Instructor: Ben Linowitz

Office: 241 Kemeny Hall

Office Hours:

Mondays - 11AM - 12:30PM

Wednesday - 3PM - 4:30PM

Course Content:

This course will provide an introduction to abstract algebra and in particular to group theory and ring theory. We will also explore a few of the many exciting applications of abstract algebra, for instance, the RSA cryptography scheme.

A second, and equally important, goal of this course is to teach you how to write a concise, correct mathematical proof. Several x-hours will be devoted to proof-writing, and a number of the homework / exam problems will ask you to prove certain assertions.

Prerequisite: Math 22 or Math 24 (Linear Algebra).

Textbook: Contemporary Abstract Algebra by Joseph Gallian.

Scheduled Lectures:

MWF: 1:45PM - 2:50PM in 105 Kemeny Hall

Thursdays (x-hour): 1PM - 1:50PM

Unless I announce otherwise we will be using all of our x-hours.

Homework:

Homework will be assigned once a week, generally on Wednesday, and will be collected the following Wednesday. The homework problems will be of two types. Some of the problems will be computational in nature and will ask you to perform a calculation or explain why a specific assertion is true (or to provide a counterexample if the assertion is false).

Other homework problems will be more proof oriented. Because proof-writing takes time to master, you may resubmit your proof oriented assignments (the following Wednesday) in order to receive a higher score. Therefore there is no reason why anyone should not be receiving full credit on their proof assignments. There will not be many problems of this type at first; perhaps only one or two a week. As the term progresses and you become more comfortable writing proofs, the number and difficulty of these problems will correspondingly increase.

Quizzes:

On most Fridays there will be a short quiz which should take no longer than fifteen or twenty minutes to complete. The problems on the quiz will not be difficult and are meant to ensure that you are keeping up with the class (i.e. know all of the relevant definitions and can perform routine calculations).

Exams:

There will be two exams. The first will be a midterm and will be around the half-way point of the course. The other exam will be the course final. Both exams will be take-home. I will speak more about these exams in class.

Grading:

Your final score will be out of 500 points and will be determined as follows:

150 Points: Homework

100 Points: Quizzes

100 Points: Midterm

150 Points: Final Exam

Honor Code:

Collaboration on homework is both allowed and encouraged. I simply ask that you write the names of any students that you collaborated with on the homework that you turn in each week. It is important to keep in mind that every student is responsible for what he or she turns in. It may be tempting to believe that you understand an argument that was figured out by a friend. By turning in the solution, you are saying that you understand the it well enough to explain it to others.

Collaboration is not allowed on the the midterm or final exam. Students may not seek assistance from any source (electronic or otherwise) except the instructor.

Disabilities:

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.

The Student Disabilities Coordinator, Nancy Pompian, can be reached at 6-2014 if you have any questions. 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.