Linear Algebra

Linear algebra is an important field of study in mathematics. It has a wide range of applications in many fields, such as analysis, probability or differential equations. However, the study fields of chemistry, biology, economy, finance and engineering can also be added to the list. Among its numerous modern applications are, for example, Google’s PageRank method and the global positioning system (GPS). Due to its versatility, linear algebra is one of the most widely taught subjects in college-level mathematics. Once you have learnt it, you will see it everywhere. This introductory course would cover the following topics: the notion of linearity (and its necessity if it comes to more complicated problems), systems of linear equations (now, in more than three variables), row-reduction and echelon forms, matrix operations (step towards the abstraction of numbers), including inverses; special matrices, how they emerge; vector spaces, linear dependence and independence; subspaces, bases and dimension; characteristic polynomials and determinants, linear transformations and eigensystems.