## Math 252: Abstract Algebra II

### Spring 2012

**Course Info:**

**Lectures:**Monday, Wednesday, Friday, 11:45 a.m. - 12:35 p.m.**Dates:**18 January 2012 - 2 May 2012**Room:**Lafayette L210**Course Record Number (CRN):**11078**Instructor:**John Voight**Office:**16 Colchester Ave, Room 207C**Phone:**(802) 656-2271**E-mail:**jvoight@gmail.com**Office hours:**Wednesdays, 9-10 a.m. and 2-3 p.m.; or just make an appointment!**Course Web Page:**http://www.cems.uvm.edu/~voight/252/**Instructor's Web Page:**http://www.cems.uvm.edu/~voight/**Prerequisites:**Math 251.**Required Text:**David Dummit and Richard Foote, Abstract Algebra, third edition, 2004.**Grading:**Weekly homework will count for 50% of the grade and daily "readiness" homework will count for 15%. Class participation and preparedness will count for 10% of the grade. One "challenge problems set" will count for 25% of the grade.

**Syllabus:**

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**Syllabus**

**Homework:**

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**Homework Submission Guidelines**

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**HW #1 (due 27 January 2012)**

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**HW #2 (due 3 February 2012)**; updated 30 January 2012

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**HW #3 (due 10 February 2012)**

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**HW #4 (due 17 February 2012)**; updated 16 February 2012

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**HW #5 (due 24 February 2012)**

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**HW #6 (due 16 March 2012)**; updated 16 March 2012

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**HW #7 (due 23 March 2012)**; updated 19 March 2012

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**HW #8 (due 30 March 2012)**

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**HW #9 (due 6 April 2012)**

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**HW #10 (due 13 April 2012)**

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**HW #11 (due 20 April 2012)**

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**HW #12 (due 27 April 2012)**; typo fixed 26 April 2012

**Readiness Problems:**

The readiness problem is due on the same day as the row in which it appears. Problem 3.5.2 means in section 3.5, exercise 2.

Euclidean domains, PIDs, and UFDs, and polynomial rings |
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1 | 18 Jan | (W) | 8.1: Euclidean domains | |

2 | 20 Jan | (F) | 8.1 | 8.1.1(b) |

3 | 23 Jan | (M) | 8.2: Principal ideal domains | 8.1.4(a) |

4 | 25 Jan | (W) | 8.3: UFDs | 8.2.3 |

5 | 27 Jan | (F) | 7.5: Rings of Fractions | 8.3.5(a) |

6 | 30 Jan | (M) | 9.2, 9.5: Polynomial rings over fields I, II | 7.5.4, 8.1.A |

7 | 1 Feb | (W) | 9.4: Irreducibility criteria | 9.2.A |

Modules |
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8 | 3 Feb | (F) | Linear algebra crash course (11.1) | 9.4.1, 9.4.2(a) |

9 | 6 Feb | (M) | Linear algebra crash course (11.1) | 11.1.1 |

10 | 8 Feb | (W) | 10.1: Basic definitions and examples | (Worksheet) |

11 | 10 Feb | (F) | 10.1 | 10.1.1 |

12 | 13 Feb | (M) | 10.2 : Quotient modules and module homomorphisms | 10.1.15 |

13 | 15 Feb | (W) | 10.2 | 10.2.1 |

14 | 17 Feb | (F) | 10.2 | 10.2.3 |

20 Feb | (M) | No class, Presidents Day |
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15 | 22 Feb | (W) | 10.3: Generation of modules, direct sums, and free modules | |

Vector spaces |
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16 | 24 Feb | (F) | 11.2: The matrix of a linear transformation | 10.3.23 |

17 | 27 Feb | (M) | 11.2 | 11.2.1 |

18 | 29 Feb | (W) | 11.3: Dual vector spaces | 11.2.2 |

19 | 2 Mar | (F) | 11.4: Determinants | 11.3.2(a) |

5-9 Mar | (M-F) | No class, spring break |
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Modules over PIDs |
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20 | 12 Mar | (M) | 12.1: Basic theory | |

21 | 14 Mar | (W) | 12.1 | 12.1.1(a) |

22 | 16 Mar | (F) | 12.2: Rational canonical form | 12.1.5 |

23 | 19 Mar | (M) | 12.2 | 12.2.8 |

24 | 21 Mar | (W) | 12.3: Jordan canonical form | 12.2.9 (just the two easy ones!) Bring your laptop! |

Field theory |
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25 | 23 Mar | (F) | 13.1: Basic theory of field extensions | 12.3.5 |

26 | 26 Mar | (M) | 13.1 | 13.1.1 |

27 | 28 Mar | (W) | 13.2: Algebraic extensions | 13.1.3 |

28 | 30 Mar | (F) | 13.2 | 13.2.1 |

29 | 2 Apr | (M) | 13.3: Classical straightedge and compass constructions | 13.2.3 |

30 | 4 Apr | (W) | 14.1: Basic definitions | 13.3.2 |

Galois theory |
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31 | 6 Apr | (F) | 13.4: Splitting fields and algebraic closures, 13.5: Separable and inseparable extensions | 14.1.2, 14.1.3 |

32 | 9 Apr | (M) | 14.1 | 13.4.1 |

33 | 11 Apr | (W) | 14.2: The fundamental theorem of Galois theory | 14.1.4 |

34 | 13 Apr | (F) | 14.2 | 14.2.3 |

35 | 16 Apr | (M) | 14.2 | 14.2.4 |

Finite fields and insolvability of the quintic |
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36 | 18 Apr | (W) | 14.3: Finite fields | 14.2.12 |

37 | 20 Apr | (F) | 14.3 | 14.3.2 |

38 | 23 Apr | (M) | 14.5: Cyclotomic extensions and abelian extensions over QQ | 14.3.5 |

39 | 25 Apr | (W) | 14.7: Solvable and radical extensions | 14.5.3 |

40 | 27 Apr | (F) | 14.7 | 14.7.1 |

41 | 30 Apr | (M) | 14.6: Galois groups of polynomials | 14.7.12 |

42 | 2 May | (W) | 14.6 |

**Links:**

There are additional resources on the 252 Spring 2008 website.