## "Babes-Bolyai" University of Cluj-Napoca Faculty of Mathematics and Computer Science

 Mathematical logic and set theory
 Code Semes-ter Hours: C+S+L Credits Type Section MA005 1 2+2+0 6 compulsory Matematică MA005 1 2+2+0 5 compulsory Matematică-Informatică MA005 1 2+2+0 6 compulsory Matematici Aplicate
 Teaching Staff in Charge
 Assoc.Prof. COVACI Rodica, Ph.D., rcovaci@math.ubbcluj.roProf. MARCUS Andrei, Ph.D., marcus@math.ubbcluj.roLect. SACAREA Cristian, Ph.D., csacarea@math.ubbcluj.ro
 Aims An introduction to the elements of mathematical logic concerning the logic of sentences and predicates as a completion of the high school knowledge. Presentation of Cantor's theory of sets. Study of binary relations and functions. Considerations on cardinal numbers, finite and countable sets and ordinal numbers.
 Content 1. Elements of mathematical logic: propositional calculus, logical operators and formulae, identic true and identic false formulae, logical implication and logical equivalence, decision problem; predicate calculus, quantifiers, theorems. 2. Sets, relations, functions: set algebra, binary relations, equivalence relations and partitions, functions, one-to-one correspondence, the kernel of a function, factorization theorems, ordered sets, lattices, homomorphisms, direct product and exponentiation of sets and functions. 3. Cardinal numbers: definition, operations with cardinal numbers, ordering of cardinal numbers, countable and noncountable sets, infinite and finite sets, the set of natural numbers (the Frege-Russell construction and Peano's axiomatic study).
 References 1. Becheanu M. si colectiv, Algebra, Editura ALL, Bucuresti, 1998. 2. Both N., Elemente de teoria numerelor pentru examenele de definitivat si perfectionare, lit., UBB, Cluj-Napoca, 1983. 3. Busneag D., Boboc F., Piciu D., Elemente de aritmetica si teoria numerelor, Editura RADICAL, Craiova, 1998. 4. Miron R., Branzei D., Fundamentele aritmetici si geometriei, Editura Academiei, Bucuresti, 1983. 5. Vraciu C., Vraciu M., Elemente de aritmetica, Editura ALL, Bucuresti, 1998.
 Assessment Exam.