Algebra 1 

Prerequisites:

Basic mathematical knowledge from final high school classes (sets, functions, equations, etc.).

Course Objectives:

This first course in Algebra I is mainly devoted to standardizing students’ mathematical knowledge at the beginning of university. The new concepts are introduced progressively to guide students toward more advanced mathematics. The notions covered in this subject are fundamental and among the most commonly used in the fields of Science and Technology.

Course Content:

Chapter 1: Sets, Relations, and Functions (5 weeks)

1. Set theory.

2. Order relations, Equivalence relations.

3. Injective, surjective, bijective functions and inverse functions: definition of a function, direct image, inverse image, and properties of a function.

Chapter 2: Complex Numbers (5 weeks)

1. Definition of a complex number.

2. Representation of a complex number: algebraic form, trigonometric form, geometric representation, exponential form.

3. Roots of a complex number: square roots, solving the equation a*z² + b*z + c = 0, n-th roots of a complex number.

Chapter 3: Vector Space (5 weeks)

1. Vector space, basis, dimension (definitions and elementary properties).

2. Linear mapping, kernel, image, rank.

Dr . Bencheikh Abdelkrim

krimbench@yahoo.fr