Introduction to Algebraic Number Theory: Higher Mathematics (Linear & Abstract Algebra, Galois theory, Polynomials...)

In July 2019, I attended a class by Gabriel Dospinescu where he exposed a bit of algebraic number theory (roughly chapter 1 of this book). Amazed by what I had seen, the thought of writing a handout inspired by the content of Gabriel’s class crossed my mind. Two years later, I have finally finished crafting it. This book is intended to serve as a transition from high school math curriculum and math olympiads topics to higher mathematics, for high school or college students who are interested in learning more advanced and beautiful theory.

More than 350 problems and solutions are presented in the book to develop the mathematical intuition of the reader and give concrete worked examples of the exposed material. Ranging from topics like group, ring and field theory, to linear algebra, polynomials, and an introduction to Galois theory, the different chapters of this book expose the readers to a wide variety of algebra and number theory related topics, and immerse them in a beautiful journey through the world of higher mathematics.