### Duration

Introduction à l'enseignement universitaire de l'algèbre : 10h Th, 5h Pr

Matrix calculation : 30h Th, 25h Pr

### Number of credits

Bachelor in physics | 7 crédits |

### Lecturer

Introduction à l'enseignement universitaire de l'algèbre : Michel Rigo

Matrix calculation : Michel Rigo

### Coordinator

### Language(s) of instruction

French language

### Organisation and examination

Teaching in the first semester, review in January

### Schedule

### Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

### Learning unit contents

#### Introduction à l'enseignement universitaire de l'algèbre

This part prepares students for the algebra course. The aim is to introduce the complex numbers and apply the main proof techniques.

#### Matrix calculation

The course is dedicated to matrix computations and the study of finite dimensional linear algebra. We present:

- Algebraic structure of the fields of real and complex numbers

- Matrices with coefficients in a field (of zero characteristic), operations, product, determinant, inverse, rank, ...

- Systems of linear equations, structure of the solutions, compatibility

- Introduction to vector (or linear) spaces

### Learning outcomes of the learning unit

#### Introduction à l'enseignement universitaire de l'algèbre

At the end of this part, the student will be able to handle complex numbers, the summatory symbol, etc. with ease.

#### Matrix calculation

At the end of this course, the student should have mastered the rigor of mathematical reasoning and a strong ability to grasp abstract structures and concepts arising in matrix calculus and vector spaces. He/she will be able to give arguments about his/her assertions.

The student will have at his/her disposal a set of deeply understood theoretical results for which he/she will be able to give a proof. He/she will be able to arrange several results from the course to solve an exercise. The student will easily manipulate and work with classical matrix computations, study the compatibility of a system, give a base of a vector space, etc.

In particular, the student will master the notions of linear algebra needed for the study of affine geometry or linear maps between vector spaces.

### Prerequisite knowledge and skills

#### Introduction à l'enseignement universitaire de l'algèbre

Perfect knowledge from secondary school is expected. Being trained to abstraction and mathematical reasoning is an advantage.

#### Matrix calculation

Perfect knowledge from secondary school is expected. Being trained to abstraction and mathematical reasoning is an advantage. Students should master complex numbers, mathematical proofs and logic as presented in the part "Mathématiques élementaires".

### Planned learning activities and teaching methods

#### Introduction à l'enseignement universitaire de l'algèbre

The practical sessions are mainly dedicated to solve exercises corresponding to the theory considered during the lecture sessions. These sessions are also useful to obtain extra informations or enlightenments on the concepts presented during the lecture sessions. The schedule will be communicated on the first day of the academic year.

Moreover, the preparation of lists of exercises for the next practical session will be systematically asked .

#### Matrix calculation

The practical sessions are mainly dedicated to solve exercises corresponding to the theory considered during the lecture sessions. These sessions are also useful to obtain extra informations or enlightenments on the concepts presented during the lecture sessions. The schedule will be communicated on the first day of the academic year.

Moreover, the preparation of lists of exercises for the next practical session will be systematically asked .

### Mode of delivery (face to face, distance learning, hybrid learning)

#### Introduction à l'enseignement universitaire de l'algèbre

Face-to-face course

*Additional information:*

The theoretical lectures are given on a three hours a week basis. The schedule is available on-line. Theoretical lectures using "blackboard and chalk" interacting with students and recorded using "podcast" (students have later on access to recorded courses).

#### Matrix calculation

Blended learning

*Additional information:*

The theoretical lectures are given on a three hours a week basis. The schedule is available on-line. Theoretical lectures using "blackboard and chalk" interacting with students and recorded using "podcast" (students have later on access to recorded courses). A pre-recorded version is also available. During exercises sessions, students are facing exercises that must be solved. Depending on the evolution of the health situation, distance learning videos and question/answer sessions in the classroom could also be considered.

### Recommended or required readings

#### Introduction à l'enseignement universitaire de l'algèbre

Lecture notes are available (in french) and can be downloaded from http://www.discmath.ulg.ac.be/

#### Matrix calculation

Lecture notes are available (in french) and can be downloaded from http://www.discmath.ulg.ac.be/

### Assessment methods and criteria

**Any session :**

- In-person

written exam

- Remote

written exam

- If evaluation in "hybrid"

preferred in-person

*Additional information:*

See the component "calcul matriciel".

#### Introduction à l'enseignement universitaire de l'algèbre

**Exam(s) in session**

Any session

- In-person

written exam ( open-ended questions )

*Additional information:*

**Exam(s) in session**

Although the examination relates to the material coverede by the algebra course (MATH0069), it will be assumed that the student is able to handle expressions involving complex numbers with ease.

#### Matrix calculation

**Exam(s) in session**

Any session

- In-person

written exam ( open-ended questions )

*Additional information:*

A test is organized during the year. This test should help students to evaluate themselves. Bad results to those tests are not taken into account but constitute a serious reminder.

The *examination* is a written one. It is about both theory and exercices: statement and proof of results, statement of definitions, reasoning, resolution of problems and exercises. A serious deficiency in one of the two parts will penalise the final mark.

First-year students failing during the January session have the opportunity to represent the exam during the May/June session. Any student who has not acquired credits for the course may represent it during the August/September session.

### Work placement(s)

### Organisational remarks and main changes to the course

#### Introduction à l'enseignement universitaire de l'algèbre

Some useful informations are given on http://www.discmath.ulg.ac.be/ In particular, one has access to the log of the year and also the ones of previous years.

#### Matrix calculation

Some useful informations are given on http://www.discmath.ulg.ac.be/ In particular, one has access to the log of the year and also the ones of previous years.

### Contacts

#### Introduction à l'enseignement universitaire de l'algèbre

M. Rigo Institut de Mathématique (B37) - Allée de la découverte 12 - Sart Tilman, 4000 Liège Tél. : (04) 366.94.87 - E-mail : M.Rigo@uliege.be

#### Matrix calculation

M. Rigo Institut de Mathématique (B37) - Allée de la découverte 12 - Sart Tilman, 4000 Liège Tél. : (04) 366.94.87 - E-mail : M.Rigo@uliege.be

### Association of one or more MOOCs

### Items online

#### Matrix calculation

Notes de cours

ensemble des notes