Spring 2013

Course information (with Syllabus)

Gallian's ADVICE FOR STUDENTS FOR LEARNING ABSTRACT ALGEBRA: You'll actually get more out of it now, after having completed one semester of abstract algebra.

Instructor: Michael Pelsmajer

Email: pelsmajer[AT]iit[DOT]edu

Office Hours: *Flexible*. To arrange a meeting, talk to me before or after class, or send an e-mail with a list
of convenient times. (You can also just stop by, and if I'm not too busy, I'm happy to talk.)

Office: Engineering 1 Building, Room 206 (312.567.5344 but email is usually better)

Date | Problems assigned today |
---|---|

Monday, January 14 |
Chapter 12: 12*, 13, 27, 38, 40*, 43
Chapter 13: 1, 2, 6*. For 7th edition, also 16*, 42. For 8th edition, also 18*, 46. Chapter 14: 1, 2, 3, 5, 7, 15, 17, 18*, 27, 41, 44* (* are to be written up nicely and handed in) |

Wednesday, January 16 | Chapter 14: 6*, 20, 28, 35, 39, 52* |

Monday, January 21 | (NO CLASS) |

My expectation is that everyone will manage to do all of the homework problems, alone or together with other students, and will seek help from me before the due date if necessary. Then, the quiz should be no problem for anyone. | |

I probably haven't presented even one proof properly during the first two lectures, and I don't want to give you the wrong impression. For the problems that you are not handing in, you may at times be satisfied by doing a sketch of a proof rather than writing every detail carefully --- although my sketches at the board are still more `sketchy' than you'd want, even for those problems. For the written problems, that style of sketch would be Totally Inadequate. Rather, the level of detail and care required in 431 should be exactly the same as for 430. I assume that after one semester of 430, you ought to understand what that means. | |

Wednesday, January 23 |
Read Theorems 15.1, 15.2, 15.3, 15.4.
Chapter 15 #2*, 5, 10, 14*, 15, 17, 28 |

Monday, January 28 |
Chapter 13 #54*,55 in 7th edition, or #58,59* in 8th edition
Chapter 15 #7, 43, 45, 46*, 66* |

I will also accept missing and very bad problems from the previous homework, redone. I probably won't do this in future weeks, but there's always some confusion at the beginning of the semester which is why I'm making an exception this time. | |

On the first homework and quiz, I love how everyone takes care to justify all steps clearly. If you continue to do that, it frees me as an instructor to not have to stress proof basics, and give better lectures about the course material itself. | |

Wednesday, January 30 and Monday, February 4 |
Chapter 16 #1, 5, 7, 9,10*, 11, 17*,18*, 21,22*, 23,24, 41, 44*, 47 in 7th edition, or
Chapter 16 #1, 5, 9, 11,12*, 13, 19*,20*, 23,24*, 25,26, 45, 48*, 57 in 8th edition |

Wednesday, February 6 and Monday, February 11 |
Chapter 17 #2*,3, 9,10*, 12*,13,14*, 20,21, 34* and Chapter 17 #2*,3, 11,12*, 14*,15,16*, 22,23, 36* and |

Wednesday, February 13 and Monday, February 18 |
Chapter 18 #1, 6, 8*, 14*,15,16*,17, 20*, 24*, 27, 30*, 34*, 39 in 7th edition, or
Chapter 18 #1, 6, 8*, 14*,15,16*,17, 20*, 24*, 31, 34*, 38*, 43 in 8th edition |

Wednesday, February 20 and Monday, February 25 | Chapter 19 #1, 2*, 3, 5, 9, 10*, 11, 13, 19, 20*, 22* (7th or 8th edition) |

Exam 1: Wednesday February 27 | |

Monday, March 4 | Just read ahead in Chapter 20. (We didn't get far enough in the lecture to do any problems.) |

Wednesday, March 6 and Monday March 11 | Chapter 20 #1, 3,4*,5,6*,7,8*, 10*,11, 19, 29, 34* |

Wednesday, March 13 |
Chapter 20 #30*, 31, 32*, 33, and:
40*. Let f(x) be an irreducible polynomial over a field F. Prove that the number of distinct zeros of f(x) in a splitting field divides the degree of f(x). |

Monday, March 25 | Chapter 21 #1*, 3, 6*, 9, 11, 14* |

Wednesday, March 27 | Chapter 21 #8*, 10*, 19, 22*, 28*, 33, 38*, 41 |

Monday, April 1 |
Chapter 21 #2*, 4*, 17
Chapter 22 #8*, 9, 10*, 11 |

Wednesday, April 3 |
Chapter 22 #1, 4*, 5, 7*, 11, 13, 15, 17, 18*, 19, 28*, 29, 34*. (8th edition)
Or, Chapter 22 #1, 4*, 5, 7*, 11, 13, 15-not-in-7th-ed (Find the smallest field of characteristic 2 that contains an element whose multiplicative order is 5, and find the smallest field of characteristic 3 that contains an element whose multiplicative order is 5.), 15, 16*, 17, 26*, 27, 32*. (7th edition) Hint: we know a lot about cyclic groups (Chapter 4). Hint for #13: Look at the splitting field in the proof of Theorem 22.1, to get started. |

Monday, April 8 |
Chapter 23 #3*, 5, 6*, 8*, 9*, 10*, 15, 17
Notes: 1. The hints/solutions in the back of the book are sometimes incomplete (which is what is allowing me to ask you odd numbered problems for credit). 2. For many of these, I found direct geometric constructions rather than using algebra. You can use either or both techniques. 3. In practice, these problems should feel light, even though they rely on deep results. |

Wednesday, April 10 | Review today. Study for the exam. |

Monday, April 15 | Chapter 31 #3,5 |

Wednesday, April 17 | (Exam today.) |

Monday, April 22 | See attachment |

Wednesday, April 24 | See attachment |

Monday, April 29 | Chapter 32 Read Example 5, do #1, 2*, 3, 5, and read more. |

THE FUTURE Wednesday, May 1 | Chapter 32 #4*, 7, 11, 12*, 13 |