Course description
The second semester of the Honors Algebra sequence.
The course will cover textbook material from Algebra
by Michael Artin, chapters 11 through 16.
Chapters 11 through 14 are mostly "commutative algebra".
Chapters 11 and 12 are definitions and examples for rings:
(integral domains, the euclidean algorithm and principal ideal
domains, unique factorization domains) then ideals quotients,
homomorphisms, etc.
Chapters 13 and 14 are quadratic number rings, the lattices
they define, ideal and prime factorization, and the ideal class group.
Chapters 15 and 16 are about fields and field extensions -- which
is Galois theory.
We will compare the approach to Galois theory in the main
text to that of the small book
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. Scrutinizing mathematical reasoning carefully, whether from a source or your own, will allow you to be confident in the things you understand and to pinpoint things you do not understand.
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 Thursdays, an early quiz, a midterm exam, and a final exam. Dates are on the Details, resources page.
Communication:
Please use the Forum page of the NYU Brightspace 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 (illness, grading issues, etc.).
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.