Algebra

Elementary mathematics, Part 1

This course component is given both to students in Mathematics and in Physics.
The course contains concepts of Boolean logic and naive set theory. These are used to deduce some proof techniques. We will review elementary theory of complex numbers and summation symbols. We will prove a few famous formulas, as a matter of illustration.


 

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

Elementary mathematics, Part 1

The topics that are considered here ar of fundamental interest for both students in mathematics and in physics.
At the end of the series of lectures, the students will have a deep knowledge of the course contents. They will know the proofs of the theory that is exposed in the lectures and will be able to explain them in full detail.
They will be able to use techniques learnt in this course to produce valid arguments and will be able to compute with complex numbers.

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 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.

Elementary mathematics, Part 1

None

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".

Elementary mathematics, Part 1

The theroy is explained in lectures of classical type (ex cathedra). However, students are most often required to make exercises during the lectures, on the concepts that are explained.
The lectures are followed by exercises sessions where personnal work is mandatory.
  Online exercise sessions can be proposed to the students during the semester.

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 .

Elementary mathematics, Part 1

The theory will be given online through videos (podcasts). Question and answer sessions will also be organized in face-to-face.
Exercise sessions will organized in face-to-face.
Some exercises will also be organized online on WIMS.

Matrix calculation

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). 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.

Matrix calculation

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Elementary mathematics, Part 1

The lecture notes are available on my web page
http://www.discmath.ulg.ac.be/leroy/Teaching-fr.htmlwww.geodiff.ulg.ac.be
They can also be ordered at the secretariat of the department of mathematics.

Matrix calculation

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

Elementary mathematics, Part 1

Any session :

- In-person

written exam ( open-ended questions )

- Remote

written exam ( open-ended questions )

- If evaluation in "hybrid"

preferred in-person


Additional information:

As usual in mathematics, there will be a theory part in the exams. Students will be asked to explain a part of the theory that is explained during the lectures. A deep understanding is required, obviously. This part will be asessed in a written or oral exam, depending on the possibilities in the schedule of the exams.
There will also be a part of the exam devoted to the exercises. This will be a written exam.
The final grade is a certain average of the grades obtained in both parts. However, a grade less than or equal to 6/20 at one of the parts will lead to a final grade less than 10/20.
The schedule of the exam is set by the conseil des études en mathématiques/ and or CE en Physique.
In mathematics, this course component is a part of the"Mathématiques élémentaires", and the evaluation will be merged with the evaluation of this course.The score obtained on WIMS counts for 10% of the final score.
In Physics, it is a part of Algèbre I, and the evaluation will be merged with the one of Algèbre I.

Matrix calculation

Any session :

- In-person

written exam ( open-ended questions )

- Remote

written exam ( open-ended questions )

- If evaluation in "hybrid"

preferred in-person


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.
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.

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.

Elementary mathematics, Part 1

Julien Leroy
Institut de mathématique Quartier Polytech, Allée de la découverte 12, Bâtiment B37 4000 Liège
Téléphone: 04/366 94 70 Email: J.Leroy@ulg.ac.be

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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

Elementary mathematics, Part 1

Notes
Lecture notes will be set on my webpage as soon as they are ready.

Matrix calculation

Notes de cours
ensemble des notes