
Course unit
ALGEBRA AND GEOMETRY
INP8083358, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
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 
Examination board
Board 
From 
To 
Members of the board 
1 2018 
01/10/2018 
30/11/2019 
BONATTO
MARCO
(Presidente)
BENVEGNU'
ALBERTO
(Membro Effettivo)

Prerequisites:

High School level Mathematical skills. 
Target skills and knowledge:

The student will learn new techniques in linear algebra and geometry, that will be essential for future academic studies. The topics covered in this course will give the tools to solve algebraic and geometric problems that can be described by linear models (in particular the solution of linear systems using the associated matrix and problems on linear subvarieties in the Euclidean space). 
Examination methods:

Written exam. 
Assessment criteria:

Correctness of the solution presented. Sufficient motivation of the solutions presented. Clarity. 
Course unit contents:

Introduction to Linear algebra and its principal application to analytic geometry.
Extended Program:
Vector spaces: subspaces, linear combination, basis and dimension. Grasmann formula.
Matrices and linear systems: matrix computation, rank of a matrix, linear systems, Capelli's Theorem, Gauss' Algorithm.
Linear maps: linear maps and matrices, kernel and Dimension Theorem, eigenvalues and eigenvectors, diagonalization.
Metric structures: scalar and cross product, orthogonality, distance and Euclidean norm, linear subvarieties of R^3. 
Planned learning activities and teaching methods:

Frontal lecture. The students will be given exercises to practice. 
Additional notes about suggested reading:

The students will find the lecture notes, proposed exercises for self evaluation and exams examples in the moodle of the module. 
Textbooks (and optional supplementary readings) 

Novelli, Carla, Esercizi di algebra lineare e geometria. Bologna: Esculapio, 2016.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 One Note (digital ink)

