- Frederick M. Goodman,
*Algebra: Abstract and Concrete*

free pdf available here - Thomas W. Judson,
*Abstract Algebra: Theory and Applications*

free pdf available here - Keith Conrad, Two Applications of Unique Factorizations
- Keith Conrad, The Gaussian Integers

- Homework 1, due Friday, January 12, solutions.
- Homework 2, due Monday, January 22, solutions.
- Homework 3, due Monday, January 29, solutions.
- Homework 4, due Wednesday, February 7, solutions.
- Homework 5, due Wednesday, February 14, solutions.
- Homework 6, due Wednesday, February 28, solutions.
- Homework 7, due Friday, March 9, solutions.

Lecture | Date | Topics covered | Remarks |
---|---|---|---|

Week 1 | |||

1 | Wed Jan 3 | Introduction and simple groups (Goodman 10.1) | |

2 | Fri Jan 5 | Composition series and solvable groups (Goodman 10.1) | |

Week 2 | |||

3 | Mon Jan 8 | Solvable groups and properties of the alternating group (Goodman 10.1, 10.3) | |

4 | Wed Jan 10 | Simplicity of A_n for n >= 5 (Goodman 10.3) | |

5 | Fri Jan 12 | Introduction to rings (Judson 16.1) | HW 1 due |

Week 3 | |||

Mon Jan 15 | No class--Martin Luther King Day | ||

6 | Wed Jan 17 | Integral domains and fields (Judson 16.2) | |

7 | Fri Jan 19 | Ring homomorphisms and ideals (Judson 16.3) | |

Week 4 | |||

8 | Mon Jan 22 | Prime and maximal ideals, polynomials (Judson 16.4, 17.1) | HW 2 due |

9 | Wed Jan 24 | Polynomials: the division algorithm (Judson 17.2) | |

10 | Fri Jan 26 | Problem discussion | |

Week 5 | |||

11 | Mon Jan 29 | Midterm 1 | HW 3 due |

12 | Wed Jan 31 | Polynomials: k[x] is a PID (Judson 17.2-3) | |

13 | Fri Feb 2 | Polynomials: greatest common divisors and Eisenstein's criterion (Judson 17.2-3) | |

Week 6 | |||

14 | Mon Feb 5 | Problem discussion | |

15 | Wed Feb 7 | Gauss's Lemma and Eisenstein's criterion (Judson 17.3) | HW 4 due |

16 | Fri Feb 9 | Irreducible and prime elements in integral domains (Judson 18.2) | |

Week 7 | |||

17 | Mon Feb 12 | Discussion | |

18 | Wed Feb 14 | Euclidean domains, PIDs and UFDs (Judson 18.2) | HW 5 due |

19 | Fri Feb 16 | Field of fractions (Judson 18.1) | |

Week 8 | |||

Mon Feb 19 | No class--Presidents' Day | ||

20 | Wed Feb 21 | Discussion | |

21 | Fri Feb 23 | Midterm 2 | |

Week 9 | |||

22 | Mon Feb 26 | More on UFDs (Judson 18.2) | |

23 | Wed Feb 28 | Proof that R UFD => R[x] UFD (Judson 18.2) and Applications of UFDs (Conrad) | HW 6 due |

24 | Fri Mar 2 | Solving y^2=x^3-2 (Conrad) and writing primes as the sum of two squares (Conrad, Theorem 9.6 ) | |

Week 10 | |||

25 | Mon Mar 5 | Discussion | |

26 | Wed Mar 7 | Primes in the Gaussian Integers (Conrad) | |

27 | Fri Mar 9 | Pythagorean triples (Conrad) | HW 7 due |

Final | |||

Wed Mar 14 | Final examination, 8:30 - 10:20 am |

- Date: Wednesday, March 15
- Time: 8:30-10:20 am
- Location: CDH 125 (usual location)

- Homework: 30%
- Midterm: 30%
- Final: 40%