To show the organization of the course that includes this module, follow this link Course organization
First of all, the students are introduced to the language and formal reasoning required for the study of higher mathematics. Furthermore, the main notions and techniques of linear algebra and matrix theory are presented, focussing both on theoretical and computational aspects. Moreover, the course provides an introduction to planar and spatial analytic geometry, within the projective, affine, and euclidean setting. Finally, the main properties of conics will be discussed. Both analytical (coordinates, matrices) and synthetic tools will be employed.
At the end of the course the student must be able to demonstrate an adequate synthesis and abstraction ability, be able to recognize and produce rigorous demonstrations and be able to formalize and solve problems of moderate difficulty, limited to the syllabus of the teaching.
Groups, fields. The field of complex numbers. Matrices, matrix operations and their properties. Determinant and rank of a matrix. Inverse matrix. Systems of linear equations. The method of Gaussian elimination. Vector spaces, subspaces, bases, dimension. Linear maps.
The course consists of front lessons and classroom exercises. Moreover optional tutoring activities are offered. In particular, weekly home exercises are given. They are individually corrected by a tutor and discussed during the exercise hours.
|Alberto Facchini||Algebra e Matematica Discreta (Edizione 1)||Edizioni Decibel/Zanichelli||2000||978-8808-09739-2|
|E.Gregorio, L.Salce||Algebra Lineare||Libreria Progetto Padova||2005|
|Abate, M.||Algebra Lineare||Mc Graw Hill||2001|
|Candilera,Bertapelle||Algebra lineare e primi elementi di Geometria||Mc Graw Hill||9788838661891|
|Giuseppe de Marco||Analisi Zero, presentazione rigorosa di alcuni concetti base di matematica per i corsi universitari (Edizione 3)||Edizione Decibel/Zanichelli||1997||978-8808-19831-0|
|M. Abate, C. de Fabritiis||Geometria analitica con elementi di algebra lineare||McGraw Hill||2010||9788838665899|
See the web page of the whole course