Topics in Algebra (Math 31)

Fall 2014

Instructor: Professor Dorothy Wallace

Class MWF 12:30-1:35, xhour Tues 1-2, 108 Kemeny

Office hours MWF 2-3, 204 Kemeny

Fall 2014

Instructor: Professor Dorothy Wallace

Class MWF 12:30-1:35, xhour Tues 1-2, 108 Kemeny

Office hours MWF 2-3, 204 Kemeny

Math 31 Abstract Algebra is a (relatively) new branch of mathematics only a few hundred years old. Through the abstract structures that describe objects and their relationships with each other, this branch of mathematics has proved to be both a unifying approach to superficially different parts of mathematics. It has proven to be one key to understanding natural phenomena based on symmetry. It illumates deep properties of numbers. Algebra is an active research area in pure mathematics, and continues to grow and expand its reach, touching many parts of mathematics, physics, and chemistry.

The specific goals of this course are to 1) familiarize you with the structures known as groups and rings 2) become acquainted with a broad class of examples of groups in particular, 3) improve your proof writing skills, 4) practice learning mathematics independently through reading, and 5) have a chance to discover some mathematics for yourself. In practice, what this means is that sometimes I will lecture, but sometimes you will spend the whole hour working on proofs together, sometimes you will be asked to read a section of the text in advance in preparation for class, and sometimes there will be opportunities for you to make your own conjectures and prove them. We will do many things in class that are not in the text. Therefore attendance is more or less required.

Grading: Grades are based on one midterm (100 each), the final exam (150), four biweekly homework sets (100 total, 25 each), and a small project (50) with presentation in class.

Attendance: This quarter we meet MWF 12:30-1:35, in 108 Kemeny, and occasionally use the x-hour Tues 1-2. We spend class time on many examples and problems not included in the text. Attendance is more or less required.

Final Exam: The final exam is scheduled for Monday, Nov 24 at 3 p.m. Plan to be there!

Text: Abstract Algebra, third edition, by I.N. Herstein

Office hours: Wallace's office: Kemeny 204. Office hours: MWF 2-3 and by appointment.

Syllabus: Will be sent via email.

Honor principle: (This prose was modified from Shemankse's 2010 course page)

On Homework and the project: 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 who rely on solutions to problems that are posted on the web must reference them with the URL. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Honor Code.

Moreover, if in working with someone they have provided you with an important idea or approach, they should be explicitly given credit in your writeup. Hints I give in office hours need not be cited. Note: It is not sufficient to annotate your paper with a phrase like “I worked with Joe on all the problems.” Individual ideas are to be credited at each instance; they represent intellectual property.

On Exams: Students may not receive assistance of any kind from any source (living, published, electronic, etc), except the professor (or designated proctor), and may not give assistance to anyone. Matters of clarification are to be left to the professor (or designated proctor).

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.

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.

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.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations. The same goes for anything that might interfere with coming to class (e.g. sports trips).