Jack Huizenga |
|Brief course description: We will cover the first six chapters of the textbook. This is a first course in abstract algebra, focusing on the three main topics of study in algebra: groups, rings, and fields. On the one hand, groups explore the concept of symmetry in mathematics; on the other hand, rings and fields generalize the familiar concept of number to more abstract settings. The interplay between these two seemingly different ideas is incredibly important in modern mathematics. Students will learn to analyze concrete examples of these objects, as well as to reason abstractly and provide their own proofs of theorems in abstract algebra.|
|Prerequisites: Math 311W, Concepts of Discrete Mathematics is the only formal prerequisite. On the other hand, this is one of the more challenging 400-level math courses, and it will be helpful to have seen other material at a similar level before. If for example you plan on taking Math 436 (Linear Algebra) at some point, it would be natural to take that before taking this course, as it is generally an easier course that will prepare you well for the more challenging topics in this course. Familiarity with proof writing will certainly be helpful, although one of the main goals of this course is to become more proficient in proof writing.|
|Course Delivery: The course will be presented online via Zoom in a remote synchronous mode. Students are strongly encouraged to both ask and answer questions by "raising their hand" within Zoom. The instructor will record lecture notes on a tablet device and post the notes from class each day. Recordings of lectures will also be posted after class, but in-class attendance is strongly encouraged whenever feasible. You and other students will and *should* have many questions to be answered, and you should always feel free to interrupt when something is not clear. If you have a question, many of your fellow students probably have the same question, and we can save a great deal of time and confusion by addressing it.|
Homework is by far the most important part of the course. The only way to learn advanced mathematics is to do advanced mathematics. Weekly homework assignments will be posted on Canvas most
Fridays, and you will upload a pdf of your homework on Canvas by the next Friday at class time. A typical homework set will consist of a reading assignment, 5 exercises to be turned in, and a list of additional textbook exercises that you should complete for yourself. You should expect the homework to take 5-10 hours per week to complete.
Please write your solutions clearly and carefully, using complete sentences and paragraphs to explain all steps of your proofs or computations. |
Solutions to homework will be posted after class on the day it is due, so late homework will not be accepted for any reason. Your lowest score will be dropped at the end of the semester.
|Collaboration: You are encouraged to discuss homework problems with your fellow students. However, you have to write up your solutions by yourselves and show originality. Please write the names of any students you collaborated with on your assignment.|
We will tentatively have exams on the following dates.
Week 6: Exam 1, Friday Oct. 2|
Week 11: Exam 2, Friday Nov. 6
Final exam: To be announced Grading: The homework and exams will count for the following portions of your grade. Homework: 20%
Exam 1: 20%
Exam 2: 20%
Letter grades will be assigned based on the cumulative score; the ranges corresponding to letter grades will be determined based on the difficulty of the exams and the following rubric. A: Able to perform basic computations in algebra and recite the definitions from the course. Demonstrates solid understanding of the theoretical aspects of the course.
B: Able to perform basic computations in algebra and recite the definitions from the course. Demonstrates some understanding of the theoretical aspects of the course.
C: Able to perform basic computations in algebra and recite the definitions from the course.
D/F: Fails to meet the expectations for a C.
Cumulative scores of 85/75/65 will receive at least an A-/B-/C-; however, the final breakpoints may be lowered slightly. Grade ranges will be discussed in more detail after each exam. Make-up exams: Any conflict with scheduled exams should be discussed with the instructor as soon as possible. No accomodations will be provided for missed exams without a valid excuse. Final exam scheduling: Conflicts for the final exam are determined by scheduling; they cannot be scheduled through the Mathematics Department. A student with a final exam conflict must take action to request a conflict exam through eLion during the final exam conflict filing period.
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