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PURPOSE:
Modern Algebra is the study of certain mathematical structures generally
given as sets with associated operations, in particular, groups, rings and
fields. But more than this, modern algebra is a contemporary living, growing
area of knowledge that is currently being used by working physicists, chemists,
and computer scientists. It also is fundamental to such fields as cryptography
and coding theory.
The role preparation model for Trevecca's Teacher Education Program is "the
teacher as holistic developer." Efforts will be made throughout the course to enhance
the student's development in the psychomotor, social, emotional, and spiritual domains as
well as the cognitive domain.
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OBJECTIVES:
The students will develop competency:
- working with examples of algebraic structures.
- doing computations on algebraic structures.
- proving theorems.
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RESOURCES NEEDED:
Textbooks:
Required:
An Introduction to Abstract Algebra, by by Olympia E. Nicodemi,
Melissa A. Sutherland, and Gary W. Towsley, published by Pearson/Prentice Hall,
ISBN 0-13-101963-5.
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COURSE REQUIREMENTS:
- Successful completion of two tests, a take-home final exam and an in-class final exam. The
in-class final exam will be given
Tuesday, December 9, 2:00-4:00. You may use your text
and your notes only. You may ask me questions. The take-home final is due at
the beginning of class on the final exam day. Tests are to be taken as scheduled except in cases of
emergency, in which case the instructor must be notified in advance and the test must be
made up within two days of the student's return to class.
- Assigned problems are to be completed and turned in.
Assignments
will be given for each section covered. Each problem will be graded on a
10 point scale.
- Presentations of at least 2 substantial proofs in
class. The proofs to be presented will be assigned in class and students
will give a presentation of the proof to the class. The presentation should
be an explanation of the proof, not just a repetition of the proof given in
the book. The presentations will each be graded on a 25 point scale.
- Two short biographical sketches, at least 1-2 pages in length, will be
written on mathematicians to be selected from the following list: Fermat,
Euler, Gauss, Abel, Cardano, Cayley, de Moivre, Eisenstein, Galois, Klein,
Lagrange. The papers
should contain information about the life of the subject and about their
contribution to abstract algebra.
- Regular class attendance is strongly recommended. Mathematics is a deductive science and thus most lessons depend upon
the previous lessons. It is imperative that you miss class only when absolutely necessary.
- Academic Honesty: (See Academic
Honesty Policy statement in the student handbook on page 42.)
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EVALUATION PROCEDURE:
All grading will be based on the work done and procedures used, not on the answer
obtained. This means that partial credit will be given for correct or partially correct
procedures and also that a correct answer does not necessarily imply that full credit will
be given.
Final grades will be determined by a combination of all tests and homework
and presentations. The total of
all of the homework grades will count
the same as one test. The total of the presentations will
count as half a test. The total of the two biographical papers will count as
half a test. The tests, the take home final, and the in class final will
all be weighted equally. Thus, out of 700 points, 200 will come from the
homework grade average, 50 will come from the presentations,
50 will come from the papers,
100 will come from each of the tests, and 100 will come from each
part of the final exam.
Grading
Test 1
100
points
Test 2
100 points
Take home final 100 points
In class final 100 points
Homework 200
points
Presentations 50 points
Biographies
50 points
The following cutoffs can be use as a guide for the final grade:
A+ , 97%; A,93%; A-,90%; B+,87%; B,83%; B-,80%; C+,77%; C,73%; C-,70%; D+,67%;
D,63%; D-,60%.
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