
Course unit
ALGEBRA AND GEOMETRY
INP8083358, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/03 
Geometry 
6.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Start of activities 
01/10/2018 
End of activities 
18/01/2019 
Examination board
Examination board not defined
Prerequisites:

The basic knowledges from the high school program. 
Target skills and knowledge:

The student will learn new techniques on linear algebra and geometry which will be essential on his university studies. The techniques and the contents of the class will be useful for modeling and solving algebraic or geometric problems of linear type (in particular solving linear equations using the associated matrix and geometric problems relative to linear sub varieties of the Euclidean space). 
Examination methods:

Mandatory written test and optional oral examination. 
Assessment criteria:

Correctness of the proposed solution. Clarity of exposition. 
Course unit contents:

Vector spaces: subspaces, linear combinations, basis and dimension. Grassmann formula.
Matrixes and systems of linear equations: matrix calculus, rank of a matrix. Systems of linear equations, Capelli's theorem, Gauss algorithm.
Linear mappings: linear mappings and matrixes, kernel and dimension theorem. Eigenvalues and eigenvectors, diagonalizable matrixes.
Metric spaces: scalar product and normality. Euclidean norm and distance. Linear subvarieties of Rˆ3. 
Planned learning activities and teaching methods:

Class lectures and exercises in class. 
Additional notes about suggested reading:

Notes: http://www.dm.unibo.it/%7Enicoletta.cantarini/didattica/InfoCesena/dispense/dispense.pdf 
Textbooks (and optional supplementary readings) 

Cantarini, Nicoletta; Chiarellotto, Bruno, Un corso di matematica: teoria ed esercizi. Nicoletta Cantarini, Bruno Chiarellotto, Luisa Fiorot. Padova: Libreria progetto, 2008.

Bottaccin Francesco, Algebra Lineare e geometria. : Esculapio, 2011.


