MFoCS Mathematical Foundations of Computer Science Tom Heskes and Jasper Derikx

MFoCS organisation & goals MFoCS is a joint Computer Science – Mathematics specialisation It can be followed as a CS master and also as a Math master Goal: educate students in The mathematical theories that underly computer science The computer science techniques to study and solve mathematical problems. Required: –Bachelor in computer science with a strong mathematical background and theoretical interests. –Mathematical maturity is essential –Basic knowledge of logic and discrete mathematics

Scientific Questions On the shoulders of giants: Turing, Dijkstra, Brouwer, Scott, McCarthy,... What is algorithmically decidable? o What is “hard”, what is “easy”? o In theory? In practice? How to build correct software? o Which level of certainty can we reach? o How can we use computer support to verify computer systems? What are the new programming and computing paradigms? o Quantum computing? o New generation programming languages? How can we bring mathematics and CS closer together? o Mathematical proof = algorithm? o Algorithmic view of mathematics (representation, data, functions)

Researchers Herman Geuvers, Freek Wiedijk -- type theory, proof assistants, semantics Alexandra Silva, Jan Rutten – formal languages and automata, coalgebra Bart Jacobs -- categorical methods, quantum computing Frits Vaandrager, Jan Tretmans -- I/O automata and testing theory

Researchers Hans Zantema -- term rewriting and automated reasoning Bas Terwijn -- mathematical logic and complexity Bernd Souvignier -- computable algebra and group theory Wieb Bosma -- computer algebra and number theory

Structure Specialisation basis (mandatory) –MFoCS seminar –Type Theory and Coq (6ec) – Geuvers, Wiedijk –Computer Algebra (6ec) – Souvignier Specialisation electives (mandatory) –choose at least one mathematics and at least one computer science course. Specialisation basis15 EC Specialisation electives56 EC CS and society / Philosophy3 EC Free electives6 EC Master thesis project40 EC

Courses (studiegids.science.ru.nl) RU-CS –Semantics and Domain Theory (6 EC) –Model Checking (6 EC) –Advanced Lambda Calculus (6 EC) –Advanced Programming (6 EC) RU-Math –Complexity Theory (6 EC) –Computability Theory (6 EC) –Intuïtionistic mathematics (6 EC) –Category Theory (6 EC) Furthermore: –Mastermath (mandatory for master in mathematics) –Courses offered on demand (as self-study) –Foreign University

Examples of Research projects Example topics: Extracting programs from (classical) proofs – Geuvers Computation and reasoning with infinite objects – Silva, Geuvers Formalization of (parts of) the C standard – Wiedijk Grammars and fractals in nature – Silva Some projects: –Formal proof of correctness of an algorithm for finding zeroes of complex polynomials –Coinductive lazy computation –The inference problem for D0L-Systems –Equality of infinite objects –Call-by-name, call-by-value and abstract machines –Classical logic, control calculi and data types

Unique Selling Points Track is unique in the Netherlands Unique concentration of expertise within iCIS and IMAPP o Formal Methods (Automata, Formal Lang., Coalgebra) o Computer Aided Verification (Model Checking) o Theorem proving o Type Theory o Proof Theory o Computer Algebra and Algorithmic Number Theory Ideal track for those interested in computer science and mathematics Good opportunity for a career in academic research

Job Perspective Students with a Master in MFoCS typically go into academic research: Freek Verbeek: PhD with Vaandrager/van Eekelen/ Schmaltz; now assistant professor (OU) Robbert Krebbers: PhD-student with Wiedijk & Geuvers Rutger Kuijper: PhD student with Terwijn Not formally MFoCS students: – Hans Bugge Grathwohl: PhD student in Aarhus (DK) – Bram Geron: PhD student in Birmingham (UK) (Exception: Remy Viehoff: Marine)

Coordinators Alexandra Silva (CS - iCIS)Bas Terwijn (Math - IMAPP) Contact the coordinators if you have questions!