Syllabus for Math 221: Algebra

Fall 2016

Course description. A first graduate level course in algebra.

Prerequisites. Math 123 or equivalent. Familiarity with rings and the theory of finitegroups.

Meeting time and place. MWF 11:00 am - 11:59 am, SC 310.

Instructor. Hector H. Pasten Vasquez.

e-mail. hpasten at math dot harvard dot edu

Office hours. Thursday from 10:00 am to 11:59 am, or by appointment, SC 235.

Text. The primary reference texts are:

• Atiyah, MacDonald, Introduction to Commutative Algebra.

• Fulton, Harris, Representation theory: A first course (selected topics from Chap-ters 7 - 10).

You might find it useful to consult the following texts for alternative points of view:

• Eisenbud, Commutative Algebra with a view toward algebraic geometry.

• Matsumura, Commutative ring theory.

Course website. http://www.math.harvard.edu/∼hpasten/F2016math221.html

Topics to be covered (tentative)

• General theory of commutative rings and modules: Cayley-Hamilton theorem,Nakayama’s lemma, tensor product, localization, primary decomposition, integraldependence, Noether normalization, Nullstellensatz, noetherian rings, Hilbert basistheorem, Dedekind domains.

• Galois theory and applications.

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• Representation theory of finite groups.

• Introduction to Lie groups and Lie algebras.

Grading. We will have weekly assignments and one take-home final exam. The followinggrading scheme is for all students expecting to obtain a final grade (both undergraduateand graduate students):

• Weekly assignments (75%): It will be assigned the first day of class of each week,due on the first day of class of the following week.

• Take-home final exam (25%): Tentative due date: end of reading period in De-cember.

Collaboration.

• Weekly assignments. Discussion and the exchange of ideas are essential to doingacademic work. For assignments in this course, you are encouraged to consultwith your classmates as you work on problem sets. However, after discussionswith peers, make sure that you can work through the problem yourself and ensurethat any answers you submit for evaluation are the result of your own efforts. Inaddition, you must cite any books, articles, websites, lectures, etc that have helpedyou with your work using appropriate citation practices. Similarly, you must listthe names of students with whom you have collaborated on problem sets.

• Take-home final exam. The take-home final exam is individual and collaborationis not permitted.

Late assignments. Weekly assignments received after the due date will not be consid-ered, unless previously discussed with the instructor. Late take-home final exams willnot be considered.

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