Elementary mathematics

Duration

30h Th, 30h Pr, 15h Mon. WS

Number of credits

Lecturer

Pierre Mathonet

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

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.
The course contains concepts of Boolean logic and naive set theory. These are used to deduce some techniques to write proofs. We will review number theory, from the natural numbers to the complex numbers and we will review some basics of combinatorics, as a matter of illustration.
We will 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

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

None

Planned learning activities and teaching methods

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 test will be organized during the smester in order to encourage the students to work regularly.

Mode of delivery (face-to-face ; distance-learning)

It's a face to face mode of delivery.

Recommended or required readings

The lecture notes are available on my web page
www.geodiff.ulg.ac.be
They can also be ordered at the secretariat of the department of mathematics.

Assessment methods and criteria

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.

Work placement(s)

Organizational remarks

Contacts

For theory and exercices, feel free to contact me by email (see below) to make an appointment or come to my office : Email : P.Mathonet@ulg.ac.be Phone : +32(0)4/366.94.80 Department of Mathematics, Allée de la Découverte, 12, B37, 4000 Liège Belgium Office 0/27.
You can also contact Mr. J. Leroy, by e-mail, or at his ofice (building B37).

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