Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MML0015 Mathematical Logic
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
1
2+2+0
fundamental
compulsory
Mathematics and Computer Science
1
2+2+0
fundamental
compulsory
Teaching Staff in Charge
Assoc.Prof. COVACI Rodica, Ph.D.,  rcovacimath.ubbcluj.ro
Assoc.Prof. SZANTO Csaba Lehel, Ph.D.,  szantomath.ubbcluj.ro
Aims
Introductory concepts and results on mathematical logic and set theory.
Content
1. ELEMENTS OF MATHEMATICAL LOGIC: Propositional calculus, the decision problem. Predicate calculus, quantifiers.
2. SETS, RELATIONS, FUNCTIONS: Operations with sets, binary relations, functions, injective, surjective, bijective functions, equivalence relations and factor sets, the kernel of a function, factorization theorems, ordered sets, lattices, order homomorphisms, Boole algebras.
3. CARDINAL NUMBERS: Definition, direct product and exponentiation of sets and functions, operations with cardinals, ordering of cardinals, finite and infinite sets.
4. NUMBER SETS: Introduction to axiomatic set theory, natural numbers (the Frege-Russell construction and Peano@s axioms), the construction of integers.


References
1. ADAMSON, I.T., A Set Theory Workbook, Birkhauser, Boston, 1998.
2. BILANIUK, S., A Problem Course in Mathematical Logic, Trent University, Ontario, 2003.
3. BREAZ, S.; COVACI, R., Elemente de logica, teoria multimilor si aritmetica, Editura Fundatiei pentru Studii Europene, Cluj-Napoca, 2006.
4. GRATZER, G., General Lattice Theory, Birkhauser, Boston, 1998.
5. HALMOS, P.R., Naive Set Theory, D. Van Nostrand Company Inc., Princeton, 1967.
6. KRANTZ, S.G., Logic and Proof Techniques for Computer Science, Birkhauser, Boston 2002.
7. MARCUS, A.; SZANTO, C.; TOTH, L., Logika es halmazelmelet, Sapientia Kiado, Kolozsvar, 2004.
8. NASTASESCU, C., Introducere in teoria multimilor, Editura Didactica si Pedagogica, Bucuresti, 1981.
9. PURDEA, I.; POP, I., Algebra, Editura GIL, Zalau, 2003.
10.PURDEA, I.; PELEA, C., Probleme de algebra, Editura EIKON, Cluj-Napoca, 2008.

Assessment
Test paper(25%) + Exam(75%).

Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject