Linear Algebra 1

Cursus

Omschrijving

Systems of linear equations, matrices and vector spaces are the core topics in this course. Systems of linear equations and matrix arithmetic can be seen as the computational vehicles for working in vector spaces, but are also interesting in themselves and used everywhere in science. Vector spaces are a convenient way of mathematically modelling and working with space (and to generalize!) and elementary vector space theory mostly focuses on linear aspects. Vector spaces consist of vectors (just think of arrows with a certain direction and a certain length, arrows that can be added and multiplied by scalars - that's the algebra!) and provide a way to define and work with notions like distance, angle, dimension, linear objects, maps between linear objects. We introduce vector spaces in an abstract setting so that the corresponding theory can be applied and used in various settings, for instance in other (mathematics) courses ranging from vector analysis to probability theory to optimization to machine learning. Linear algebra is indispensable for all branches of mathematics, and also for many of the engineering sciences. It is also the starting point for studying more advanced non-linear objects and more advanced computational techniques (in other courses). Since this course is primarily aimed at mathematics students, we specifically pay attention to the way linear algebra is mathematically structured, and that includes attention for precise mathematical statements and proofs. It is advised to take both Linear Algebra 1 and Linear Algebra 2 (focussing more on linear maps between vector spaces like reflections and rotations), since together they cover the standard topics in linear algebra. In Linear Algebra 1 we also discuss how complex numbers, next to vector methods, can be used in planar geometry.
Cursusperiode 1/09/23 → … Introductie Cursus