Modern Algebra I- MA541 - Fall
2012 |

Course Home Page |

Course: MA541, Modern Algebra I

Instructor: Jared Weinstein

Lectures: TR 3:30 pm - 5:00 pm in PSY B39

Office Hours: M 10:00 am - 12:00 pm and Th 2:00 pm - 3:00 pm in MCS 227

This course is an introduction to abstract algebra, with an emphasis on groups. A group is an algebraic structure which was invented to capture the notion of symmetry. Groups appear in almost every field of mathematics, so it is important to master them. Topics include permutation groups, Lagrange's theorem, homomorphisms, the isomorphism theorems, and the Sylow theorems.

John B. Fraleigh, *A First Course in Abstract Algebra*, 7th ed.,
Addison-Wesley.

**Assignments and Exams**

In order to gain mastery of the concepts it is crucial to do many exercises. I will be assigning problem sets every week which will usually be due on Tuesdays. You are allowed and encouraged to work together on homework assignments, but you must hand in solutions which are written in your own words. Select problems from each problem set will be graded and returned to you the following week.

On Tuesday, October 16, I will hand out a take-home midterm, which will be due on Tuesday, October 23. Here are the solutions. You are not allowed to work together on the midterm.

HW | Assignment | Due |
---|---|---|

#1 | § 0: 1, 2, 9, 10, 11, 12, 14, 15, 17, 18, 19, 29, 30, 36 | Sept. 11 |

#2 | § 1: 1-4, 16-18, 22-27, 33, 34, 37. § 2: 1-9, 26 | Sept. 18 |

#3 | § 3: 6,7,16,33. § 4: 8, 19, 20, 28, 29, 32, 34, 35 | Sept. 25 |

#4 | § 5: 8, 10, 13, 26, 30, 40, 43, 49, 53. § 6: 53 | Oct. 2 |

#5 | § 8: 1, 2, 18b, 35, 51b. § 9: 1, 4, 5, 7, 10, 13, 17, 34, 35. | Oct. 11 |

#6 | § 12: 6, 8, 10, 16. § 13: 17, 20, 27, 44, 47, 50. | Nov. 1 |

#7 | § 14: 4, 6, 8, 30, 33. § 15: 4, 9, 13, 23, 25, 37. | Nov. 8 |

#8 | § 16: 13b, 13c. § 17: 1, 4, 7. § 34: 2, 7, 9. | Nov. 20 |

#9 | § 35: 8, 9, 22. § 36: 1, 2, 3, 5, 13, 19, 20. | Dec. 6 |

#10 | § 37: 4, 6, 8. § 38: 2, 4. § 39: 12c, 13c. | Dec. 13 |

The final will be given on Wednesday, December 19, 3:00 pm - 5:00 pm, location TBA. You must take the final to receive a passing grade.

The grading scheme is: Homeworks 70%, Midterm 10%, Final 20%. Because doing homework assignments regularly is so important for this class, I have given them a high weight in the grading scheme. It may be the case that an
emergency prevents you from handing in an assignment on time. That is why I will drop the lowest score from your homework average. *Late homework will not be accepted.*

The course won't be graded on a curve, so that it is possible that all of you receive As (or Fs!). At this stage I cannot be very specific about how many points you must get to achieve each letter grade. An A grade will only be given to those students who have a very deep understanding of group theory, who not only know the definitions and theorems but can easily apply them to various situations. To achieve this understanding, I recommend the obvious: Attend every lecture, read every page of the text, attempt every assignment, come to office hours, and discuss the material with each other.

MA541 Home Page | Jared Weinstein | Department of Mathematics | Boston University |