\vskip 2cm

{\bf\centerline {Math 222: Algebraic Structures}}

{\bf \centerline{Spring, 1997}}

{\centerline{Instructor: M. Dyer}}

\vskip 1cm

{\bf Textbook} Abstract Algebra; A Geometric Approach by Theodore
Shiffrin, Prentice Hall, Upper Saddle River, New Jersey, 1996.

{\bf Syllabus} It is intended to cover the following, together
 with topics from the appendices and, if time permits, selected
 additional topics.

\vskip .5cm

{\bf 1 The Integers}  1.1 The integers, mathematical induction and the
binomial theorem 1.2 The Euclidean algorithm, prime numbers and factorization
1.3 Modular arithmetic and solving congruences 1.4 $Z_m$, rings, integral
domains and fields

\vskip .5cm

{\bf 2 From the integers to the complex numbers} 2.1 The rational numbers
2.2 From the rational numbers to the real numbers
2.3 The complex numbers

\vskip .5cm

{\bf Polynomials} 3.1 The Euclidean
algorithm 3.2 Roots of polynomials 3.3 Polynomials with integer coefficients

\vskip .5cm

{\bf 4 Homomorphisms and quotient rings} 4.1 Ring homomorphisms and ideals
4.2 Isomorphisms and the fundamental homomorphism theorem

\vskip .5cm

{\bf 6 Groups} 6.1 The basic definitions 6.2 Group homomorphisms and
isomorphisms 6.3 Cosets, normal subgroups and quotient groups
6.4 The symmetric group $S_n$ and the $15$-puzzle.

\vskip .5cm


{\bf Honor Code} The course will be conducted under the Honor Code.
If you are aware of a violation of the Honor Code,
contact the Mathematics Department Honor Code Committee. 

{\bf Grading} There will be three in-class exams worth 100 points each
and a cumulative, two hour final exam worth 150 points. In addition,
homework grades will be scaled to give an additional possible 50
points; and your performance on the course will be determined primarily
by your total points score  out of  the possible total of 500 points.
Grade cutoffs for major grades (A, B, C,  D, F) will be assigned for
each exam and for the homework total, and the grade cutoffs for the
course will reflect these individual cutoffs.

The exam dates will be:

Exam 1: Wednesday, February 19

Exam 2: Friday, March 21

Exam 3: Wednesday, April 16

Final Exam: Thursday, May 8.

{\bf Homework} Homework problems will be assigned daily and collected
weekly (on Wednesdays). While not all problems will be graded, all the
assigned problems must be turned in. Homework is expected to be turned
in on time, and unexcused late homework will not be accepted.

The homework is an integral part of the course. One of the goals of the
course is to develop skills in communicating in mathematical language;
it is important that you do all the homework and make serious efforts
to make your written homework solutions clear and comprehensible.

You may discuss the homework with other students, and are strongly
encouraged to do so because it is a good way to learn and test your
ideas, and to develop facility in communicating mathematical ideas.
However, direct copying of another students homework is unacceptable;
your final written homework solutions should reflect your own
understanding of the problems.


\bye
