Abstract Algebra Homepage


		Mon/Wed/Fri 10-11am in Science Center 309

	Faculty	Benedict Gross George Vasmer Leverett Professor of Mathematics 506 Science Center (617) 495-9063 gross@math.harvard.edu

	Teaching fellow	Peter Green 425b Science Center (617) 493-7381 green@math.harvard.edu

	Course assistants	Peter Anderegg pandereg@fas.harvard.edu Elizabeth Schemm schemm@fas.harvard.edu

	Required text	Algebra, M. Artin (Prentice Hall 1991)

	Online resources	Registered students will be able to access video feed and handwritten notes from each lecture, which should appear online within 48 hours of the lecture time and remain available for on-demand viewing until the end of the semester. Homework and solutions will also be available online. Online resources from the first two weeks of lectures (including video, notes, homework assignments and solutions) are freely available. To access them, click on the login button above this syllabus and enter username guest with no password. To access material beyond the first two weeks of lectures, students must be registered in the course. Registered students can login using their Harvard University ID number as the username, with password being the student's last name, all lowercase, alphabetic characters only (a-z), up to 8 letters.

	Section	The course assistants will give two independent weekly sections: Tuesdays - 3pm in Science Center 411 Thursdays - 7pm in Science Center 411

	Office hours	Gross - by appointment Green - every Tuesday, 5:30-7pm in the Small Dining Room at Mather House Anderegg/Schemm - every Sunday, 8-9pm in the Cabot House Dining Hall

	Homework	Problems will be assigned in each lecture, and should be submitted at the beginning of the following lecture. Late assignments will not be accepted. Assignments will be graded by the course assistant. Homework assignments and solutions can be accessed online. Refer to the Online resources section above for instructions. Collaboration between students is strongly encouraged, and must be accompanied by complete understanding of all solutions and crediting of collaborators. You should note that problem sets are a critical part of the learning process. Final exam scores tend to replicate performance on homework. In addition to the regularly assigned problems, you may find it useful to try these supplementary solved problems.

	Midterm exams	There will be midterm exams on Wednesday, October 15 and Monday, November 24, each during the usual class hour.

	Final exam and review	The final exam will be on Friday, January 23, 2:15-5:15pm in Boylston 110. It will be closed book with no aids permitted. Students who are approved to take out of sequence exams will be informed of new exam dates and times by the exams office in early January. There will be review sessions given by Prof. Gross and Peter Green on Wednesday, January 14 and Friday, January 16, 10-11am in Science Center 309. It is recommended that you attend both sessions. Review Session I: video / notes Review Session II: video / notes You may also find it useful to consult this study sheet.

	Grading	The final grade will be the maximum of the final exam grade and 40% final + 20% first midterm + 20% second midterm + 20% problem sets.

	Prerequisites	Math 21b and experience writing proofs (Math 101, 121, or equivalent).

	Schedule	Week 1. Review of linear algebra. Groups. Examples of groups. Basic properties and constructions. Week 2. Permutations. Cosets, Z/nZ. Week 3. Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces. Week 4. Abstract linear operators and how to calculate with them. Properties and construction of operators. Week 5. Exam 1. Orthogonal groups. Week 6. Isometries of plane figures. Cyclic and dihedral groups. Finite and discrete subgroups of symmetry groups. Week 7. Group actions. Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation. Week 8. A₅and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups. Week 9. Rings. Examples of rings. Basic properties and constructions. Week 10. Quotient rings, extensions of rings. Integral domains, fields of fractions. Week 11. Exam 2. Special lecture. Week 12. Euclidean domains, PIDs, UFDs. Gauss’ lemma. Eisenstein’s criterion. Algebraic integers. Week 13. Structure of ring of integers in a quadratic field. Dedekind domains. Ideal class groups. Week 14. Wrap-up.