Course syllabus - Algebra

Objectives

Matrix algebra is a fundamental tool for handling huge amounts of data, which is usually needed when mathematics is applied in solutions of problems from the area of economics and business. Another fundamental tool used both in matrix algebra and in other areas within mathematics and science, is vector algebra. This course is devoted to basic parts of theories of vectors and matrices and economical applications of these.

Learning outcomes

At the end of the course the student is expected to be able to
- use algorithms to solve a system of linear equations.
- perform basic operations on matrices, solve a matrix equation and determine if a vector is an eigenvector to a given quadratic matrix.
- evaluate determinants and apply properties of determinants.
- apply algebraic operations on vectors and apply the properties of vectors to lines in three dimensions and planes.
- find scalar and vector products and use them in solving simple geometrical problems.
- determine whether or not a given set of vectors is linearly independent and be able to identify bases in the plane and in space.
- perform calculations with complex numbers in Cartesian and polar form, use de Moivres theorem and find the complex roots of simple algebraic equation.
- in both oral and written form explain reasoning and solutions to problems that are solved to achieve the learning outcome specified above.

Course content

Systems of linear equations, Gaussian elimination, augmented matrix, matrix operations. Matrices, matrix arithmetic, matrix equations, transposes, inverses. Vectors in 2-space and 3-space. Dot product, orthogonality, projection, lines and planes, linear dependence and independence, bases. Eigenvalues and eigenvectors. Complex numbers.

Tuition

Lectures combined with exercises. Continuous examination of problems and projects combined with written tests. Work with and presentation of written reports.

Requirements

Mathematics D or Mathematics 4.

Examination

Continuous examination and quiz (INL1), 1.5 credits, marks Pass (G) or Pass with distinction (VG)
Seminar (SEM1), 1.5 credits, marks Pass (G) or Pass with distinction (VG)
Written and/or oral examination (TEN1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass, Fail