First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
GEOMETRY (Iniziali cognome A-L)
SCN1032568, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
SC1160, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination GEOMETRY
Website of the academic structure
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge LUISA FIOROT MAT/03

Course unit code Course unit name Teacher in charge Degree course code
SCN1032568 GEOMETRY (Iniziali cognome A-L) LUISA FIOROT SC1158

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/03 Geometry 8.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 16 34.0 No turn
Lecture 6.0 48 102.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
11 Geometria (iniziali cognomi M-Z) 01/10/2018 30/11/2019 URBINATI STEFANO (Presidente)
10 Geometria (iniziali cognome A-L)) 01/10/2018 30/11/2019 KLOOSTERMAN REMKE NANNE (Presidente)
URBINATI STEFANO (Membro Effettivo)

Prerequisites: None
Target skills and knowledge: Knowledge of the basic notions and results on vector spaces. Familiarity with matrix calculus. Knowledge of the interaction between linear algebra and geometry.
Examination methods: Written exam consisting both of exercises and theoretical questions. Students with a grade of 28 or higher have also to take an oral exam.

It will be possible to replace the written exam by two small tests, one halway through the course and one at the end of the course.
Assessment criteria: Knowledge of the main definitions and theorems.

Capacity to solve exercises in which one applies linear algebra.

Capacity to show results concerning vector spaces.
Course unit contents: Solving a system of linear equations. Gauss elimination method.
Matrix calculus, invertible matrices. Rank of a matrix.

Vector spaces, subspaces, linear dependence, bases. Dimension of a vector space.
Sums of vector spaces, intersection of vector spaces.

Linear maps. Kernel and image of a linear map. Matrix of a linear map. Matrix associated with a change of basis. Determinant of a matrix. Eigenvalues and eigenvectors of a linear map. Diagonalizable matrices.

The space of geometric vectors: inner product and its properties, the norm of a vector, Schwarz inequality.

Quadratic forms. Symmetric bilinear forms. Spectral theorem for real symmetric matrices. Affine spaces and subvarieties. Affine coordinates. Affine transformations. Euclidean space. Isometries. Parallel, incident and skew subvarieties. Distance, angles. Volume of parallelepipeds: explicit formulas. Classification of conics.
Planned learning activities and teaching methods: Theoretical lessons (50% of the time) alternated with sessions of problem-solving (50% of the time).
Additional notes about suggested reading: The instructor will provide notes, which will be available on the moodle page of the course.
Textbooks (and optional supplementary readings)
  • Candilera, Maurizio; Bertapelle, Alessandra, Algebra lineare e primi elementi di geometriaMaurizio Candilera, Alessandra Bertapelle. Milano: McGraw-Hill, ©2011, --. Cerca nel catalogo
  • Mauri, Luca; Schlesinger, Enrico, Esercizi di algebra lineare e geometria. Bologna: Zanichelli, 2013. Cerca nel catalogo

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)
  • Latex