Math 71
Algebra
Instructor: Carl Pomerance (carl.pomerance@dartmouth.edu)
Abstract  Classes  Staff  Textbook  News and current assignment  Grading  Homework  Past assignments  Exams  Honor Code  Other
News and current assignment 
Please hand in your test at my office or leave in my mailbox. On problem 4 on the test, you are permitted to assume that not only is n composite, but that it is divisible by at least two different primes. You will get 5 points extra credit if you solve it as originally stated. 
Abstract 
The theme of the course is abstract algebra. Most people think of algebra as that part of math where you solve equations or manipulate expressions which have letters in them. This actually is not all that closely related to abstract algebra, though there is a connection. Abstract algebra deals with the structures of familiar objects, such as the integers, the complex numbers, matrices, etc. The idea is that when these more concrete sets are studied in the abstract, certain of their properties are forced upon them because of other properties already assumed. Thus, one can then deduce these other properties for any system that has the basic assumed properties. Depending on how many of these basic axioms are assumed, we have groups, rings, and fields. These will be our object of study.
A very brief syllabus (chapters from Dummit and Foote, Abstract Algebra): 
Classes 
Room: 108 Kemeny 
Staff 

Textbook 
Abstract Algebra, 3rd edition, by Dummit and Foote
This book is available
at Wheelock Books and elsewhere. (Yes, I know its expensive.)

Grading 
Homework 20%, two mid term exams each 20%, final exam 40%. As much as possible, grades will be based on demonstrated knowledge. However relative performance may be used as a criterion for increasing grades, and grade borderlines will be chosen to place a relatively small number of students on borderlines. At the end of the term, the lowest of your 4 grades (hw, midterms, final) will be dropped, except if your final exam is your lowest grade, in which case the weight of the final exam will be halved. (So, if one of the midterms or hw is dropped, then the remaining 3 grades have weights 1/4, 1/4, 1/2; while if the final is the lowest, the four grades have equal weight 1/4, 1/4, 1/4, 1/4.) 
Homework 
Homework is due at the start of the class period on the due date. Late homework is generally not accepted unless there is a prior arrangement. 
Past assignments 
Homework due Monday, Sept. 25: Homework due Monday, Oct. 2:
Homework due October 9:
Homework due Wednesday, Oct. 18:
Homework due Monday, Oct. 23:
Homework due Monday, October 30:
Homework assignment due Monday, Nov. 13: Homework due Monday, Nov. 20: 
Exams 
The two midterm exams will be openbook, opennotes takehome tests and will be given out on October 11 and November 1, each due in class two days later. The final exam will also be openbook, opennotes takehome. It will be given out on the last day of classes and will be due by 11:00 AM on December 4 (the end of our regularly scheduled exam period). 
Honor Code 
Students are encouraged to work together to do homework problems. What is important is a student's eventual understanding of homework problems, and not how that is achieved. The honor principle applies to homework in the following way. What a student turns in as a homework solution is to be his or her own understanding of how to do the problem. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. Students are discouraged from using solutions to problems that may be posted on the web, and as just stated, must reference them if they use them. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's code or solutions, in whole or in part, is a violation of the Honor Code. The honor principle applies to exams as follows: Students may not give or receive assistance of any kind on an exam from any person except the professor or someone explicitly designated by the professor to answer questions about the exam. Students may not use a computer during an exam, but they may use a calculator to help with simple arithmetic. If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. It is always easier to ask beforehand. 
Other 
I encourage any students with disabilities, including "invisible" disabilities such as chronic diseases and learning disabilities, to discuss appropriate accommodations with me, which might help you with this class, either after class or during office hours. Dartmouth College has an active program to help students with disabilities, and I am happy to do whatever I can to help out, as appropriate. students with disabilities, and I am happy to do whatever I can to help out, as appropriate.Any student with a documented disability requiring academic adjustments or accommodations is requested to speak with me by the end of the second week of the term. All discussions will remain confidential, although the Academic Skills Center may be consulted to verify the documentation of the disability and advise on an appropriate response to the need. It is important, however, that you talk to me soon, so that I can make whatever arrangements might be needed in a timely fashion. I realize that some students may wish to take part in religious observances that fall during this academic term. Should you have a religious observance that conflicts with your participation in the course, please come speak with me before the end of the second week of the term to discuss appropriate accommodations. 
This page was inspired by the web site for Math 19 in Fall 04, written by Alin Popescu