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Instructor |
Dr. Anda Gadidov |
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Office |
Science Building Room 529 |
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Phone |
(770)423-6098,
e-mail: agadidov@kennesaw.edu |
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Office
hours |
MW
11:00am- 12:30pm; T after 2:00 pm; other times by appointment |
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Class
meets |
MW |
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Text |
Abstract Algebra with Notes to
the Future Teacher
by Nicodemi, Sutherland, and Towsley. |
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Course |
The
main goal is to introduce students to the process of abstraction, of
understanding more general structures starting from concrete examples. It is
in this respect aimed at the future teachers who will learn how to relate the
abstract mathematics to the knowledge they acquired in earlier courses. |
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Description |
An introduction to the fundamental structures of
abstract algebra (groups, rings, and fields), the connections of these
structures with the algebra studied at the elementary level, and the
historical development of modern algebra. Applications will be selected from
the classical problems of solvability of polynomial equations, and the modern
applications of groups to cryptography, and of
finite fields to coding and computer design. |
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Learning |
1. Students will
understand the Well Ordering Principle and will be able to prove simple results
that require the use of this principle. 2. Students will
be able to apply the Division Algorithm and will be able to apply 3. Students will
be able to state the Fundamental Theorem of Arithmetic and to apply this
theorem in solving some elementary problems involving prime factorization. 4. Students will
understand the concept of congruence and will be able to carry out
computations and solve equations involving modular arithmetic. 5. Students will
understand the concepts of ring, field, and group, will be able top give
examples of such structures and will be able to check if a given structure is
one of a ring, group of field. 6. Students will
understand the notions of isomorphism and homomorphism and be able to solve
problems involving these notions. 7. Students will
be able to define the concept of subgroup and will be able to determine
(prove or disprove), in specific examples, whether a given subset of a group
is a subgroup of the group. 8. Students will learn problem
solving techniques that involve not only logic and deduction, but also
experimentation, conjecture or guessing and arguments from analogy. 9. Students will learn how to read
a mathematical text and understand the logical steps. 10. Students will learn the specific
language of mathematical proofs. 11. Students will learn how to write
a rigorous mathematical proof. 12.
Students will learn how to communicate mathematics with their
instructor and with their peers. |
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Prerequisite |
A grade
of C or higher in Math 3260. |
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Technology |
A
graphic calculator may be handy at times. |
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Topic
outline |
Part
1. Topics in
number theory. Part
2. Modular
arithmetic and systems of numbers. Part 3. Polynomials. |
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Grading |
Homework
will be assigned and collected for a
grade. There will be a list of assigned problems and one of suggested
problems. I encourage you to work as many problems as you can, until you feel
you grasp the concept. In this
course you will have to work with many new concepts and formal definitions.
Do not try to memorize them. The best way to achieve understanding and to
succeed in this course is to work many problems involving the new concepts. Write the
homework neatly and show your reasoning arguments. The homework will be
checked for both accuracy and editing. Answers without work will not be given
any credit. Another
component of the course will be class presentations. You will be asked to
come in front of the class to present a proof or a homework problem. If you
can do it without looking at your notes this will be the best proof that you
grasp the concept and master the material. Check
my homepage http://math.kennesaw.edu/~agadidov
for updates on the course. Your
grade will be based on your performance on homework assignments, class
participation, and tests. There will be four semester exams and a final
comprehensive exam. The final is scheduled on Monday, December 10, Make-up tests will not be given unless there are
exceptional circumstances. If you must miss a test, you should notify
me in writing before the scheduled test time. Regular attendance is assumed.
Students are responsible for all material covered and any announcements made
in class. Please notify me if you know you will be absent for certain class
periods. We can work together to ensure understanding of the material you
might have missed. By all means, do not wait until it is too late to ask for
help, and do not try to find help outside the department. If you cannot come
to my office during the official office hours I can try to accommodate you at
another time. Grades will be assigned
as follows:
Tentative schedule of
exams: |
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Academic |
Every KSU student is responsible for upholding the provisions
of the Student Code of Conduct, as published in the Undergraduate and
Graduate Catalogs. Section II of the
Student Code of Conduct addresses the University's policy on academic
honesty, including provisions regarding plagiarism and cheating, unauthorized
access to University materials, misrepresentation/falsification of University
records or academic work, malicious removal, retention, or destruction of
library materials, malicious/intentional misuse of computer facilities and/or
services, and misuse of student identification cards. Incidents of alleged academic misconduct
will be handled through the established procedures of the University
Judiciary Program, which includes either an "informal" resolution
by a faculty member, resulting in a grade adjustment, or a formal hearing
procedure, which may subject a student to the Code of Conduct's minimal one
semester suspension requirement. |
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Withdrawal |
Students who find that they cannot continue in college for
the entire semester after being enrolled, because of illness or any other
reason, should complete an official withdrawal form. Forms may be obtained from the Office of
the Registrar. Students who officially withdraw from the university
with the approval of the registrar before mid-semester (including
registration days) will be assigned grades of “W”, which will not
affect their grade point average.
Students who officially withdraw after mid-semester (and before the
last three weeks of the semester) will receive a "WF," which will
be counted as an "F" in the calculation of the grade point
average. Those students who stop
attending classes without notifying someone will be assigned failing grades,
which jeopardize their chances of future academic success. Students may, by means of the same withdrawal form and
with the approval of the university Dean, withdraw from individual courses
while retaining other courses on their schedules. This option may be
exercised up until This is the date to withdraw without academic penalty
for Fall Term, 2007 classes. Failure
to withdraw by the date above will mean that the student has elected to
receive the final grade(s) earned in the course(s). The only exception to those withdrawal
regulations will be for those instances that involve unusual and fully
documented circumstances. |
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