Algebra

This course is for the student of the first year preparatory classes of the national higher school of mathematics. The main objective of this course is to provide students with a basic knowledge of algebra, This course details chapters for students on logic (methods of reasoning) and set theory, Binary relations and applications (mappings), algebraic structures, Polynomials and rational fractions, vectors spaces. These chapters will familiarize the student with mathematical formalism in order to develop clear, structured, and rigorous reasoning that can be applied in complex situations. The main objective is to : Understand and apply fundamental concepts of mathematical logic, including logical statements and truth tables. Perform operations on sets and use set theory to represent and solve problems. Analyze and interpret binary relations, including their properties and classifications. Identify and describe different types of functions, including injective, surjective, and bijective functions. Explore and work with basic algebraic structures such as groups and rings. Develop mathematical reasoning, problem-solving abilities, and the ability to clearly communicate mathematical ideas.