28570 - Geometry and Algebra T-A

Learning outcomes

Knowledge of fundamental methods in Linear Algebra and in Analytic Geometry

Course contents

Requirements/Prior knowledge

A prior knowledge and understanding of symbolic computation, plane analytic geometry and Euclidean geometry is required to attend with profit this course.

Fluent spoken and written Italian is a necessary pre-requisite: all lectures and tutorials, and all study material will be in Italian.

 

Course contents

Set Theory:

Operations with sets, partitions, applications. Algebraic structures.

Analytic Geometry:

Cartesian coordinates on the line, the plane and 3-space. Geometric loci, equations (cartesian or parametric) of lines and planes in 3-space. Planes and lines in 3-space, equations, parallelism, ortogonality.

Linear Algebra:

Vector spaces, linear dependence, generators and bases. Dimension and subspaces.
Linear systems . Matrices - Row reduction - rank of a matrix - Theorem of Rouché-Capelli . Determinant -linear transforms - Base change.
Eigenvalues and eigenvectors - Diagonalizing matrices.
Metric spaces, scalar product- Norm - Orthonormal Bases

Readings/Bibliography

Gimigliano A., Bernardi A.,  Algebra lineare e geometria analitica, Città Studi,  Torino,  2018. 
 

Teaching methods

Front Lessons for part of the students (in turns), all the lessons will be followed by the other students in streaming on line. 

Assessment methods

Achievements will be assessed by the means of a final exam. This is based on an analytical assessment of the "expected learning outcomes" described above.

In order to properly assess such achievement the examination is composed of two different sections: a written session, which consist of a test (duration two hours), composed of several questions (both about the Algebra part, one about Analytic Geometry in space); to be eligible to take the oral exam the student must score in the written test a minimum total of 15 points (out of 30).

The oral session, consists of: a review of the written output, in which examiners inform the student on grading criteria, and receive any student appeal supported by appropriate and explanation; a conversation (starting with a subject chosen by the candidate) about the theory introduced in the course.

The structure of these sessions will be online, on EOL + Zoom for the written test, on Teams for the oral exams.

Higher grades will be awarded to students who demonstrate an organic understanding of the subject, capability to demonstrate theorems, and a clear and concise presentation of the contents .

To obtain a passing grade, students are required to at least demonstrate a knowledge of the key concepts of the subject, some ability for exercises and examples, and a comprehensible use of technical language.

A failing grade will be awarded if the student shows knowledge gaps in key-concepts of the subject, inappropriate use of language, and/or logic failures in the analysis of the subject.

The exam is part of the exam of "Analisi Matematica e Geometria e Algebra", together with the module of "Analisi Matematica". The final mark will be the avarage between the two marks. If at the end of the academic year (September) only the exam of one of the two modules will be given, the mark obtained will be cancelled. 

Teaching tools

On the web site:
http://www.dm.unibo.it/matematica/
There are web pages dedicated to Linear Algebra and Geometry in 3-space, with many excercises.

On the IOL website you can find examples of text for the past written exams

Links to further information

http://www.dm.unibo.it/~gimiglia

Office hours

See the website of Alessandro Gimigliano