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Computer Algebra for Computer Engineers

Prof. Priyank Kalla verbringt sein Forschungssemester an der Universität Bremen in der Arbeitsgruppe Rechnerarchitektur (Prof. Rolf Drechsler). Neben den inhaltlichen Aspekten bietet sich hier die Möglichkeit eine Veranstaltung nach amerikanischem Vorbild zu besuchen. Die Veranstaltung wird in englischer Sprache abgehalten.

In many applications, it is required to devise mathematical models of engineering systems, along with associated computational procedures, to reason about their design characteristics and optimization. Such systems are mostly non‐linear, and can often be modeled using polynomial algebra. Over the years, there have been significant advances in algorithmic solutions to many algebraic problems, which allow us to analyze large systems practically and automatically. This course will introduce students to selective (yet diverse) Computer Algebra techniques that find applications in Electrical and Computer Engineering. One use of these techniques is in developing and verifying embedded systems.

Focus of the Course:
In general, we model engineering systems with a set of polynomial equations. To reason about the design characteristics, we may have to solve this system of equations. However, since enumerating the solutions is often infeasible, modern computer algebra techniques reason about the solution‐sets without actually enumerating them. In the course, we will study these concepts, (namely, ideals, varieties, Gröbner bases) and their applications to engineering problems such as embedded system design. Importantly, many engineering systems operate over a finite set of inputs (e.g. finite‐precision computer arithmetic). Therefore, a good portion of the course will target polynomial decision procedures over Finite Integer Rings and Galois Fields. A few other topics from factorization, interpolation, number theory, etc. may also be covered.

Example Applications:
Applications are wide ranging in: i)logic design and verification; ii) cryptography; iii) coding and information theory; iv) contraint satisfaction; v) automated theorem proving; among many others.

Target Audience:
The course is primarily targeted towards graduate (Master, Diploma) and senior undergraduate (Bachelor) students from Electrical & Electronics Engineering, Computer Science, Systems Engineerung, and Mathematics. No prior Algebra background is required of the students.

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