GEOMETRY

Course objectives

Basics in linear algebra and geometry. Linear systems and their geometrical interpretation for 2 or 3 unknowns. Familiarity with rigorous reasoning, with numerical and symbolic calculus, with the analysis of problems using an optimal strategy. Familiarity with vectors and matrices, and with geometrical entities in 2 or 3 dimensions in connection with equations of degree 1 or 2. Understanding of linear applications and, in particular, of diagonalization. Expected learning outcomes: I expect constant learning as the course goes on; learning will be increased by tutorials and tests. Little difficulties can be solved also by an email contact. Although the beginning may be difficult, mostly due to faults in the mathematical background, after the first impact - in several cases after the first or second written examination - one expects a neat improvement.

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Bruno Antonio Cifra Lecturers' profile

Program - Frequency - Exams

Course program
Algebraic structures and geometrical structures. Linear spaces and linear subspaces. Matrices and linear systems. Affine Geometry: Affine Plane and Affine Space. Euclidean structure Linear applications. Changes of coordinates Eigenvectors and Diagonalization. Conics and Quadrics
Prerequisites
elementary algebra
Books
A.Vietri: Itinerario di geometria e algebra lineare, ed. CISU. S. Capparelli, A. Del Fra: Geometria, ed. Esculapio. S. Capparelli, A. Del Fra: Esercizi di Geometria, ed. Esculapio. A. further material is available on the web site https://sites.google.com/view/brunocifra/didattica-geometria
Teaching mode
The written exam (lasting 140 minutes) consists of 5 exercices (6 points for each exercice) The theory exam (lasting 60 minutes) consists of 2 questions (15points for each question)
Frequency
The attendance is optional, but strongly recommended
Exam mode
Written exam: the student must obtain a score greater or equal to 18 Written theory: the student must obtain a score greater or equal to 18 The final score is a weighted mean between the scores of the written exam and theory exam.
Bibliography
A.Vietri: Itinerario di geometria e algebra lineare (ed. CISU) S. Capparelli, A. Del Fra Geometria (ed. Esculapio) S. Capparelli, A. Del Fra: Esercizi di Geometria (ed. Esculapio) Mario Landucci N esercizi svolti di Geometria e Algebra Lineare (Ed. LaDotta) L. Grenié - M. Pedroni Esercizi di Geometria e Algebra Lineare (Ed. LaDotta) Enrico Schlesinger Algebra lineare e geometria (Ed. Zanichelli ) L. Mauri, E. Schlesinger Esercizi di algebra lineare e geometria (Ed. Zanichelli ) further material is available on the web site https://sites.google.com/view/brunocifra/didattica-geometria
Lesson mode
The written exam (lasting 140 minutes) consists of 5 exercices (6 points for each exercice) The theory exam (lasting 60 minutes) consists of 2 questions (15points for each question)
  • Lesson code1015375
  • Academic year2024/2025
  • CourseGreen Transition Mechanical Engineering
  • CurriculumSingle curriculum
  • Year1st year
  • Semester1st semester
  • SSDMAT/03
  • CFU9
  • Subject areaMatematica, informatica e statistica