Algebra with Geometry I

General data

Course ID:	1100-1ENALGE11
Erasmus code / ISCED:	11.101 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Algebra with Geometry I
Name in Polish:	Algebra z geometrią I
Organizational unit:	Faculty of Physics
Course groups:
Course homepage:	http://www.impan.pl/~pmh/teach/algebra/algebra.html
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Short description:	The purpose of the course is to explain basic notions of algebra such as complex numbers, polynomials, groups, vectors and matrices.
Full description:	The purpose of the course is to explain notions that appear in mathematics and physics throughout the entire period of studies. These abstract notions will be illustrated with various examples to make them maximally comprehensible and to demonstrate their usefulness in physics. 1. Complex numbers, number fields. 2. Third degree algebraic equations. 3. Basic properties of polybomials, the greatest common divisor. 4. The notion of a group, permutation groups, permutation sign and the decomposition of permutation into cycles. 5. Vector spaces, linear independence, basis, subspaces, sums and intersections of subspaces. 6. Linear maps, kernel, image, the matrix of a linear map. 7. Determinant.
Bibliography:	1. S. Zakrzewski, Algebra i geometria, Warsaw University publication. 2. P. Urbański, Algebra liniowa i geometria, Warsaw University publication.
Learning outcomes:	After having completed the course students should: a) be familiar with the notion of complex numbers and calculations involving complex numbers; b) understand the notions of a vector space, linear independance, a basis; c) understand the notion of a linear map and a matrix; d) be able to solve systems of linear equations; e) be able to compute determinants and find the inverese matrix.
Assessment methods and assessment criteria:	Midterms and written exam -- computational part; oral exam -- theoretical part.
Practical placement:	none

This course is not currently offered.

Course descriptions are protected by copyright.
Copyright by University of Warsaw.