Course description
The second semester of the Honors Algebra sequence. Topics are taken from Algebra by Michael Artin. First, it's Chapter 12 on rings and factorization with the Gaussian integers as an example. Then it's Chapters 15 and 16 on fields and Galois theory. High points include the Galois correspondence between subgroups and fixed fields, and impossibility theorems (can't trisect the angle with ruler and compass, can't solve a general degree 5 polynomial by root formulas). Finally, it's Chapter 13 on the algebra and geometry of quadratic number fields. The schedule is in the syllabus.
There are several goals. One is the definitions, techniques, and theorems of abstract algebra. Another is an understanding of specific examples that the theory was invented to explain -- being able to find structures in the examples that theorems say should be there. We seek to develop mathematical maturity, which is the ability to understand, work with, and develop mathematical structures and examples. In addition to understanding other peoples' arguments, it is important to be able to communicate your own reasoning clearly and correctly so people can understand you.
Prerequisites:
Honors Algebra I or the permission of the instructor.
Assignments, exams, grading:
The final grade will be based on weekly homework assignments, due most Tuesdays, a reality check quiz, a midterm exam, and a final exam. Dates are in the syllabus.
Communication:
Please use the Forum page of the NYU Classes site for this course for all content related communication, including questions about assignments, lectures, or notes. This way all questions and answers are visible and shared by everyone in the class. Feel free to contact the instructor or TA directly about anything that does not involve others.
Academic integrity:
Students are encouraged to collaborate on understanding the material and learning how to do the assignments. Students may not share ("borrow" or lend) assignment solutions -- all writing must be done individually. Students may not plagairize solutions from other sources such as books or web sites. Policies for the quiz and exams wil be announced.