TAOG19 - Linear Algebra and Optimization

Course Code:	TAOG19
Confirmed:	Feb 06, 2025
Valid From:	Jan 19, 2026

Education Cycle:	First-cycle level
Disciplinary domain:	Natural sciences
Subject group:	Mathematics
Specialised in:	First cycle, has only upper-secondary level entry requirements

Intended Learning Outcomes (ILO)

On completion of the course the student shall:

Knowledge and understanding

display knowledge of vectors, matrices and the basic operations, defined for these objects
display knowledge of systems of linear equations, their possible solution sets, as well as how can these be formulated as matrix equations
display knowledge of what constitutes a linear programming problem

Skills and abilities

demonstrate the ability to use Gauss elimination and basic matrix algebra to solve systems of linear equations
demonstrate the ability to use vector operations and linear systems to solve geometrical problems in two or three dimensions
demonstrate the ability to calculate determinants, eigenvalues of square matrices, draw conclusions about unique solvability of square linear systems, matrix singularity and linear dependence of vectors
demonstrate the ability to formulate a real world problem as a linear programming problem
demonstrate the ability to use graphs and the Simplex algorithm to solve limited-sized linear programming problems and to draw sensitivity conclusions from the solutions
demonstrate the ability to formulate the dual of a linear programming problem and to draw conclusions from its solution
demonstrate the ability to use computer software to solve linear algebraic and optimization problems

Content

The course introduces several elements from the linear algebra as well as techniques for linear optimization.

The course includes the following elements:

Systems of simultaneous linear equations and Gauss elimination
Vectors, basic operations and some vector geometry
Matrices and matrix algebra
Eigenvectors and eigenvalues
Linear programming
Graphical solutions to two-dimensional linear programming problems
The Simplex method and sensitivity analysis
Duality in linear programming
Examples of computer software for optimization.

Type of instruction

Lectures, seminars and computer exercises.

Language of instruction is in English.

Entry requirements

General entry requirements and Physics 1, Chemistry 1, Matematics 3c or Physics A, Chemistry A, Matematics D and English 6 or English B in the Swedish upper secondary school system or international equivalent (or the equivalent).

COURSE SYLLABUS