Algebra I, first part

Duration

30h Th, 25h Pr

Number of credits

Lecturer

Michel Rigo

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

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

• Algebraic structure of field - examples of R and C
  
• Permutations, their first properties (notion of a group), signature of a permuttion
  
• 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

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 linear algebra. 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

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

Planned learning activities and teaching methods

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)

The theoretical lectures are given on a three hours a week basis. The schedule will be communicated on the first day of the academic year. Theoretical lectures using "blackboard and chalk" interacting with students and recorded using "podcast" (students have later on access to recorded courses). During exercises sessions, students are facing exercises that must be solved.

Recommended or required readings

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

Assessment methods and criteria

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 in January consists of two parts: a written one and an oral one. The written part is about both theory and exercices: statement and proof of results, statement of definitions, reasoning, resolution of problems and exercises. The oral part is devoted to the theory but also includes direct applications of the theory. 

Work placement(s)

Organizational remarks

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

M. Rigo
Institut de Mathématique (B37) -
Grande Traverse 12 -
Sart Tilman, 4000 Liège
Tél. : (04) 366.94.87 -
E-mail : M.Rigo@ulg.ac.be

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