First semester

This Algebra course provides a comprehensive introduction to the foundational concepts of mathematical logic, set theory, and functions. It is designed to build essential problem-solving skills and develop a deep understanding of abstract mathematical reasoning. The course is divided into three key chapters:

Mathematical Logic and Reasoning
This chapter introduces students to the principles of mathematical logic, focusing on propositions, truth tables, and logical equivalence. The emphasis is on formal reasoning techniques, including proof methods such as direct, indirect, and proof by contradiction, enabling students to approach mathematical statements with rigor.

Set Theory and Binary Relations
Students explore the concept of sets, including operations such as union, intersection, and complement. The chapter covers Venn diagrams, Cartesian products, and introduces binary relations and their properties like reflexivity, symmetry, and transitivity. This lays the groundwork for understanding more complex structures in algebra.

Functions
The final chapter delves into the concept of functions, including one-to-one, onto, and inverse functions. Students will learn to work with function notation, perform function composition, and explore the properties of different types of functions such as polynomial, exponential, and logarithmic.