Foundations of algebra and geometry
Course objectives
General objectives. The class is aimed to provide the first tools in linear Algebra which are necessary to the study of Matrix Algebra and Affine and Euclidean Geometry. Specific objectives. Knowledge and understanding: Once acquired the basic linear algebra, the student should be able to understand the connections between endomorphism and matrices and to solve diagonalization problems. Moreover he should know the geometry in an affine space and particularly the Cartesian Geometry in dimension 2 and 3. Application skills: Geometry has also the aim to make the student able to apply these tools. In particular, the student will have to be able to use matrices, to solve linear equations, problems concerning vector spaces and linear functions, to solve exercises about the diagonalization for operators and matrices. Moreover the student should be able to solve problems about affine spaces. Briefly, he should be able to apply the acquired knowledge to translate a problem (in terms of vectors) in a simpler numerical one by using matrices representations. Communication skills: The student will have to learn to present in a clear and rigorous way both theoretical and applicative acquired knowledge. Judgement autonomy: Students will be guided to learn in a critical and responsible way all what will be dealt with in class, and to enrich their judgement through the study of the didactic material indicated by the professor.
Channel 1
ANTONIO CIGLIOLA
Lecturers' profile
Program - Frequency - Exams
Course program
Matrices. Determinants. Rank. Linear systems of equations. Vector spaces. Bases and dimension. Linear operators. Eigenvalues and eigenspaces. Diagonalization. Dot product. Vector product. Simmetric operators. Orthogonal operators. Spectral theorem.
Affine Geometry and Euclidean Geometry of the plane and space. Conics. Quadric surfaces.
Prerequisites
Notions of secondary school mathematics, e.g. numbers (natural, integer, rational, real), operations between numbers, elementary algebraic calculus, sets, elements of Euclidean geometry, and trigonometry.
Books
Geometria, Antonio Cigliola, La Dotta Editrice 2016
Exam mode
The following elements will be considered in the evaluation of the exam :
1. the logic followed by the student in solving the exercises in the written exam
2. the correctness of the procedure adopted for the solution of the exercises
3. the appropriateness of the proposed solution in relation to the skills that the student is expected to have acquired at the end of the course;
4. the acquired knowledge of the theoretical results described during the course, also taking into account the property of language and formalism in describing them.
Satisfaction of aspects #1 and #4 is a necessary condition for achieving a grade of 20. Grades above 24 will be awarded to students whose evidence satisfies all four aspects listed above.
ANTONIO CIGLIOLA
Lecturers' profile
Program - Frequency - Exams
Course program
Matrices. Determinants. Rank. Linear systems of equations. Vector spaces. Bases and dimension. Linear operators. Eigenvalues and eigenspaces. Diagonalization. Dot product. Vector product. Simmetric operators. Orthogonal operators. Spectral theorem.
Affine Geometry and Euclidean Geometry of the plane and space. Conics. Quadric surfaces.
Prerequisites
Notions of secondary school mathematics, e.g. numbers (natural, integer, rational, real), operations between numbers, elementary algebraic calculus, sets, elements of Euclidean geometry, and trigonometry.
Books
Geometria, Antonio Cigliola, La Dotta Editrice 2016
Exam mode
The following elements will be considered in the evaluation of the exam :
1. the logic followed by the student in solving the exercises in the written exam
2. the correctness of the procedure adopted for the solution of the exercises
3. the appropriateness of the proposed solution in relation to the skills that the student is expected to have acquired at the end of the course;
4. the acquired knowledge of the theoretical results described during the course, also taking into account the property of language and formalism in describing them.
Satisfaction of aspects #1 and #4 is a necessary condition for achieving a grade of 20. Grades above 24 will be awarded to students whose evidence satisfies all four aspects listed above.
Channel 2
ANTONIO CIGLIOLA
Lecturers' profile
Program - Frequency - Exams
Course program
Matrices. Determinants. Rank. Linear systems of equations. Vector spaces. Bases and dimension. Linear operators. Eigenvalues and eigenspaces. Diagonalization. Dot product. Vector product. Simmetric operators. Orthogonal operators. Spectral theorem.
Affine Geometry and Euclidean Geometry of the plane and space. Conics. Quadric surfaces.
Prerequisites
Notions of secondary school mathematics, e.g. numbers (natural, integer, rational, real), operations between numbers, elementary algebraic calculus, sets, elements of Euclidean geometry, and trigonometry.
Books
Geometria, Antonio Cigliola, La Dotta Editrice 2016
Exam mode
The following elements will be considered in the evaluation of the exam :
1. the logic followed by the student in solving the exercises in the written exam
2. the correctness of the procedure adopted for the solution of the exercises
3. the appropriateness of the proposed solution in relation to the skills that the student is expected to have acquired at the end of the course;
4. the acquired knowledge of the theoretical results described during the course, also taking into account the property of language and formalism in describing them.
Satisfaction of aspects #1 and #4 is a necessary condition for achieving a grade of 20. Grades above 24 will be awarded to students whose evidence satisfies all four aspects listed above.
ANTONIO CIGLIOLA
Lecturers' profile
Program - Frequency - Exams
Course program
Matrices. Determinants. Rank. Linear systems of equations. Vector spaces. Bases and dimension. Linear operators. Eigenvalues and eigenspaces. Diagonalization. Dot product. Vector product. Simmetric operators. Orthogonal operators. Spectral theorem.
Affine Geometry and Euclidean Geometry of the plane and space. Conics. Quadric surfaces.
Prerequisites
Notions of secondary school mathematics, e.g. numbers (natural, integer, rational, real), operations between numbers, elementary algebraic calculus, sets, elements of Euclidean geometry, and trigonometry.
Books
Geometria, Antonio Cigliola, La Dotta Editrice 2016
Exam mode
The following elements will be considered in the evaluation of the exam :
1. the logic followed by the student in solving the exercises in the written exam
2. the correctness of the procedure adopted for the solution of the exercises
3. the appropriateness of the proposed solution in relation to the skills that the student is expected to have acquired at the end of the course;
4. the acquired knowledge of the theoretical results described during the course, also taking into account the property of language and formalism in describing them.
Satisfaction of aspects #1 and #4 is a necessary condition for achieving a grade of 20. Grades above 24 will be awarded to students whose evidence satisfies all four aspects listed above.
- Lesson code10606929
- Academic year2024/2025
- CourseComputer and System Engineering
- CurriculumInformatica
- Year1st year
- Semester2nd semester
- SSDMAT/09
- CFU9
- Subject areaMatematica, informatica e statistica