General Information 
What is Abstract Algebra II? The second semester of Abstract Algebra will pick up where MATH 335 ended, focusing primarily on rings and fields. Serving as a good generalization of the structure and properties exhibited by the integers, a ring is an algebraic structure consisting of a set together with two operations addition and multiplication. If a ring has the additional property that division is welldefined, one gets a field. Fields provide a useful generalization of many familiar number systems: the rational numbers, the real numbers and the complex numbers. Topics to be covered include: polynomial rings; ideals; homomorphisms and ring quotients; Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains; the Gaussian Integers; factorization techniques and irreducibility criteria. The final block of the semester will serve as an introduction to field theory, covering algebraic field extensions, symbolic adjunction of roots; construction with ruler and compass; and finite fields. Throughout the semester there will be an emphasis on examples, many of them coming from calculus, linear algebra, discrete math, and elementary number theory. There will also be a heavy emphasis on the reading and writing of mathematical proofs. Prerequisite: MATH 335.  
The Text. John B. Fraleigh A First Course in Abstract Algebra, Seventh Edition, Addison Wesley Longman, 2003  
Daily Homework. Homework assignments will typically include a mixture of computation and proofwriting. Computations will serve to develop problemsolving 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 after you figure out the correct line of attack. The presentation of your proof is equally important.  
HOMEWORK POLICY


Academic Honesty. In general, the rules set forth in the 20072008 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 writeup 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.  
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.  
Exams. There will be 2 hourly exams and a final exam. All exams will have a takehome component as well as an inclass component. The takehome component of the hourly exams will be worth twice as much as the inclass portion of the exams (100pts and 50pts respectively), and you will choose a 72hour period over which to work on the takehome portion. Each component of the final exam will be worth 150 points.


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


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; Office of the Dean for Academic Advising, 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. 
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