Topic outline

  • General

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    • Faculty: Mathematics and Computer Science
    • Department: Mathematics
    • Target Audience: 1st year

    • Course title: Algebra One

    • Coefficient : 03

    • Instructor:  Dr Kheir Saadaoui
    • Contact : kheir.saadaoui@univ-msila.dz

  • Course objectives


    The objectives of this Algebra 1 course are to develop students' understanding of logical concepts, sets and functions, binary relations, and algebraic structures. Students will learn to construct logical statements, perform set operations, understand functions, analyze binary relations, and explore algebraic structures. This will enhance their problem-solving skills, mathematical reasoning, and communication of mathematical ideas.

  • Chapter one (Logical consepts)

    This chapter introduces the foundational principles of logic that are crucial for understanding and constructing mathematical arguments. Topics include statements, truth values, logical connectives (and, or, not), implications, biconditional statements, and logical equivalence

  • Chapter Two Sets and Functions

    In this chapter, we will explore the fundamental concepts of sets and functions, which are key to understanding algebraic structures. Topics include definitions and notation for sets, subsets, set operations (union, intersection, difference, complement), and the Cartesian product of sets. The chapter also covers functions, including the definition of a function, domain and range.

  • Chapter Three Binary Relations on a Set

    This chapter delves into binary relations, which describe how elements from one set relate to elements of the same or another set. Topics include the definition and types of binary relations (reflexive, symmetric, transitive, antisymmetric), properties of relations, equivalence relations and their equivalence classes, and partial orders.

  • Chapter Four Algebraic structures

    In this chapter, you will be introduced to various algebraic structures that form the backbone of algebraic theory. Topics include groups, rings, fields, and vector spaces.

  • policopy algebra1

  • Topic 8