Math 3231 - Spring 2017
Abstract Algebra II

Syllabus: We plan to cover properties of rings (esp. polynomials), leading up to field extensions and Galois theory with its applications. Our focus will be on the following topics, in Chapters 4 to 8 of the text. There will be handouts to supplement the textbook.

• Polynomials (esp. in one variable)
• Rings and ideals
• Field extensions
• Galois groups
• Applications of Galois theory

For an indication of what Galois theory is good for, go here.

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Prerequisites: Math 3230. In particular, you are expected to be comfortable with group theory (including homomorphisms and quotient groups).

Course grade:  This will be based on the following weighting:

• homework (20%), quizzes (20%), midterm (20%), and final (40%). The lowest homework and quiz grade will be dropped.

Homework: Homework assignments will be posted on the bottom of this web page, and are due at the time and place indicated on the assignment. As a general rule, no late homeworks will be accepted.

• An integral part of each homework is the assigned reading from the text (or handout) and the re-reading of your lecture notes. Focus on both explanations and examples.
• You are encouraged to discuss homework problems with the instructor during office hours.
• It is a mistake to skip homework, because no skills (in mathematics, foreign language, athletics, and so on) can be learned by passive involvement, but only by regular practice. Moreover, many skills are learned over time, so do not expect to understand everything perfectly right away. You should find your understanding of basic topics improving gradually from one week to the next.
• Proofs on homeworks should not be simply a string of logical and mathematical symbols, but include complete sentences in English. The role of English is to explain the strategy of your proof and the details as well. There will not be partial credit based on having misunderstood a question.

Quizzes:  In weeks when homework is not due, there will be a short quiz at the start of one class, usually Thursday's class. The purpose of quizzes is to provide you some feedback about how well you are following the basic ideas of the course.  

• The quizzes will be short.
• You are not allowed to bring any aids with you to the quiz. (Compare with exams below.)
• There are no makeup quizzes. If you miss a quiz, your grade is 0.

Exams:  There is one midterm and one final.  

• There is no makeup exam. If you miss the midterm, the midterm grade is 0.
• If you need exam accommodations based on a documented disability, you need to speak with both the Center for Student Disabilities and the course instructor within the first two weeks of the semester.

Attendance: Regular attendance is expected, so you can see techniques and examples discussed in real time, and so you can ask lots of questions. The way you should think about the material will develop from the way it is presented in class.

Course conduct: To respect everyone's right to a productive learning environment, please refrain from disruptive activities during class. This includes reading newspapers or magazines, and using smartphones. If your phone receives a message, you can check it after class. Please turn off all other electronic gadgets before entering the classroom. On a positive note, do feel free to ask questions!

Academic integrity: Students are expected to avoid academic misconduct. Your integrity is not worth losing (and the course not worth failing) by falsely presenting yourself in any aspect of this course. For further information on academic integrity, see Appendix A of the Student Code.