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Algebre 1

ECOLE Sup Informatique - IA et Mathématiques( intelligence artificielle) L1 · PREMIÈRE ANNÉE L1

5 chapitres · 12 séances · 41 vidéos · 3 textes · 9 PDF · 1 quiz

Description à venir.

Accéder à ce module Cours vidéo, TD, PDF et quiz — accès après inscription.

Au programme

  1. Chapter 1 : Logic and Sets

    Par Mr Abdelmalek

    Algebra 1 – Chapter 1: Logic and Set Theory This chapter introduces the fundamental concepts of mathematical logic and set theory, which form the basis of rigorous mathematical reasoning and proof.

    • Cours 1
      • TexteDetails
      • PDFChapter 1
      • PDFChapitre 1 (fr)
      • VidéoPart 1
      • VidéoPart 2
      • VidéoPart 3
      • VidéoLogic Concepts Part 3
      • VidéoLogic Concepts Part 4
      • QuizQuiz 1
    • TD 1
      • VidéoTD 1 Part 1
      • VidéoTD 1 Part 2
      • VidéoTD1 Part 3
      • VidéoTD1 Part 4

  2. Chapter 2 : Sets and Functions

    Par Mr Abdelmalek

    In this chapter, we introduce the fundamental concepts of **sets and functions**, which are essential tools in algebra and mathematics. We will study set notation, subsets, operations on sets, Cartesian products, and relations. We will then explore functions, including their definitions, domain, codomain, image, and preimage, as well as injective, surjective, and bijective functions. The chapter also covers composition of functions and inverse functions, with examples and exercises to develop a clear understanding of these concepts and their applications.

    • cours
      • TexteSets and Functions
      • PDFChapter 2 : Sets and Functions
      • VidéoChapter 2 Part 1
      • VidéoChapter 2 Part2
      • VidéoChapter 2 Part 3
      • VidéoChapter 2 Part 4
    • cours (version 2)
      • TexteChapter 2: Sets and Functions
      • PDFChapter 2: Sets and Functions
      • VidéoPart 1
      • VidéoPart 2
      • VidéoPart 3
      • VidéoPart 4
    • suite cours
      • VidéoPart 5
      • VidéoPart 6
      • VidéoPart 7
      • VidéoPart 8
      • VidéoPart 9
    • TD 2
      • PDFTutorial Sheet 2
      • VidéoTD 2 Part 1
      • VidéoTD 2 Part 2
      • VidéoTD 2 Part 3
      • VidéoTD 2 Part 4
    • TD 2 (suite)
      • VidéoTD 2 Part 5
      • VidéoTD 2 Part 6
      • VidéoTD 2 Part 7

  3. Binary Relations on a Set

    Par Mr Abdelmalek

    ### Chapter Description This chapter introduces **binary relations on a set**, a fundamental concept in discrete mathematics. Students will learn how to define, represent, and analyze relations between elements of a set, and how to determine their important properties. The chapter also develops the concepts of equivalence relations and order relations, which are essential for understanding mathematical structures and classifications. ### Contents 1. **Introduction to Binary Relations** * Definition of a binary relation * Relation on a set *Representations of Relations** 2. **Properties of Relations** * Reflexivity * Symmetry * Antisymmetry * Transitivity 3. **Types of Relations** * Equivalence relations * Partial order relations * Total order relations 4. Equivalence Relations * Definition and examples * Equivalence classes 5**Order Relations *Partial orders *Comparable and non-comparable elements Applications and Exercises

    • cours
      • PDFBinary relations
      • VidéoPart 1
      • VidéoPart 2
      • VidéoPart 3
    • TD 3
      • PDFTutorial Sheet 3
      • VidéoTD 3 Part 1
      • VidéoTD 3 Part 2

  4. Algebraic Structures

    Par Mr Abdelmalek

    ### Chapter Description This chapter introduces the fundamental concepts of **algebraic structures**, which provide a framework for studying sets equipped with one or more operations. Students will learn how algebraic operations are defined and how their properties lead to different structures such as semigroups, monoids, groups, and rings. The chapter emphasizes definitions, properties, examples, and the relationships between these structures. ### Contents 1. **Binary Operations** * Definition of a binary operation * Properties of binary operations * Examples 2. **Algebraic Structures** * Definition of an algebraic structure * Closure, associativity, commutativity * Identity elements * Inverse elements 3. **Groups** * Definition of a group * Abelian (commutative) groups * Subgroups * Examples 4. **Rings** * Definition of a ring * Commutative rings * Rings with unity * Examples 5. **Fields** * Definition of a field * Properties

    • cours
      • PDFAlgebraic Structures
      • VidéoPart 1
      • VidéoPart 3

  5. Vector Spaces

    Par Mr Abdelmalek

    This chapter introduces the fundamental concepts of **vector spaces**, an essential topic in linear algebra. Students will learn the definition and properties of vector spaces, subspaces, linear combinations, and generating sets. The chapter also develops the concepts of linear independence, bases, and dimension, providing the foundations needed to study linear transformations and more advanced topics in linear algebra. ### Contents 1. **Vector Spaces** * Definition of a vector space * Basic properties of vectors 2. **Subspaces** * Definition of a subspace * Subspace criteria 3. **Linear Combinations and Span** * Linear combinations of vectors * Span of a set of vectors * Generating sets * Applications and examples 4. **Linear Independence** * Definition of linear independence * Linear dependence 5. **Bases of Vector Spaces** * Definition of a basis * Existence 6. **Dimension** * Definition of dimension * Dimension of a vector space

    • cours
      • PDFVector Spaces
      • VidéoPart 1
      • VidéoPart 2
      • VidéoPart 3
      • VidéoPart 4
    • cours
      • Vidéovid1

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