Math 120 - Modern algebra - Fall 2011

Writing in the Major The assignment is to present a short (4-7 pages), readable and complete proof of the Fundamental Theorem of Finite Abelian Groups. The theorem is discussed in Section 5.2 (and in fact a more general form, the fundamental theorem for finitely generated abelian groups, is discussed there). A proof is sketched at the end of section 6.1, and there is enough there for you to work out a complete proof.

Target audience You should write your text for someone at a similar stage in a similar class (for example, someone in class who have not yet read this section. Ideally by someone in a similar class using a different textbook). The emphasis in this assignment is on the presentation (so don't think of this as "solving an exercise", or "finding the solution").

Do: Write whole sentences in proper English. Make sure you define your notation ("Let G be a group and H a subgroup"...). Begin your text with a less technical introduction: What does the theorem say, why is it interesting, how does it fit into the rest of the mathematics, etc (if this were a chapter in a book, the reader should be able to read just this introduction and get an idea of what's going to happen). Proof read! (and maybe ask someone else to proof read too). When you proof read, try to imagine you're someone else who didn't just write the text (can be difficult), and notice which parts which are difficult to comprehend.

Don't: Use abbreviations or unnecessary symbols (you won't need symbols for "for all", "exists", "implies", "therefore").

Deadlines Submit a draft for comments November 8th. Final text due November 29th.