Math 251 Syllabus (Abstract Algebra I) Fall 2017
MWF 2:20-3:10pm in 107 Perkins

Instructor: Jonathan Sands, Room 406, 16 Colchester Ave. (Henry Marcus Lord House)
Office hours:
MTW 3:30-4:45, F 11-12  and by appointment.
Or send me your question by email. No question is too small!
Reach me at:
656-4339 or
Course website:

Goals: Can we identify certain powerful algebraic principles that pervade higher mathematics? Can we hone our skills at using these general principles so as to become better analytical thinkers and problem-solvers? Absolutely! That is just what we aim to do in this course, emphasizing the basic concepts of abstract algebra as presented in chapters 1-5 and 7 in our textbook.

Topics: Basic theory and examples of groups, rings, fields, homomorphisms, and isomorphisms.

Prerequisites: Students are expected to have a solid knowledge of linear algebra and experience in writing proofs.

Text: Abstract Algebra, Third Edition, By Dummit and Foote. The library has many good supplementary texts (see Resources).

Homework: I will assign weekly homework for your fun and profit. Problem sets will normally be due on Wednesday at the beginning of class. Your solutions should be complete, concise, grammatical, logical, written on your own, and in your own words. Use of help sites or solutions written by others is not allowed, and is a violation of academic integrity. Consultation with other students or the instructor is allowed after attempting the problems on your own, but writing of solutions should always be done individually. Give proper credit when using the ideas of others. Homework assignments will include some extra problems to be done by those taking the course for graduate credit.  

Quizzes: To help you learn the material effectively, an online multiple choice quiz will be posted on Blackboard after Wednesday's class and after Friday's class, covering the material presented in class since the previous quiz and due before the next class.   

Tests: There will be tests in class on Wednesday October 4 (chapters 0 and 1) , Wednesday November 1 (chapters 2 and 3), and Wednesday November 29 (chapters 4 and 5) . Please warn me at least one week in advance if you must miss a test.

Final Exam: Comprehensive exam, on Monday, December 11 at 4:30-7:15pm in 107 Perkins.

Course Grades: Each of the 3 tests will be worth 12% of your grade and the final exam will be worth 24%.  Online quizzes will count for 10%. The remaining 30% of your grade will be based on your homework. Letter grades will be assigned in accordance with the traditional standards for this course. In particular, a numerical grade of 88% will translate into at least an A-, 76% will translate into at least a B-, 64% will translate into at least a C-, etc.

Expectations: Students are expected to spend at least 6 hours per week on coursework outside of class. The UVM Code of Academic Integrity and Classroom Code of Conduct is in effect, as always. In particular, always be sure to give proper attribution for work or ideas that are not your own. All coursework should be presented clearly and completely. Expectations for homework are spelled out in detail on the homework web page. Students must respect the thoughts and ideas of both the instructor and the other students. Such respect calls for good attendance, promptness, and making every effort to avoid interrupting class time. Please turn off all personal communication and media devices during the class. 

Special Needs: If you are eligible and need an accomodation, please inform me and provide appropriate documentation during the first two weeks of class so that this can be implemented. 

Missed work: Make-up tests can be arranged in the case of an emergency, if you inform me before the start of the test. UVM policy also allows students to make up work that conflicts with documented religious observances or intercollegiate athletic events. Meet with me to discuss this during the first two weeks of the semester.