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	Category	Status	
1	2+1+0	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.
5. http://www.informatik.uni-bremen.de/cofi/CASL-RM.pdf

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

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

VIII. Assessment
Presentation (2/3 of the grade), test paper (1/3 of the grade).	

IX. Additional references
1. G. Gratzer, Universal algebra, The University Series in Higher Mathematics, Van Nostrand, London, 1968.
2. 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,
       26.10.2009			               Assoc.Prof. PELEA Cosmin, Ph.D.