MPRI

Level 2 modules

Level 2 modules offer a specialised training constitutive of a true introduction to research; they require a good knowledge of the contents of the level 1 modules. Each level 2 full module is taught over the course of a semester, represents 75 student-hours (typically 50 contact hours and 25 hours of private study), and entitles students to 6 ECTS credits. Half modules are taught either 1.5h/week over the course of the semester or 3h/week over half the semester. Each such module represents 37.5 student-hours and entitles students to 3 ECTS credits.

At least twenty level 2 modules will be made available for the first semester exclusively. The MPRI's Executive Committee will set a list of level 2 modules each year; the modules thus selected will of course only be actually maintained if they attract a sufficient number of students. The level 2 modules will be taught preferably on the premises of the university of Paris 7. The table herebelow contains a list of titles and heads of level 2 modules as well as links to a description of each module.

List of level 2 modules

Courses marked with a (S) are suspended in the academic year 2014-2015.

Module	Title	Nb. H	ECTS	Period(s)	Nb. Week	H/Week	Person(s) in charge	Teaching Language	Breakable
2.1	Logique linéaire et paradigmes logiques du calcul Linear logic and logical paradigms of computation	48	6	1-2	16	3	R. Di Cosmo	3/4 French by default, 1/4 English
2.2	Modèles des langages de programmation: domaines, catégories, jeux Models of programming languages: domains, categories, games	48	6	1-2	16	3	P.-A. Melliès	English upon request
2.3	Concurrence Concurrency	48	6	1-2	20	2.5	R. Amadio	1/4 English, 3/4 French	Yes
2.4	Programmation fonctionnelle et systemes de types Functional programming and type systems	48	6	1-2	20	2.5	D. Rémy	French by default
2.5.1	Démonstration automatique Automated deduction	24	3	2	8	3	E. Contejean	French by default
2.6	Interprétation abstraite: application à la vérification et à l'analyse statique Abstract interpretation: application to verification and static analysis	48	6	1-2	16	3	A. Miné	English upon request
2.7.1	Fondements des systèmes de preuves Foundations of proof systems	24	3	1-2	16	1.5	G. Dowek	English upon request
2.7.2	Assistants de preuves Proof assistants	24	3	2	8	3	B. Barras	French by default
2.8.1	Théorie non-séquentielle des systèmes distribués Non-sequential theory of distributed systems	24	3	1	10	2.5	B. Bollig	1/2 English upon request 1/2 French upon request
2.8.2	Fondements des systèmes temps-réel et hybrides Foundations of real time and hybrid systems	24	3	2	10	2.5	E. Asarin	French by default
2.9.1	Fondements mathématiques de la théorie des systèmes infinis Mathematical foundations of the theory of infinite transition systems	24	3	1	8	3	A. Finkel	French by default
2.9.2	Vérification algorithmique des programmes Algorithmic verification of programs	24	3	1	8	3	A. Bouajjani	English upon request
2.10	Aspects algorithmiques de la combinatoire Algorithmic aspects of combinatorics	48	6	1-2	20	2.5	G. Schaeffer	French
2.11 (S)	Complexité randomisée (long) Randomness in complexity (long)	48	6	1-2	16	3	F. Magniez	English	Yes
2.11.1	Algorithmes probabilistes Randomized algorithms	24	3	1	8	3	N. Schabanel	English upon request
2.11.2	Complexité randomisée (court) Randomness in complexity (short)	24	3	1	8	3	I. Kerenidis	English
2.12.1	Techniques en cryptographie et cryptoanalyse Techniques in cryptography and cryptanalysis	24	3	1-2	16	1.5	M. Abdalla	English
2.12.2	Algorithmes arithmétiques pour la cryptologie Arithmetic algorithms for cryptology	24	3	1-2	16	1.5	F. Morain	1/3 English by default 2/3 English upon request
2.13.1	Systèmes polynomiaux, calcul formel et applications Polynomial systems, computer algebra and applications	24	3	2	8	3	J.-C. Faugère	English upon request
2.13.2	Codes correcteurs d'erreurs et applications à la cryptographie Error correcting codes and applications to cryptography	24	3	1-2	16	1.5	A. Canteaut	French by default
2.14.1	Analyse géométrique des données Computational geometry learning	24	3	1	10	2.5	J.-C. Boissonnat	English upon request
2.15	Analyse d'algorithmes Analysis of algorithms	48	6	1-2	16	3	M. Soria	French
2.16	Modélisation par automates finis Finite automata modelling	48	6	1-2	16	3	T. Colcombet	English upon request
2.17.1	Fondements sur la modélisation des réseaux Foundations of network models	24	3	2	10	2.5	J. Mairesse	English upon request
2.18.1	Algorithmique distribuée pour les réseaux Distributed algorithms on networks	24	3	1-2	16	1.5	P. Fraigniaud	1/2 French by default 1/2 English
2.18.2 (S)	Algorithmique distribuée avec mémoire partagée Distributed algorithms on shared memory	24	3	1	8	3	C. Delporte	French
2.19	Méthodes informatiques pour la biologie systémique et synthétique Computational methods for systems and synthetic biology	48	6	1-2	16	3	F. Fages	French by default
2.20.1	Techniques de théorie des jeux en informatique Game theory techniques in computer science	24	3	1	8	3	W. Zielonka	French
2.20.2	Fondations mathématiques de la théorie des automates Mathematical foundations of automata theory	24	3	1-2	16	1.5	J.-E. Pin	English upon request
2.22 (S)	Algorithmes efficaces en calcul formel Efficient algorithms in computer algebra	48	6	1-2	16	3	B. Salvy	French by default	Yes
2.23.1	Systèmes synchrones Synchronous systems	24	3	1	8	3	M. Pouzet	English upon request
2.24.1	Optimisation Optimization	24	3	1	10	2.5	Ch. Durr	English
2.26.1 (S)	Logique, complexité descriptive et théorie des bases de données Logic, descriptive complexity and database theory	24	3	1	8	3	L. Segoufin	French by default
2.26.2	Gestion de données sur le web Web data management	24	3	2	8	3	S. Abiteboul	English upon request
2.27.1	Structures informatiques et logiques pour la modélisation linguistique Computational structures and logics for natural language modelling	24	3	1	8	3	S. Schmitz	English upon request
2.29.1	Algorithmique des graphes Graph algorithms	24	3	1-2	16	1.5	M. Habib	French by default
2.30	Protocoles cryptographiques : preuves formelles et calculatoires Cryptographic protocols: computational and symbolic proofs	48	6	1-2	16	3	H. Comon-Lundh	English upon request	Yes
2.31.1 (S)	Algorithmique et complexité des problèmes de satisfaction de contraintes Constraint Satisfaction Problems: algorithms and complexity	24	3	2	8	3	M. Hermann	1/2 English by default 1/2 English upon request
2.33.1	Théorie des calculs Theory of computations	24	3	1	8	3	S. Perifel	French
2.34.1	Informatique quantique et applications Quantum information and applications	24	3	2	8	3	S. Laplante	English upon request
2.35.1 (S)	Programmation par contraintes Constraint programming	24	3	1	8	3	S. Soliman	French by default
2.36.1	Preuve de programmes Proofs of programs	24	3	2	8	3	C. Marché	English upon request
2.37.1	Sémantique, langages et algorithmes pour la programmation multicore Semantics, languages and algorithms for multicore programming	24	3	2	8	3	A. Cohen	English upon request
2.38.1	Algorithmique et combinatoire des graphes géométriques Algorithms and combinatorics for geometric graphs	24	3	1	8	3	E. Colin de Verdiere	French by default

Semantics of the teaching languages annotations:

“English upon request” means that the module will be taught in French, unless one non-French speaking student requests English
“French by Default” means that the module is taught in French, unless at least one non-French speaking student requests English and no French speaking students requests French
“English by Default” is obtained by transposing “French” and “English” in the above case.
“English” (resp. “French”) means that the module will be taught in English (resp. French) independently of the students attending. Most of the time, however, some of the teaching material is available in French (resp. English)

For a more detailed information on the teaching language of each module, as well as concerning the language of the exams, please look at the web page of the module.

Themes covered by the level 2 modules (this was last updated in 2013)

MPRI provides excellent coverage of the following themes in Computer Science:

COCO = Computability and Complexity,

ALGO = Algorithms,

COCA = Combinatorics and Computer Algebra,

CCSE = Cryptography, Coding, and Security,

LSPR = Logics and Semantics of Programs,

AUDE = Automated Deduction,

AUFL = Automata and Formal Languages,

SPAV = System Programming, Analysis, and Verification.

The following table roughly summarizes the main themes covered by each level 2 module.

Module	COCO	ALGO	COCA	CCSE	LSPR	AUDE	AUFL	SPAV
2.1 Linear logic					X	X
2.2 Models of programming languages: domains, categories, games					X
2.3 Concurrency					X			X
2.4 Functional programming and type systems					X			X
2.5.1 Automated deduction						X
2.6 Abstract interpretation: application to verification and static analysis					X			X
2.7.1 Foundations of proof systems					X	X
2.7.2 Proof assistants						X
2.8 Foundations of real time systems verification							X	X
2.9.1 Mathematical foundations of the theory of infinite transition systems						X	X	X
2.9.2 Algorithmic verification of programs						X	X	X
2.10 Algorithmic aspects of combinatorics		X	X
2.11.1 Randomized algorithms	X	X
2.11.2 Randomness in complexity	X	X
2.12.1 Techniques in cryptography and cryptanalysis				X
2.12.2 Arithmetic algorithms for cryptology				X
2.13.1 Polynomial systems, computer algebra and applications			X	X
2.13.2 Error correcting codes and applications to cryptography				X
2.14.1 Computational geometry learning		X
2.15 Analysis of algorithms		X	X
2.16 Finite automata modelling							X	X
2.17.1 Foundations of network models							X	X
2.18.1 Distributed algorithms on networks		X						X
2.18.2 Distributed algorithms on shared memory		X						X
2.19 Computational methods for systems and synthetic biology								X
2.20.1 Game theory techniques in computer science							X
2.20.2 Mathematical foundations of automata theory							X
2.22 Efficient algorithms in computer algebra	X	X	X
2.23.1 Synchronous systems					X			X
2.24.1 Optimization		X
2.26.1 Logic, descriptive complexity and database theory	X				X		X
2.26.2 Web data management	X				X		X
2.27.1 Computational structures and logics for natural language modelling					X
2.29.1 Graph algorithms		X
2.30 Cryptographic protocols: computational and symbolic proofs				X		X
2.31-1 Constraint satisfaction problems: algorithms and complexity	X	X				X
2.33.1 Theory of computations	X	X
2.34.1 Quantum information and applications	X			X
2.35.1 Constraint programming					X	X
2.36.1 Proofs of programs					X	X
2.37.1 Semantics, languages and algorithms for multicore programming					X			X
2.38.1 Algorithms and combinatorics for geometric graphs		X	X
Module	COCO	ALGO	COCA	CCSE	LSPR	AUDE	AUFL	SPAV

Level 2 modules

List of level 2 modules

Semantics of the teaching languages annotations:

Themes covered by the level 2 modules (this was last updated in 2013)

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