58414 - Algebra and Geometry

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

Modular arithmetic, congruence classes modulo n

Readings/Bibliography

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

Teaching methods

Lectures and exercises will be alternated in order to explain theoretical concepts through a large number of examples. Students will be asked to actively participate in the lessons, asking and answering questions.

Assessment methods

The exam consists of two written tests, the first containinig exercises and the second about theorethical issues. Both are compulsory and concern the whole program covered in the lectures.

The first written test lasts two and a half hours and has the aim of testing the ability of the student in solving exercises. It is not possible to make use of textbooks or personal notes, only one side of a sheet of paper size A4 is allowed, containing whatever formula the student thinks might be useful.

The theory exam lasts 30 minutes and aims to assess the student’s knowledge and understanding of the topics covered in the course, as well as their ability to present them coherently using specific terminology and correct mathematical formalism. Examples, counterexamples, and the demonstration of theorems will also be required. The theory exam will be corrected and discussed with the student on the same morning/afternoon in which it was taken, and may be complemented by a brief oral question.

The student can access the theory exam after passing the written exam with a score of at least 18/30. The theory exam must take place in the same session or in the following one, as long as it is within the same exam period (winter, summer, autumn). The schedule for the oral exams will be published together with the results of the first written exam.

The final result of the exam takes into account the outcomes of both exams, but it is not an arithmetic average, as the first exam carries decisive weight. If the final result of the exam is insufficient, both exams must be repeated. The student has the option to withdraw from each exam and to reject the final grade once.

Registrations for the exam sessions are done through AlmaEsami [https://almaesami.unibo.it/almaesami/welcome.htm ]

Registration for both exams is mandatory, and please note that registration closes 5 days before the scheduled date for the written exam.

It is necessary to present the university ID card at the exams.

Students with disabilities and Specific Learning Disorders (SLD)Students with disabilities or Specific Learning Disorders have the right to special accommodations according to their condition, following an assessment by the Service for Students with Disabilities and SLD. Please do not contact the teacher but get in touch with the Service directly to schedule an appointment. It will be the responsibility of the Service to determine the appropriate adaptations. For more information, visit the page:

https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students

Teaching tools

Exercises and samples of exam texts will be given.

Office hours

See the website of Marta Morigi