General Information and Course Policies

What is Abstract Algebra?

Here's the boring answer: As the name indicates, Abstract Algebra involves the study of algebraic equations and the methods used to solve them. The abstraction refers to the perspective taken in the subject, which is very different from that of high school algebra courses. Rather than looking for the solutions to a particular problem, we will be interested in such questions as: When does a solution exist? If a solution does exist, is it unique? What general properties does a solution possess? Our exploration will go beyond such algebraic structures as the integers and the rationals, and our approach will be axiomatic. Indeed, working from a fairly small set of axioms one can describe the properties of a wide range of algebraic structures concisely and elegantly. More importantly, however, abstract algebra will allow you to take a concrete problem Focusing on group theory, our study will be motivated by the desire to describe algebraic structures in a rigorous, concise, and elegant way.

Here's the exciting answer: Abstract Algebra is a rich set of tools that will allow you to answer questions relating to concrete situations in the world around you. For example, how can one find strategic moves that are helpful in solving the Rubic's cube? What is the probability that one will have a "SET" in the first round of the card game SET? How can one keep confidential information out of the hands of evil-doers? With the tools provided by Abstract Algebra, one can apply an algebra structure to each of these situations and use this structure to compute, explore, understand and solve. Abstract Algebra is very powerful.

The Text. John B. Fraleigh A First Course in Abstract Algebra, Seventh Edition, Addison Wesley Longman, 2002
Daily Homework. Homework assignments will typically include a mixture of computation and proof-writing. Computations will serve to develop problem-solving ability while providing the motivation and intuition necessary to understand the theory of the course. Proof writing will serve to develop the presentation skills necessary to communicate rigorous mathematical ideas to others. Keep in mind that you are not done with a proof when you figure out the correct line of attack. The presentation of your proof is equally important.

HOMEWORK POLICY

1. Homework is due at the START of class on the assigned due date, unless I specify otherwise. Late homework will not be accepted. If you know you will be missing class for some reason (e.g., an athletic event), turn in your assignment BEFORE you leave. Under extenuating circumstances extensions may be granted, but this should be discussed with me in advance.
2. Your homework will be evaluated on neatness, completeness, and correctness.
3. Group work is encouraged, but assignments must be written up INDIVIDUALLY unless specified otherwise. Copied work is considered to be an academic infraction even if the work was discussed in collaboration with a classmate before write-up (see Academic Honesty below).
Daily Reading. Reading the textbook before each lesson is a necessity. Come to class prepared with questions and comments for discussion. There will not be enough time to cover all aspects of each topic during class. You will still be held responsible for the material.
Projects. On occasion, we will be using the software package GAP (Groups, Algorithms, and Programming). GAP is a freely distributed program designed to handle large computations within and relating to groups. See GAP projects for more information on this. We will also work through a fun project relating to the card game SET that does not rely on GAP at all (see the syllabus).

Exams. There will be 2 hourly exams and a final exam. Each of the 2 hourly exams will have a take-home component as well as an in-class component. The take-home component will be worth twice as much as the in-class portion of the exam (100pts and 50pts respectively), and you will choose a 48-hour period over which to work on the take-home.

 Exam I..........................................................Friday, Sept. 26 (The take-home portion will be distributed on Wed., Sept. 26 and due Mon., Oct. 1) Exam II........................................................Wednesday, Nov. 7 (The take-home portion will be distributed on Wed., Nov. 7 and due Mon., Nov. 12) Final Exam..................................................Monday, Dec. 17 (The final exam will be distributed on Mon., Dec. 10 and will be due at 11:30AM on Monday, Dec 17. This date/time was chosen to agree with the scheduled exam period defined by the college. There is no limitation on the number of hours you can work to complete the final.)

Grades. Your grade will be based on the daily homework, presentations & participation, projects, 2 exams, and the final exam. Each will be weighted as follows.

 % of Total Daily Homework (Written Presentations) & Quizzes 25 Projects & Participation (including Oral Presentations) 15 2 Exams (15% each) 30 Final Exam _30_ TOTAL: 100

Academic Honesty. In general, the rules set forth in the 2007-2008 Course of Study apply. Presenting the work of others as your own is strictly prohibited. In the case of homework, you may collaborate with others in discussing how a problem may be solved, but your write-up must be your own. If you submit work that contains the ideas or words of someone else, then you must provide proper citation. Assistance can not be given nor received (other than by the instructor) on any quiz, or exam associated with this course, except where explicitly allowed by the instructor. In the case of a group assignment, all members of the group should contribute equally to writing the final product. And every member of the group is responsible for the content of the entire paper, not just the section(s) that are written by that person. Don't put your name on a paper written by others. For further information, consult your instructor.
Learning Disabilities. If you have a disability which requires an accommodation in this class, please feel free to discuss your concerns with me, but you should also consult Ms. Erin Salva, (Coordinator of Disability Services; Old Bank Building, PBX 5453) as soon as possible. Ms. Salva (in consultation with the L.E.A.R.N. committee) has the authority and the expertise to decide on the accommodations that are proper for your disability. Though I am happy to help you in any way I can, I cannot make any accommodations for learning (or other) disabilities without proper authorization from Ms. Salva.

 Back to the Kenyon Homepage Back to the Math Homepage Back to JAH's Homepage Back to JAH's Abstract I Homepage