Course Content (Syllabus)
The course is part of the module of courses that aim to offer dexterities for teaching mathematics in Secondary Education.
Sets, Functions. Cartesian product. Equivalence relations. Ordering. Operations on a set. Semigroups., Monoids. Natural numbers. Mathematical induction. Well ordering principle. Complex Numbers. Countable sets. Elements of combinatorial theory. The ring of integers. Divisibility. Euclidean algorithm. GCD, LCM. Bezout's identity. Solutions of the linear equation ax+by= c. Rationals in base n. Prime numbers. Wilson's theorem. Fundamental theorem of arithmetic. Rings modulo n. Fields modulo p. Linear equivalences and systems. Chinese Remainder Theorem, Euler's function, Fermat's Small Theorem, Groups, Euler's Theorem, Groups, ISomorphism of Groups, Classification of groups of small order.
Course Bibliography (Eudoxus)
Ε. Ψωμόπουλου, Εισαγωγλη στην Άλγεβρα, Εκδ. Ζήτη
Δ. Πουλάκης, Άλγεβρα, Εκδ. Ζήτη
Κ. Κάλφα, Εισαγωγή στην Άλγεβρα, Εκδόσεις Ζήτη