Algebra 1 is a foundational branch of mathematics dedicated to studying abstract structures, operations, and the relations between elements. It provides the essential mathematical framework for describing structures, relations, and formal calculations across pure mathematics, applied sciences, and engineering. Designed for first-year undergraduate students, this course bridges the gap between high school arithmetic and abstract university-level mathematics.

About This Course

This course provides a clear, structured introduction to the core topics of first-year university algebra. It is organized into two primary chapters:

• Chapter 1: Sets, Relations, and Applications
  Master set operations, binary relations (equivalence relations, quotient sets, and order relations), mappings, domain properties, injectivity, surjectivity, bijectivity, and composite/inverse functions.
• Chapter 2: Complex Numbers
  Explore algebraic, geometric (Argand plane), trigonometric, and exponential representations of complex numbers. Learn to apply De Moivre's and Euler's formulas, compute square roots and n-th roots, and solve polynomial equations in ℂ.

Requirements

Students are expected to have a basic knowledge of:

• Fundamental algebraic operations with real numbers.
• Solving equations and inequalities.
• Basic notions of functions (domain, graph, and simple properties).
• Elementary set theory (sets, subsets, and operations).
• Basic geometric representation in the Cartesian plane.

Targeted skills

The Algebra 1 course aims to help students:

• Define and identify fundamental concepts related to sets, relations, functions, and complex numbers.
• Explain and distinguish the properties of relations and functions.
• Apply algebraic and set-theoretic operations in various mathematical contexts.
• Compute images, inverse images, and expressions involving real and complex numbers.
• Analyze and differentiate mathematical structures (equivalence relations, order relations, types of functions).
• Construct and formulate mathematical expressions and transformations.
• Justify and evaluate mathematical results and properties.

Course Staff

Dr. Chahrazed Boudefla
Dr. Chahrazed Boudefla is an assistant professor of mathematics at the University of Ain Témouchent, Faculty of Science and Technology, Department of Sciences of Matter. She holds a Ph.D. in Mathematics specializing in Functional Analysis and Differential Equations. She teaches foundational undergraduate courses in mathematics, focusing on making abstract algebraic concepts structured and accessible to students in science and technology.

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Do I need advanced prerequisites?
No. High school algebra and basic equation solving are sufficient to begin.