دانلود کتاب مقدمه ای دوستانه بر جبر انتزاعی

There are 37 chapters in the textbook. Depending on your students’ background and/or the structure of your algebra course, here are some suggested road maps: • Chapters 1 through 25 cover group theory. If students have had prior experience with proof writing, you may choose to omit Chapters 1 and 2. Similarly, students may have already studied the notion of divisibility (of integers), particularly if they have taken an introductory number theory course. In such a case, Chapter 3 may be skipped as well. I recommend not skipping Chapter 4 on modular arithmetic, however, since many group-theoretic concepts are introduced in that chapter. • Chapter 7 contains a brief introduction to matrices and covers matrix concepts that are needed in the textbook. If your students have had a linear algebra course, then Chapter 7 may be omitted or assigned to the students to read on their own as a refresher. • Chapters 26 through 37 cover ring theory, with an emphasis on polynomial rings. It is possible to end the course with Chapter 35, where we complete the proof of Theorem 35.1 (i.e., 𝐹[𝑥]/⟨𝑔(𝑥)⟩ is a field if and only if 𝑔(𝑥) is unfactorable). • Chapters 36 and 37 guide the students to prove Theorem 35.1 again using the notion of maximal ideals. It is a lovely proof, so I recommend its inclusion in your course, if time permits.