Introduction to Abstract Algebra — E-Book

Abstract algebra is an essential tool in algebra, number theory, geometry, topology, and, to a lesser extent, analysis. It is therefore a core requirement for all mathematics majors. Outside of mathematics, abstract algebra also has many applications in cryptography, coding theory, quantum chemistry, and physics. This book is intended as a textbook for a one-term senior undergraduate or gradate course in abstract algebra to prepare students for further readings on relevant subjects such as Group Theory and Galois Theory. Abstract algebra being the field of mathematics that studies algebraic structures such as groups, rings, fields, and modules, we will primarily study groups, rings, and fields in this book. The authors invite readers to experience the beauty of mathematics by studying Abstract algebra which offers not only opportunities to work on complex concepts and to develop one’s abstract reasoning abilities, but also a preliminary understanding of what it is like to do research in mathematics.