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FINITE FIELDS

ACCADEMIC YEAR2012/2013

COD. 14856

dati insegnamento:

DEGREE: Mathematics

TYPE OF COURSE: SUPPLEMENTARY COMPULSORY SUBJECTS

LANGUAGE OF INSTRUCTION: Italian

LECTURERS:

GALLINA Giordano

ACADEMIC YEAR: 2012/2013

YEAR OF STUDY: 2

SEMESTER: Second semester

NUMBER OF CREDITS: 6

UNIT COORDINATOR: GALLINA Giordano

CONTACT HOURS: 48

Learning outcomes of the course unit

Deepen the theory of finite fields, with particular regard to the problem of decomposition of polynomials over them and finding the roots of a polynomial, symbolic irreducibility, minimal q-polynomial.

Course contents summary

The course deals the following main topics: Berlekamp algorithm's, the cyclotomic polynomials, traces and norms, orders of polynomials over finite fields, linearized polynomial, symbolic irreducibility, minimal q-polynomial and the fundamental theorem about him.

Teaching methods

The preferred teaching tool for the development of such knowledge are the lectures. The note taking is seen as part of the learning process.

Assessment methods and criteria

The assessment of learning is done in classic way, through the evaluation of an oral interview. In the colloquium, the student must be able to independently conduct demonstrations related to the intrinsic properties of the studied structures using an appropriate algebraic language and a proper mathematical formalism.

OTHER COURSES

YEAR: 1

ALGEBRA
CALCULUS 1
CALCULUS 1 (UNIT 2)
CALCULUS 1 PAR. 1
ENGLISH - LEVEL I
ENGLISH B1 (Threshold level)
FUNDAMENTALS OF PROGRAMMING A
GEOMETRY (UNIT 1)
GEOMETRY (UNIT 2)
GEOMETRY 1
PHYSICS 1

YEAR: 2

ALGORITHMS AND DATA STRUCTURES
CALCULUS 2
CALCULUS 2 PART. 1
CALCULUS 2 PART. 2
FINITE FIELDS
GEOMETRY 2
GEOMETRY 2 UNIT 1°
GEOMETRY 2 UNIT 2°
NUMERICAL ANALYSIS
RATIONAL MECHANICS

YEAR: 3

COMPLEMENTARY MATHEMATICS I
ELEMENTS OF PROBABILITY
FUNCTION SPACE
GEOMETRY 3
MATHEMATICAL LOGIC
MODELS OF PHYSICAL MATHEMATICS
PHYSICS 2

Università degli studi di Parma

via Università, 12 - I 43121 Parma

P.IVA 00308780345

tel. +390521902111

email: protocollo@pec.unipr.it

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