Course Syllabus

Math 4413-01W: Abstract Algebra I

**Instructor:** Dr. David G. Robinson, Boyd #326,
678-839-4137

E-Mail: davidr@westga.edu

Office Hours
(Tentatively): *MWF* 8 – 9:50 a.m., 12
– 12:50 p.m.

**Class Meetings: ***MW*F
1 – 1:50 p.m., TLC #1106 (to be changed)

These
will consist of a combination of lectures, question-and-answer sessions,
problem presentations, and general discussions. All reading will be assigned in
advance of the meeting thereon.

**Text/Resources:** Saracino, Dan, *Abstract* *Algebra: A First Course*, Waveland Press, Inc., Long Grove, IL,
1980, 1992

**Prerequisites:** Math 3413

**Topics: ***Sets and Relations *(Sections 0,1,7, 8
and9; »
2 weeks): sets, subsets, Boolean algebra, posets and lattices, well-ordering
principle, mathematical induction, equivalence relations, partitions,
functions, permutations, binary operations, associativity, commutativity, etc.

*Groups*
(Sections 2 – 6, 8 - 14; »
7 weeks): group axioms, group tables, cancellation laws, abelian groups, cyclic
groups, subgroups, direct products, symmetric groups, cycle structure of a
permutation, dihedral groups, cosets, Lagrange’s Theorem, normal subgroups,
quotient groups, group homomorphisms, isomorphism theorems, abelian group
factorizations, etc.

*Rings*
and *Fields *(Sections 16 -21; » 5 weeks): ring
axioms, units, zero-divisors, nilpotency, integral domains, division rings,
fields, subrings, ideals, quotient rings, principal ideals, prime ideals,
maximal ideals, ring homomorphisms, isomorphism theorems, prime fields,
polynomial rings, irreducible polynomials, simple field extensions, finite
fields, principal ideal domains, unique factorization domains, Euclidean
domains, sums of squares, Fermat’s theorems, etc.

**Objectives:** Besides developing your understanding of the topics
mentioned above, there are some particular skills you should improve upon along
the way in order to be able to apply what you learn in this course to future
courses of study. These include:

·
use of appropriate mathematical
terminology and notation

·
mathematical abstraction and conjecturing

·
recognition of algebraic structures
throughout math and science

·
mathematical proof techniques

·
writing skills – both formal and informal

**WAC Objectives**

**and Requirements: **

** **This is a** **Writing
Across the Curriculum (WAC) course, as indicated by the “W” after the section
number of the course. Like all such courses, it *emphasizes writing as a tool for both learning and communication.*
Therefore the writing assignments for this course are divided into two types
according as the main objective is either “writing to learn” (WTL) or “writing
to communicate” (WTC). The specific assignments are as follows:

**WTL **

·
*Problem solutions/proofs* (approximately three or
four per week)

·
*Short-answer test questions* (two or three per test)

·
*Logbook of definitions,
theorems and conjectures* (to be submitted at the end of each test, though entries should be
made daily)

* ***WTC**

·
*Formal Paper* (five-pages, type-written)
on some *application* of or some aspect
of the *historical development* of
abstract algebra. You will submit this in three stages: (1) Description of the
topic and the references to be used (2) Rough draft (3) Final draft. (See the
attached schedule for exact due dates.)

**Evaluation **

**Procedures: **Your understanding of the subject material and
your progress toward the aforementioned objectives will be evaluated on the
basis of your written *solutions/proofs*
*of* *selected* homework *problems*,*
your performances on three written *tests*,
your *Logbook, *your *applications/history paper* , and your *class participation *(attendance,
preparedness and contributions.)

** ** [*Homework problems from the text or from
class will be assigned regularly and discussed in class whenever possible. Be
prepared to discuss them, along with the readings, *as soon as possible* after they are assigned!]

**Criteria:** Grades on all work
will be based upon

·
accuracy of information (including
calculations and

use of mathematical symbols and
terminology)

·
depth and breadth of solutions

·
logic and clarity of arguments

·
neatness and clarity of presentation

·
correctness of grammar and spelling

·
thoroughness and timeliness of work

·
intellectual honesty and creativity

·
achievement of personal potential

·
difficulty of the assignment/test

**Grades: **My
scale for converting numerical grades (i.e., percentage points) to letter
grades will be as follows:

*89-100*
A, *77-88* B, *65-76* C, *50-64* D, *below 50* F

Your final grade will be
based on your *problem solutions/proofs*
(30%), *test scores* (40%), Logbook
entries (10%), *application/history paper*
(10%) and *class* *participation *(10%). Class participation
includes attendance: Missing more than three class meetings *for any reason* will result in a
deduction of 1 point per absence (beyond the third) from the 10 points available.

**Important**

**Reminders:**

·
Attendance is important! However, should
you find for some reason that you must miss a class meeting, remember that you
are still responsible for any and all material you may have missed during your
absence.

·
Problem set solutions/proofs must be
turned in at the prescribed times (TBA) in order to be eligible for any credit.
*All work on these assignments must be
your own, i.e., no help from anyone, without prior permission from the
instructor. Failure to abide by this policy will lead to serious consequences:
automatic zero on the assignment in
question, possible expulsion from the class, etc.*

·
Tests must be taken at the prescribed
times (see attached schedule),* except by
prior permission from the instructor, which will only be given under the direst
of circumstances (serious illness, e.g.).* *In order for you to obtain such permission, I must be notified of your
“dire circumstances”, by e-mail, phone, or otherwise, before the test is over.
Otherwise you will almost certainly receive a score of zero for that test.*

·
If you find yourself falling behind in
the course, do not delay in seeking out appropriate help and advice from
someone who is competent in the subject area and who has your best interests at
heart!

·
I assume you will abide by the UWG Honor
Code. So will I!