SYLLABUS – MA 3560 – Applied Modern Algebra and Number Theory
Dr. Pante Stanica
LECTURE: M-Th
at 11-11:50am in Sp-221
INSTRUCTOR: Dr. Pante
STANICA, 242B Spanagel, 656-2714,
pstanica@nps.edu
(preferred means
of communication);
http://faculty.nps.edu/pstanica/
OFFICE HOURS: M,T,W,Th
09am-09:50am
(Be aware that office hours are not a substitute for regular class time)
TEXT: A First
Course in Abstract Algebra, 7th edition, John B. Fraleigh;
2003
Prerequisite:
MA3025 (also, recommended MA3042)
CALCULATOR POLICY: Using a
CAS like Mathematica or Maple can give more insight but it is not required.
MATERIAL TO BE COVERED (and
Objectives for the course—subject to be adjusted along the way):
Hours Topics Sections
5-5
Intro, Binary Operations, Isomorphisms, Groups, Subgroups, Cyclic Groups: S1-S6
3-8
Permutations, Cosets, Direct Products: S8, S10, S11
3-11
Homomorphisms, Factor Groups, Group Action on a set: S13-S17 (partial)
7-18
Rings and Fields, Integral Domains, Fermat and Euler’s Theorem,
Field of Quotients, Rings of Polynomials, Factorization of
Polynomials: S18-S24
3-21
Ideal and Factor Rings: S26-S28
5-26
Extension Fields, Finite Fields: S29-S31, S33
4-30
Isomorphism Theorems, Sylow Thms, S34-37
4-34
Unique Factorization, Euclidean Domains, Gaussian Integers: S45-S47
7-41
Automorphisms and Galois Theory: S48-S55
3-44
Exams and Holidays
HOMEWORK: You are encouraged to do as many
problems as you can from the book. However the standard (default) assignment
for each week is to read carefully the indicated sections and to prepare for
homework the problems I will assign in class. The homework will not be
collected. However, the exams may contain problems from the assigned homework.
TESTS: One in-class midterm will be
given (announced one week in advance) and a final comprehensive
take-home exam in Week 10 (to be returned one week later). Absolutely no
collaboration is allowed. Both the midterm and the final exam will contain
approx. 10-20 prob/que (each of the prob/que will be worth 5-10 points for a
total of 80 points for the midterm and 120 points for the final). No make-up
tests will be given except in extraordinary circumstances (e.g. illness -
present verified doctor's excuse). I reserve the right to give in-class pop
quizzes (1-5pts), which will be used toward the final grade, as an add-on
(extra credit) to the final score. If the test dates will be changed I will
announce it in class at least one week in advance. It is your responsibility to
stay informed of such changes.
GRADING: The number of possible points is 200 (quizzes could
push this over). For the letter grade I will use the following scale (be
advised that class participation will be considered, especially in the
borderline grades):
185-200: A
175-185: A-
170-174: B+
160-169: B
155-159: B-
145-154: C+
135-144: C
130-134: C-
125-129: D+
100-124: D
000-099: failing grade.
An unresolved absence from either of the two examinations will result in a
final grade of “FA”.
ACADEMIC HONESTY: Cheating in this course will
not be tolerated and will be dealt with as harshly as the University
permits. I will report any student behavior that appears contrary to the
standards of discipline and academic honesty or violations of the provisions
described in the current edition of NPS Student's Catalog.
CLASS ATTENDANCE AND ENVIRONMENT: You should do every
attempt to arrive on time and attend each class. You are responsible for the
material covered in missed classes. I do not tolerate any rude behavior;
however, I encourage constructive comments on the material and/or lecture. We
have to maintain a class environment conducive to learning therefore I am
against bringing “active” cell phones, pagers, and other similar
disruptive devices into the classroom.
NOTES:
* It is a bit of material to be covered at a fast pace, so do not fall behind.
* If it is necessary, there will be updates of
this handout. Make sure you check my homepage regularly for info on the course
(that is work in progress).
* Good luck ! I
hope you will all learn Abstract Algebra and make good grades!