This book, which is intended for undergraduate courses or independent study, covers complex mathematical concepts in a clear and approachable way. This book’s main goal is to impart mathematical thinking while showcasing the grace and beauty of mathematics. The book is filled with several exercises of varying levels of difficulty, some of which are meant to help readers understand fundamental concepts better, while others will test almost all readers. Algebra in high school is the only prerequisite for reading this text. Mathematical induction, modular arithmetic, Fermat’s Little Theorem, RSA encryption, the Euclidean algorithm, rational and irrational numbers, complex numbers, cardinality, Euclidean plane geometry, constructibility (including a demonstration that a 60-degree angle cannot be trisected with a straightedge and compass), infinite series, and higher-dimensional spaces are some of the topics covered.
This textbook is appropriate for a wide range of courses and students studying math and other subjects. Senior high school students who enjoy math will also be able to read this book.