The course is given at half-study pace during the first half of each semester. The course is given in English during the autumn semester and in Swedish during the spring semester.

Course Content

The course treats:

Elementary logic and set theory
Basic properties of the natural numbers and the integers: induction, divisibility, Euclid’s algorithm
Basic properties of polynomials: divisibility, Euclid’s algorithm
Complex numbers
Linear systems of equations, Gaussian elimination
Vectors in two and three dimensions, bases and coordinates, linear dependence, equations of lines and planes
Scalar product, calculation of distances and angles
Vector and volume product, calculation of area and volume
Matrices, determinants, matrix invertibility.

In addition, material on the axiomatic structure of the real numbers as well as the binomial theorem is treated during lectures taught jointly with the course Analysis in One Variable.

Teaching
The teaching consists of lectures, seminars, exercise classes and mentoring hours. An essential element of the seminars and exercise classes is training in problem solving and oral mathematical communication.

Group assignments and an individual task are included in the course requirements. The group assignments concern problem solving and applications of theoretical aspects. The individual task aims at providing the students with training in popular scientific communication.

Assessment and Grades
The examination consists of

assignments during the course, 1.5 credits (grading scale: Fail/Pass)
written examination at the end of the course, 6 credits (grading scale: Fail/Pass/Pass with Distinction)

For a Pass grade on the whole course, the student must have Pass grades in the assignments and in the written examination.
The final grade is determined by the grade in the written examination.

Course Literature

Kjell Elfström: An Introduction to Algebra, 2023 (distributed by the department)
Kjell Elfström: An Introduction to Linear Algebra, 2023 (distributed by the department)
Karl Gustav Andersson: Lineär Algebra, 2:a upplagan, Studentlitteratur, 2000ISBN: 9789144016085 (bredvidläsning, på svenska/complementary reading, in Swedish)
Kerstin Ekstig, Anders Vretblad: Algebra och geometri, 2:a upplagan, Gleerups förlag, 2006, ISBN: 9789140647573 (bredvidläsning, på svenska/complementary reading, in Swedish)

Official Course Description

Syllabus in English
Kursplan på svenska

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science