Advanced Algebra I serves as the foundational course for the mathematics curriculum, introducing the rigorous language and logical structures used throughout higher mathematics. The course begins with Set Theory and the formal definition of functions and relations, providing the essential vocabulary for all subsequent mathematical study.
A central component of the course is the study of the natural numbers and the Principle of Mathematical Induction, a fundamental tool for rigorous proofs. We also explore combinatorial analysis, including permutations, combinations, and the Binomial Theorem, establishing a strong background in discrete mathematics.
The final part of the course introduces the core concepts of Linear Algebra within the context of $\mathbb{R}^n$. Students learn about vector spaces, subspaces, linear independence, and bases, as well as the theory of matrices, determinants, and methods for solving systems of linear equations.
This document compiles selected notes and examples developed during the course. While not intended as a comprehensive textbook, these materials provide detailed explanations of key topics and are designed to serve as a robust supplementary resource for students.
As with the notes, this section contains a compilation of various homework assignments and problem sets. Although they do not follow a unified structure, they may serve as valuable practice material for anyone who wishes to reinforce their understanding of the topics covered in the course.
