Topics in Algebra (Math 31)
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.
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
Disabilities, religious observances, other accomodation as needed: (This prose was modified from Shemankse's 2010 course page)
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
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).