**S****yllabus**

**The course deals with systems of linear differential equations, stability theory, basic control theory, some selected aspects of dynamic programming, optimal linear quadratic control or Kalman filter. The theory of the course is useful in applications in various areas such as physics, biology (life science) and econonomy, in addition to engineering applications. Control theoretic approach has played powerful role in analysis and synthesis in complicated biochemical networks and very recently in Machine learning algorithms analysis and design.**** **

**Textbook and other material**

E. Sontag, Mathematical Control Theory, Deterministic finite dimensional systems, 2nd edition, Springer. (S)

**Please note that self-enrollment on the course page is not the same as course registration in Ladok.**

- Teacher: Salvador Rodriguez Lopez
- Teacher: Yishao Zhou

The course covers modern methods of cryptography,
which form a basis for secure electronic communication, and methods to
decrypt these. The focus is on the mathematical foundations in number
theory, algebraic geometry and statistics and how these are used in cryptography.
The course is of interest to those who work with security aspects of
electronic communication, but also for those who want to see one of the
more spectacular modern applications of mathematics.

Schedule

**Please note that self-enrollment on the course page is not the same as course registration in Ladok.**

- Teacher: Sjoerd Wijnand de Vries
- Teacher: Tuomas Tajakka

The course provides an introduction to type theory with simple and dependent types, how it can be used to represent logical systems and proofs, and how proofs give rise to computable functions. The final part of the course covers applications of type theory. The following topics are covered:

Type theory: lambda calculus, contexts, forms of judgement, simple types, inductive types. Operational semantics: confluence and normalization. The Curry-Howard isomorphism. Martin-Löf type theory: dependent types, induction and elimination rules, identity types, universes. The Brouwer-Heyting-Kolmogorov interpretation of logic. Meaning explanations. Semantics of dependent types. Explicit substitution. Category theoretical models. One or more of the following areas of application of type theory are covered: homotopy theory, models for (constructive) set theory and proof assistants.

###### Course Literature

Per Martin-Löf: Intuitionistic Type Theory. Bibliopolis

**Please note that self-enrollment on the course page is not the same as course registration in Ladok.**

- Teacher: Peter LeFanu Lumsdaine

**Syllabus**

In the course Advanced real analysis II a deeper treatment of functional analysis, measure theory, and

integration theory is carried out.

The course covers: Complex measures, the Radon–Nikodym theorem, dual spaces, weak topologies, adjoint

operators, operators on Hilbert spaces, spectral theory for compact operators and bounded operators in Hilbert

spaces.

**Please note that self-enrollment on the course page is not the same as course registration in Ladok.**

- Teacher: Kristian Bjerklöv
- Teacher: Christian Emmel
- Teacher: Annemarie Luger