Syllabus for Math 351, Section 3

Fall 2001

**Prerequisites:** Math 250 and Math 251 or 291.

**Text**: *Abstract Algebra, An Introduction*, 2^{nd} Edition, by Thomas W. Hungerford.

**Meeting times**: MW4 in SEC-217, W5 in SEC-216.

**Final Exam**: Friday, December 21, 2001, 8:00-11:00AM.

**Instructor**:

Name: |
Professor Charles Sims |

Office: |
Room 215, Hill Center, Busch Campus |

Office phone: |
732-445-2364 |

Messages: |
732-445-2390 |

Email: |
sims@math.rutgers.edu |

Web page: |
http://sites.math.rutgers.edu/~sims |

Home phone: |
732-531-0157 |

**Office hours**: Regular office hours will be announced in class at the beginning of the second week of the term. Appointments to see the instructor can be made in person, by telephone, or by email.

**Calculator**: A calculator roughly comparable to a TI-83 will be useful for homework and during the workshops, but is not required. Computers and calculators with typewriter keyboards or built-in computer algebra systems, such as the TI-89 and TI-92, will not be permitted on exams.

**Level of the course**: Math 351 should not normally be a student's first mathematics class at the 300-level. Effective with the spring 2002 term, Math 300, Introduction to Mathematical Reasoning, will be a prerequisite for Math 351. Most students currently taking Math 351 have had Math 300 and the instructor will assume that students have a basic familiarity with formal mathematical arguments, that is, proofs.

**Course topics**: The goal of Math 351 is to provide an introduction to three types of algebraic structures, groups, rings, and fields. The course will cover most of the material in Part 1 of the text, Chapters 1 to 7, and a few selected topics from Part 2, Chapters 8 to 11. Given the instructor's interests in carrying out computer calculations with algebraic objects, the text will occasionally be supplemented with discussions of algebraic algorithms.

**Course operation**: Math 351 is a 4-credit course with three 80-minute meetings per week. The MW4 classes will normally be used for fairly traditional lecturing by the instructor. The W5 class will usually be a workshop, a laboratory style class in which students work together in small groups on specially constructed problems. The workshops are a very important part of the course. They have two purposes, to deepen the students' understanding of the course material and to encourage students to talk with each other about mathematics. There will be two types of written homework assignments, problems from the text and selected workshop problems.

Students need to be clear on what sorts of collaboration are permitted. During the workshop class, students are expected to discuss the workshop problems with the members of their group. Limited discussions outside of class with classmates related to homework are permitted as long as these discussions are acknowledged and each student writes up their solutions independently. Questions about the details of writing up solutions should be discussed with the instructor only.

There is a long-standing rule of thumb that undergraduate students should expect to spend approximately two hours outside of class for every hour in class. Since Math 351 is a 4-credit course and is one of the more challenging courses offered by the Mathematics Department, students in Math 351 should be prepared to spend 8 to 10 hours per week on the course, in addition to the class meetings.

**Grading**: The term grade will be based on the results of the major examinations, occasional short quizzes, and the written homework. There will be two hour exams, each of which will count 20% of the grade, and a final, which will count 40%. The quizzes and homework together will count 20%. Exams will be closed book and student-prepared formula sheets will not be permitted. If supplemental information is required for the solution of a problem, that information will be provided by the instructor.