Weekly outline

  • Course Summary

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    This course is intended for first-year ST (L.M.D) students. The objective is to establish an essential general foundation for further studies in the coming years, by acquiring basic mathematical formalisms in analysis and algebra, along with their applications. The course is divided into a set of learning units that not only provide you with the opportunity to develop qualifications in mathematics but also, and most importantly, to acquire the necessary skills to pursue other modules, which are primarily based on mathematics, such as physics and chemistry. This module will enable students to:

    • Discover the main logical operators and their characteristics.
    • Know how to properly structure a mathematical reasoning.
    • Acquire knowledge about sets, functions, and relations.
    • Enhance the understanding of continuous and differentiable functions addressed in previous years.

    Course Information

    • Course title: Mathematics 1 ‘Algebra’
    • Target audience: 1st year Science and Technology degree (LMD)
    • Teaching unit code: Fundamental EU
    • Credit : 06
    • Coefficient: 03
    • Duration : 15 weeks
    • Hourly volume : 67h et 30 min (3 hours lessons and 1 hour 30 minutes of tutorial per week)
    • Evaluation type:  continuous control 40% and Final exam 60%


    •                              Description image

  • Information card

    TD : Dr. Ikram BOUCETTA

    Université : Mohamed Khider Biskra

    Faculté : Science et Technologie

    Département : Génie Electrique

    Contact : par mail au ikram.boucetta@univ-biskra.dz

    Disponibilité :

    Au département : Lundi et jeudi de 8 :00 -11 :00, salle ‘1’


                                       Dr



  • Target skills

    This course allows students to acquire and deepen their knowledge of mathematics,
    ensure the progressive transition to higher education considering the high school
    programs, which it consolidates and expands, and training of students in the areas
    of logic, reasoning, and calculation techniques which are essential tools both in
    mathematics and in other scientific disciplines.
    At the end of this course ‘Mathematics _Algebra' the student will be able to:
    _ Define and explain the logic operators, the quantifiers, and their properties.
    _ Identify the types of the mathematical reasoning.
    _ Explore fundamental properties of sets, applications, and relations.
    _ Apply the concepts of continuous and differential functions in depth.
    _ Define the most important properties of common functions.
    _ Analyze and calculate Taylor expansion series.

                                     TARGET 

  • Prerequisites

    Prerequisites 

    To be able to successfully complete this course (math 1), you must have
    mathematics skills at the level of the last year of secondary education before
    starting the module.
    _ a solid understanding of basic arithmetic operations.
    _ understanding the concepts of sets, inclusions, union, and intersection
    is often necessary.

     
     In the event that the student fails the prerequisites  exam, he must refer to this link to review the information


                                   prerequeste

  • course outlines

    Le cours comporte cinq unités d'apprentissages (chapitres)

    Chapitre 1 : Logique et raisonnement

    Chapitre 2 : Ensemble, relations et applications

    Chapitre 3 : Les fonctions réelles d’une variable réel

    Chapitre 4 : Les fonctions usuelles

    Chapitre 5 : Développement limité

    Mind map



  • Chapter 1:Logical and Proof Mathematics

    Specific Objectives

    At the end of this chapter the student will be able to:
    - Define the main operators, the quantifiers, and their properties: not, and, or
    - Identify the reasoning by the direct proof, Contrapositive proof, proof by contradiction, proof by induction.
    - Apply all these notions to the mathematical demonstration.

                                      LOGIC

  • Chapter 2: Sets, Relation, and Applications

    Specific Objectives
    At the end of this chapter the student will be able to:

    - Identify the uses of sets, applications, and relations.
    - Define set notations and operations such as union, intersection, and complementary.
    - Explore fundamental properties of sets, such as transitivity, reflexive, and symmetry.

     
                           Sets

  • Chapter 3: Real Functions of a real variable

  • Chapter 4: Application to elementary functions

  • Chapter 5: limited Development '' Taylor Series'

  • Final Test

                            final test

  • Bibliographic references


    • Bibliography

      - C. Degrave et D. Degrave, Algèbre 1ère année : cours, méthodes, exercices résolus, Bréal. 2003.

      - S. Balac et F. Sturm, Algèbre et analyse : cours de mathématiques de première année avec exercices corrigés,
      Presses Polytechniques et Universitaires romandes, 2003

      - Laurent, A. (2009). Infz21, logique du raisonnement valide. Consulté sur https://laurent-audibert.developpez.
      com/Cours-Logique/

      - Alain Louveau, Christian Rosendal,''Complete analytic equivalence relations''. Comptes Rendus de l'Académie
      des Sciences - Series I – Mathematics. Volume 333, Issue 10, November 2001, Pages 903-906.https://doi.org
      /10.1016/S0764-4442(01)02160-7

      - J. Franchini et J. C. Jacquens, Algèbre : cours, exercices corrigés, travaux dirigés, Ellipses, Paris, 1996.

      - M. Mignotte et J. Nervi, Algèbre : licences sciences 1ère année, Ellipses, Paris, 2004.

      - J-M. Monier. Algèbre MPSI. Dunod,2006.

      - M. Mehbali. Mathématiques. Offices des publications universitaires, 2000.


                          reference


    • Web- bibliography

      https://www.math.sciences.univnantes.fr/~pajitnov/home_page/teaching/formar/ch1.pdf

      https://doi.org/10.1016/S0764-4442(01)02160-7


  • Evaluation Grid