**Fall 2016
Semester**

**Office: **MCS 235

**Telephone: **617-353-8203

**E-mail: tkohl@math.bu.edu** (I read my e-mail
throughout the day!)

**Office Hours: **M,W 4-5** **

**Text: ***A First Couse In Abstract Algebra (7 ^{th} Ed.)*

**Remarks: ** The main
prerequisites for this course are some basic set theory and number theory, which
we will review. The content of this course is exclusively group theory. Groups
are examples of algebraic systems that are rather different from the integers,
rationals, or real numbers which you’ve worked with in other classes. Groups,
especially finite groups, are self-contained systems with their own ‘arithmetic’
that is often quite different than what one is familiar with from say calculus
or basic algebra. At a deeper level, groups are a means of encoding the notion
of ‘symmetry’ in a concise form. This has ramifications across **many **mathematical disciplines. As you
will see if you take MA 542, symmetry is important, for example, in the study
of the solutions of polynomial equations. In fact, questions regarding whether
such equations *have *solutions can be decided based on group theoretic
criteria. Also, group theory problems are an excellent means of learning how to
write good mathematical arguments. Some of the questions themselves will seem simple,
but they can be highly instructive, and are an excellent means of learning how
to reason abstractly.

**Outline of topics to be
covered:**

*(Note: Not all sections in a
given chapter are covered.)*

Part
I Groups
and Subgroups -
Chapters 1 - 7

Part
II Permutation
Groups, Cosets, Direct Products - Chapters 8 - 11

Part
III Homomorphism and Factor
Groups -
Chapters 13,14,16

Exams: During the semester, there will be a take-home mid-term
exam worth 100 points, as well as a final exam (also take-home) worth 200
points. The schedule for these exams is given on the next page.

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Homework: During the semester, I will generally assign
homework on a daily basis. This homework is your primary means of learning the
material, even more so than the lectures. Indeed, it is
only by actually working out the solutions to problems that one really learns
this material. Not doing homework is a *bad
*idea and will result in a poor performance in the course.

Additionally, there will
be, throughout the course of the semester, 10 turn-in homework assignments,
each worth 20 points, for a total possible maximum of 200 points *if you complete each perfectly.* Each
turn-in assignment will be due by the next class meeting after it was assigned.

[Note: On the homework,
you may discuss the material with each other, but plagiarism is not acceptable. Your written answers must be your own. I
do not wish to see identically worded answers on the exams or homework.]

Grading: Your grade in the course will be based on the
combined sum of the two exams, the 10 turn-ins, and the final exam, out of a
possible total of 500 points.

Cheating: I consider cheating to be a very serious
offense and any cases of it will merit action by the University Academic
Standards Committee.

Important Dates:

No class on Tuesday October 11^{th} due to
substitute Monday schedule

Thanksgiving break – Thursday November 24th

Midterm Exam – Assigned Thursday October 13 (due Thursday October 18)

Final – Assigned Thursday December 8 (due Thursday December 15)

The last lecture will be Thursday, December 8.

Web Page: There is a web page for the course where you can
find the homework assignment listings, as well as the syllabus and other
materials that will be made available during the course.

The URL is:

http://math.bu.edu/people/tkohl/teaching/fall2016/index.html

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