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Math 456: Honours Algebra III
Instructor: Eyal Goren   (eyal.goren@mcgill*dot*ca)

This course is devoted mainly to the theory of groups, but rings and modules are studied in its last third. It will start from scratch. But, assuming previous exposures to groups in math 235 (for example), will initially proceed very quickly. After we have covered (again) the material already seen in math 235, the pace will slow down (somewhat). Below you will find the official course syllabus and recommended texts. More detailed information concerning the course and all further announcements, assignments and so on will appear on my courses.


Official course syllabus: Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.
Pre-requisites: MATH 235 and either (MATH 247 or MATH 251).

Method of Evaluation: 5% assignments, 10% in-class quiz, 20% midterm, 65% final. Or, if better, 100% final.
There will be no make-up for the quiz, or the midterm; people not able to write those will get a mark of 0 for those, but can still enjoy the 100% final option.
Showing up to classes is not mandatory, but is strongly recommended. As well, attempting all the assignments is highly recommended.

Textbook: The official textbook for the course is my online notes. One can also consult the following excellent text book: D. Dummit and R. Foote: Abstract algebra. Third Edition.
(This text book will also be useful for math 457 and the "higher algebra" courses, although it does not cover every topic taught in those courses, it covers most.)

Academic integrity: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).
Submitting work: In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.
Syllabus and Grade Calculation: In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change.