Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Metode formale în programare - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MML1014	Algebraic Specification	

Semester	Hours: C+S+L+P	Category	Status	
1	2+1+0+1	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
PELEA Cosmin	Ph.D.	Assoc.Prof.	Algebra, Mathematical Analysis and Geometry	*	*		

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The aim of the course is to give an approach to algebraic specification, verification and formal development. Students will learn how to write algebraic specifications for a given mathematical model, to construct  and evaluate terms, to construct the corresponding quotient term algebras and to study related problems such as the correctness with respect to some algebras.	

IV. Course contents
1. Basics of relations, functions and algebraic structures.
2. Basics of universal algebras.
3. Multisorted algebras: signatures, terms.
4. Congruences and quotient algebras.
5. Quotient term algebras.
6. Correctness.
7. CASL (Common Algebraic Specification Language). 	

V. Bibliography
1. M. Bidoit, P. Mosses, CASL User Manual, Introduction to Using the Common Algebraic Specification Language, Lecture Notes in Computer Science, Springer-Verlag, 2004. (http://www.informatik.uni-bremen.de/cofi/CASL-UM.pdf)
2. S. Burris, H.P. Sankappanavar, A course in universal algebra, Springer-Verlag, 1981.
3. S. Crivei, Basic Abstract Algebra, Casa Cartii de Stiinta, Cluj-Napoca, 2003.
4. H. Ehrig, B. Mahr, Fundamentals of Algebraic Specification I, Springer-Verlag, Berlin, 1985.	

VI. Thematic of didactic activities per weeks
Lecture 1 and seminar 1: Preliminaries on relations, functions, algebraic structures. [3, Ch. 1-2]
Lecture 2 and seminar 2: n-ary operations, universal algebras, examples. [3, Ch. 2]
Lecture 3 and seminar 3: Subalgebras and universal algebra homomorphisms. [2, Ch. II]
Lecture 4 and seminar 4: Basic examples of algebraic specifications. [4, Ch. 1]
Lecture 5 and seminar 5: Signatures, algebras, terms. [4, Ch. 1]
Lecture 6 and seminar 6: Equational specifications and derivations. [4, Ch. 1]
Lecture 7 and seminar 7: Specification of abstract data types. [4, Ch. 2]
Lecture 8 and seminar 8: Congruence relations and quotient algebras. [4, Ch. 3]
Lecture 9 and seminar 9: Quotient term algebras. [4, Ch. 2]
Lecture 10 and seminar 10: Parametrized specification and functors [3, Ch. 7]
Lecture 11 and seminar 11: Correctness of specifications. [4, Ch. 2]
Lecture 12 and seminar 12: CASL: many-sorted specifications. [1, Ch. 3]
Lecture 13 and seminar 13: CASL: partial functions. [1, Ch. 4]
Lecture 14 and seminar 14: CASL: subsorting. [1, Ch. 5]	

VII. Didactic methods used
Exposition, conversation, didactic proof, case study.	

VIII. Assessment
Presentation (1/2 of the grade), test paper (1/2 of the grade).	

IX. Additional references
1. G. Gratzer, Universal algebra, The University Series in Higher Mathematics, Van Nostrand, London, 1968.
2. P. Mosses, CASL User Manual, The Complete Documentation of the Common Algebraic Specification Language, Lecture Notes in Computer Science, Springer-Verlag, 2004. (http://www.informatik.uni-bremen.de/cofi/CASL-RM.pdf)
3. I. Purdea, Gh. Pic, Tratat de algebra moderna, vol.1, Editura Academiei, Bucuresti, 1977	

	Dean,							Chair head,
Prof. TAMBULEA Leon, Ph.D.		    Assoc.Prof. BREAZ Simion, Ph.D.

	Date,						Course responsible,
       20.10.2010			               Assoc.Prof. PELEA Cosmin, Ph.D.