Faculty of Science Course Syllabus
Department of Mathematics & Statistics
MATH 3032: Abstract Algebra II (Winter 2025)
Instructor: Theo Johnson-Freyd, theojf@dal.ca.
Lectures: Tuesdays and Thursdays, 11:35-12:55 Atlantic Time, Chase 227.
Office Hours: Wednesdays, 14:35-16:55 Atlantic Time, Chase 214.
Course website: http://categorified.net/25Winter3032/.
This course is governed by the academic rules and regulations set forth in the University Calendar and by the Senate.
Course description
A ring is an abstract setting in which to do basic arithmetic: addition, subtraction, multiplication. Examples of rings: the integers; the real numbers; the set of polynomial functions. This course will develop the theory of rings starting from basic definitions and going into the main constructions that produce new rings from old. Specific attention will be given to the theory of factorization. In some rings, but not in others, every element can be uniquely factored into prime elements. The class will end with the theory of Gröbner bases, which offer an algorithm for simplifying systems of polynomial equations analogous to the row-eschelon reduction algorithm for systems of linear equations.
Course materials and delivery
The main textbook for the class is:
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Abstract Algebra by D. Dummit and R. Foote.
Homework assignments and other materials will be available on the Course Content page.
Lectures will be given in person. (The occasional lecture may be delivered over Zoom.) This is a small class. Although attendance is not mandatory, your presence or absence will certainly be noticed by all participants.
Course Assessment
Conversion of numerical grades to Final Letter Grades follows the Dalhousie Common Grade Scale.
Weekly homework assignments: 50%.
I encourage you to work together to complete your homework assignments. Studies have shown that social ties are a main predictor of success in STEM classes. Although you are encouraged to work together, the homework you submit must be written by you individually.
There are many online resources offering solutions to homework at all levels. If you choose to use such resources, please be cautious: they often provide too detailed an answer, and students can trick themselves into thinking that they understand more than they do by copying those answers.
Homework is due by the posted deadline. Homeworks should be well-organized and legible: either neatly hand-written or typed. Students will be allowed to drop one homework score for any reason. In the case of further extenuating circumstances, students should consult with the instructor.
Exams: 50%.
There will be one midterm exam and one final exam. Both exams will be delivered in-person. Students may bring prepared (paper!) notes with them, but may not use electronic resources during the exam. The midterm will be worth 20% of the final grade, and the final will be worth 30% of the final grade.