{"id":2241,"date":"2018-02-18T16:11:42","date_gmt":"2018-02-18T21:11:42","guid":{"rendered":"http:\/\/blogs.ams.org\/phdplus\/?p=2241"},"modified":"2018-02-19T13:42:29","modified_gmt":"2018-02-19T18:42:29","slug":"rings-first-abstract-algebra-yes-three-and-a-half-weeks-yes-recovery-in-progress","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/phdplus\/2018\/02\/18\/rings-first-abstract-algebra-yes-three-and-a-half-weeks-yes-recovery-in-progress\/","title":{"rendered":"Rings first Abstract Algebra? Yes. Three and a half weeks? Yes. Recovery? In progress."},"content":{"rendered":"
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Another year, another D4 table. Or D8 table, if you prefer.<\/p><\/div>\n

You may (or may not) have noticed that I have been totally absent from PhD Plus Epsilon for the last 6 weeks. If saw my office right now, you\u2019d definitely notice that it looks like someone ransacked the place and threw an alarming amount of paper, books, and chalk dust on every surface.\u00a0 What happened? (You may or may not ask.) The answer is that for the last month*<\/a>, I have been teaching Abstract Algebra out of a new book and that\u2019s pretty much the whole story. I am the one who ransacked my office, slowly, one hurried search for keys and dash to class at a time. I am the one who assigned the homework\u2014fair, at only one submitted problem per chapter\u2014but also mind boggling: 27 TeXed proofs in 3 weeks from 25 students.\u00a0 I am the one who effectively disappeared the last month of my life.\u00a0 However, from this end, it was definitely worth it. And if you read no further, know that I am convinced that rings first really works for Abstract Algebra. \u00a0I have been converted, at least for now.<\/p>\n

I have taught Abstract Algebra three times before, so this probably wouldn\u2019t have been such a rollercoaster if I had just used my materials and plans from the last several iterations.\u00a0 But my colleague Marlow Anderson is (with Todd Feil) the author of \u201cA First Course in Abstract Algebra: Rings, Groups, and Fields\u201d <\/a>(AFCIAA).\u00a0 Marlow is teaching Abstract Algebra II out of the book in the coming month, and it seemed like a good idea to use the same book for the first course.\u00a0 AFCIAA begins with the integers: how do they work, and what is so great about them? \u00a0The first 5 chapters cover well ordering, integer division and the Euclidean algorithm, and introduce polynomials over the integers, rationals, and complex numbers. This provides a natural setting to see how the ideas of factorization, irreducibility, and primeness generalize from the integers to new settings.\u00a0 In chapter 6, we are introduced to the definition of a ring, and the next 10 chapters cover rings, ideals, factor rings, and homomorphisms, including a discussion of maximal and prime ideals and ring isomorphism theorems (I was impressed–I definitely didn\u2019t see these until graduate school).\u00a0 Groups begin on Chapter 17, with a presentation of symmetry groups and permutations.\u00a0 By the time abstract groups are introduced, we had a lot of examples: the additive group and multiplicative unit group of every ring already provide plenty to work with.\u00a0 We got through the Fundamental Isomorphism Theorem for groups (Chapter 26) by the end of the block.<\/p>\n

This course was co-taught with Hanson Smith, a CC alum who is currently a graduate student at the University of Colorado Boulder, studying Number Theory with Kate Stange.\u00a0 Hanson did a senior thesis with me as an undergraduate, so we knew that we spoke the same mathematical language.\u00a0 We asked Hanson to come teach at CC for the block because the course was initially supposed to have 32 students, above our enrollment cap.\u00a0 Hanson was\/is a great student and deeply interested in teaching, and he already had lots of experience as a student on the block plan.\u00a0 I took the lead on some aspects of the course, but Hanson did a great job.\u00a0 He put in a ton of work, made strong contributions, and it would not have been possible to do what we did this block without him. He is already a good teacher, and I have great faith that he will become an amazing teacher as he gains more experience.\u00a0 THANKS SO MUCH, HANSON!!\u00a0 We also had help from Marlow Anderson, who acted as a \u201ccourse buddy\u201d and contributed some extra office hours to the course, and two student learning assistants, Hanbo Shao and Bob Kuo.\u00a0 Hanbo and Bob led extra help sessions in the evening, which was a great help and stress reducer for the students.\u00a0 They all made enormous contributions to the students’ success, and I am very grateful to all of them.<\/p>\n

A Breakdown of the Course <\/strong><\/p>\n

Notable strengths of the book:<\/strong> I really liked this book.<\/p>\n