COURSE PRESENTATION FORM - ALGEBRA - 2009/2010


COURSE NAME: Algebra

COURSE CODE: 70130 (BSc) / 70001 (BSc Old)

LECTURER: Michele Fedrizzi

TEACHING ASSISTANTS: Michele Fedrizzi (EN), Paolo Di Sia (IT), Kurt Ranalter (DE)

TEACHING LANGUAGE: English

CREDIT POINTS: 4 (BSc) / 6 (BSc Old)

LECTURE HOURS: 24

EXERCISE HOURS: 12

TIMESPAN: 22.02.2010 - 12.06.2010

TIMETABLE: see Timetable Page

OFFICE HOURS LECTURER: During the lecture time span: Friday 15:10 – 16:10, POS, Office no. 2.10.

OFFICE HOURS TEACHING ASSISTANTS: Michele Fedrizzi: see above. Kurt Ranalter: During the lecture time span, Thursday, 9:30-10:30, POS, room no 2.10 (prior notification by email required). Paolo Di Sia: to be determined.

PREREQUISITES
Upper school level calculus.

OBJECTIVES
Introduces the fundamental methods and models of abstract algebra. The main purpose is to give students studying computer science a solid foundation for future study of a variety of formal systems useful for applications and problem-solving.

SYLLABUS
Sets and relations
Basic notations. Union, intersection, complement and difference of sets. Fundamental laws of operations with sets. The product set. Binary relations. Equivalence relation. Partial order and total order. Mappings.
Groups
Basic definitions and properties. Subgroups. Cyclic groups. Permutation groups. The group of residue classes module m. Homomorphisms and isomorphisms.
Rings
Definitions and properties. Subrings. Types of rings. Characteristic. Divisors of zero. Homomorphisms and isomorphisms.
Vector spaces
Definition of vector space and subspace. Linear dependence. Bases of a vector space. Linear transformations and the associated algebra. Vector spaces over R.
Matrices and systems of linear equations
Square matrices and matrices of order m n. Elementary transformations on a matrix. Canonical form. Elementary matrices and their inverses. The inverse of a non-singular matrix. Determinant of a square matrix. Properties and evaluation of determinants. Solutions of a system of linear equations.

TEACHING FORMAT
Frontal classroom lectures.

ASSESSMENT
Mid-term written examination (40%) and final written examination (60%).

READING LIST
Textbook:

• Frank Ayres, Jr., Modern Abstract Algebra, Shaum’s outline series, McGraw-Hill.

Other teaching materials will be available in the Reserve Collection: past exams, lectures diary and pdf documents on some topics of the course.

SOFTWARE USED
None.

LEARNING OUTCOME
The fundamentals of algebraic structures for enhancing the formal mathematical reasoning and problem solving.

COURSE PAGE
Please see the Reserve Collection of the course.