Università Roma Tre

(1) Set theory and basic logic

Sets. Subsets
The natural, integer, rational real numbers.
Union and intersection.
Complement
Power set
Partitions
Product
Finite and Infinite sets


(2) Maps and relations

Surjective, injective and bijective maps.
Cardinality
Equivalence relations and partitions.
Classi di equivalenza e partizioni.
Quotient set
Order relations.

(3) I numeri naturali

Definizione assiomatica
Principio di induzione
Buon ordinamento

(4) The natural numbers

Arithmetic and total ordering.
The Euclidean division
Greatest commod divisor
Bézout's identoty
Prime numbers and factorization.
The fundamental theorem of arithmetic
Modular arithmetic

(5) Groups

Subgroups
Cyclic groups
Symmetric groups
Homomorfisms
Isomorfisms
Structure cyclic groups
Lagrange's theorem and properties of finite groups.

(6) Selected topics (basics only)

Rings and fields: definitions and examples.
Characterizations of infinite sets.
Countable sets: definition and examples.

Title: Algebra
Author I.N. Herstein


Notes of the course available on the TEAM of the course