73147 - Algebra and Geometry (1)

Learning outcomes

At the end of this course, students are supposed to have learnt some basic notions in abstract algebra (Euclidean algorithm and congruence relations) and in linear algebra. They will be able to solve linear systems and to study linear maps.

Course contents

Linear Systems

Matrices

Gaussian elimination

Real vector spaces and subspaces

Linear maps

Diaginalization of matrices

Orthogonality in R^n

Orthonormal bases

Orthogonl bases and spectral theorem

Modular arithmetic, congruence classes modulo n

Readings/Bibliography

Fioresi Rita, Morigi Marta, Introduzione all'algebra lineare, Edizioni CEA (2021)

Notes on https://virtuale.unibo.it/

Teaching methods

The course will alternate between theoretical lectures and practical exercises, with the aim of clarifying the theoretical concepts through examples. Students will be encouraged to participate actively in class by asking questions and providing answers.

Attendance is not mandatory; however, being present in the classroom is highly beneficial, as active participation in the lessons greatly facilitates the learning process.

Assessment methods

Student learning will be assessed through a final exam consisting of two written tests: a first written test focused on exercises, and a second written test consisting of theoretical questions (definitions, statements of main theorems, and possibly their proofs, if covered during lectures).
Both parts are mandatory and cover the entire content of the course.

The first written test lasts 2.5 hours and aims to evaluate the student’s ability to solve problems or provide brief reasoning on theoretical issues. Books and notes are not allowed, but students may use a personal formula sheet, limited to one side of an A4 sheet.

The theory test lasts 30 minutes and aims to assess the student's knowledge and understanding of the course material, as well as their ability to explain concepts coherently using appropriate terminology and correct mathematical formalism. Examples, counterexamples, and proofs of theorems will be required. The theory test will be graded and discussed with the student on the same day it is taken and may be supplemented by a short oral question if needed.

Students may access the theory test only after having passed the written test with a minimum score of 18/30. The theory test must be taken during the same exam session (winter, summer, or autumn), either in the same sitting or in the following scheduled sitting. The oral schedule will be published along with the results of the first written test.

The final grade takes into account the results of both parts, but it is not a simple average: the written test carries greater weight in the final evaluation. If the overall result is insufficient, both tests must be repeated. Students may withdraw from either test and may reject the final grade once.

Exam registration must be completed through AlmaEsami: [https://almaesami.unibo.it/almaesami/welcome.htm ]
Registration is mandatory for both tests and closes 5 days before the date of the written exam.

Students must present their university ID card to take the exam.

Students with Disabilities and Specific Learning Disorders (SLD)
Students with disabilities or specific learning disorders are entitled to special accommodations based on their condition, subject to assessment by the University Service for Students with Disabilities and SLD. Please do not contact the instructor directly. Instead, students should book an appointment with the Service, which will determine any necessary accommodations.
More information is available at:
https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students

Teaching tools

Exercise sheets and exam samples will be provided.

Occasionally, quizzes will be administered using Wooclap.

Office hours

See the website of Marta Morigi