2020-2021 / MATH0073-1

Elementary mathematics

Part 1

Part 2

Duration

Part 1 : 10h Th, 5h Pr
Part 2 : 20h Th, 25h Pr, 15h Mon. WS

Number of credits

 Bachelor in mathematics7 crédits  

Lecturer

Part 1 : Julien Leroy
Part 2 : Julien Leroy

Coordinator

Julien Leroy

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

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.


 

Part 2

This course is introduced at the begining of the studies in mathematics in order to make the transition from the secondary school to the Univesrity easier, and therefore help the students to pass the exams of the first year.
We will review some concepts of common use in the secondary school but we will get a deeper understanding of this concepts, by focusing on the logical links between the concepts and on the proofs, rather than on the computation methods.
This component is a continuation of the first component of "Mathématiques élémentaires", which contains concepts of Boolean logic and naive set theory. These concepts are used to deduce some techniques to write proofs.
In this component, we will review basic concepts of number theory, from the natural numbers to the rational numbers and we will review some basics of combinatorics and trigonometry.
We will also review important concepts of analysis and geometry, and see on concrete examples hgow to write down, read and study texts of mathematics.
 

Learning outcomes of the learning unit

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.

Part 2

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 also be able to write down proofs of new properties related to the course contents.

Prerequisite knowledge and skills

Part 1

None

Part 2

None

Planned learning activities and teaching methods

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.

Part 2

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.
Several tests will be organized during the smester in order to encourage the students to work regularly.
The students will also be asked to solve exercises online on the wims platform.

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

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.

Part 2

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.

Organisational adjustments related to the current health context

Recommended or required readings

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.

Part 2

The documents are available on my web page
http://www.discmath.ulg.ac.be/leroy/Teaching-fr.html

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

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.

Part 2

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, but a part of the grade for this exam will be obtained during the online exercises sessions.
 
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 score on WIMS will counts for 10% of the final score.
The schedule of the exam is set by the conseil des études en mathématiques.

Work placement(s)

Organizational remarks

Contacts

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

Part 2

Julien Leroy
Institut de mathématique Quartier Polytech Allée de la découverte, 12, Bâtiment 37 4000 Liège
Téléphone: 04/366 94 70 Email : J.Leroy@uliege.be

Items online

Part 1

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