Learning outcomes of the course unit
Demonstrate the existence of some algebraic theories also providing basic nomenclature and elementary information within a universal context.
Students should also show interpretation and orientation capabilities.
Course in Linear Algebra
Course contents summary
1. BASIC PRINCIPLES AND EXAMPLES. EXTERNAL AND INTERNAL OPERATIONS. GROUPOIDS, SUB-GROUPOIDS, DIRECT PRODUCTS, HOMOMORPHISMS, ISOMORPHISMS. CONVOLUTIONS, POLYNOMIALS, NUMBERS (COMPLEX, DUAL, BI REAL; GAUSS WHOLE NUMBERS) AND MATRICES. BASIC THEOREMS ON HOMOMORPHISMS, CONGRUENCES, QUOTIENTS, NORMAL SUBGROUPS, IDEALS. LATERALS AND THEOREM OF LAGRANGE. POLYNOMIALS AND POLYNOMIAL FUNCTIONS.
2. ARITHMETIC QUESTIONS AND APPLICATIONS. LOCALISATION. DOMAINS. EUCLIDEAN DIVISION, EUCLIDEAN RINGS, MAIN IDEALS. CYCLICAL GROUPS, CHARACTERISTICS OF A RING, PRIME FIELDS. QUADRATIC DOMAINS. IRREDUCIBLE AND PRIME ELEMENTS. EXTENDED EUCLIDEAN ALGORITHM AND BEZOUT’S FORMULA. FACTORISATION THEOREM. DETAILS OF Z METHODOLOGY: SECOND DEGREE EQUATIONS. POLYNOMIAL EQUATIONS THEOREM OF RUFFINI. FIELD EXTENSIONS. FIELD SIZE. ALGEBRAICALLY CLOSED FIELDS. FINITE FIELDS.
No text book has been adopted but an extensive list of classic texts, printouts from courses and notes downloadable free of charge from the Internet has been provided.