Tutorium Algebra

In an algebra lecture, the focus shifts from linear algebra to more abstract concepts. To assist students in understanding this abstract material, "Tutorium Algebra," a new volume in the tutorial series by authors Modler and Kreh, has been released. In this book, the authors explain the subject of algebra, with a primary focus on field theory, specifically Galois theory. The content is presented through clear and detailed worked examples. The concept remains tried and true: each chapter is divided into a mathematical section, which includes definitions, theorems, and proofs, and an explanatory section, where difficult definitions and theorems are presented in a relaxed and humorous manner, enriched with over 120 examples and about 30 illustrations. This way, the reader gains insight into mathematically precise formulations while also receiving aids and visualizations that are crucial for understanding the material. The book has been thoroughly revised, improved, and supplemented in its third edition. Notably, the chapter on rings and ideals includes some new examples (e.g., regarding the ring of holomorphic functions), and the localization of rings is discussed. Additionally, further criteria for the irreducibility of polynomials have been added.