Math 403 Section 0201
(Fall, 2013)
Massimo A. Picardello
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and was last updated: 9-3-13
Title: College Algebra with Applications
Lectures: 12:30-1:45 T-Th
Room: JMZ 1122
Instructor: Professor Massimo A. Picardello, email: picard@mat.uniroma2.it
Office:
MTH 4416
Office phone: (301) 405 5162
Book: Modern Algebra with Applications, 2nd edition, by W. Gilbert and W.K. Nicholson,
2004, J.Wiley & Sons, ISBN 0-471-41451-4
Supplementary book: Abstract Algebra, 3rd edition, by I.N. Herstein,
1999, J.Wiley & Sons, ISBN 0-471-36879-2
Office Hours: T-Th 9:00-9:50 From time to time it may be
necessary to change this schedule, so let me always know in
advance if you are planning to see me.
Feel free, to ask for an appointment at different times if you
cannot see me during those hours (but this should not happen too
often, and different students asking
for these out of schedule appointments should get together and
come together). You can also send me email.
I will answer queries as quickly as possible during office hours,
and as time permits otherwise.
Math 403 is the more theoretical of the two upper-level
undergraduate abstract algebra courses at the University of
Maryland, and is designed for students
planning to do graduate work in mathematics. It will cover the
basics of groups, rings, integral domains and fields. If time
allows, we shall also introduce
error correcting codes.
Students who have already had Math 406 will find some of the
topics very familiar and some of the work easier.
On the other hand, those who take Math 406 after having taken
Math 403 will find Math 406 somewhat easier.
Goals and Quality: Algebra is a very conceptual part of
Mathematics, based uniquely on connecting ideas, with no
reference to modeling physical reality
(although, for group theory, we shall present some geometrical
applications to symmetries of polygons and polyhedral, and, if
time permits, we shall present
applications to signal theory at the end of the course).
Therefore Algebra plays a deep role in mathematical formation,
and is often abstract and demanding.
Consequently, in this course understanding theorem proofs is
equally important than problem solving. Students are expected to
read and fully understand
all statements and proofs.
Most proofs of theorems will be covered in detail in the lectures.
Several lectures will be hard, and students will need full
concentration: but after all, this is
what they are expected to do
if they plan to continue with graduate work in math.
The quality of presentation of solutions will be taken seriously in
this course in the grading of tests.
More advanced students willing to continue their studies with
graduate work in Mathematics may find the textbook a bit too
elementary: it has been chosen
to grant a relatively easy
passing level.
The supplementary book, by I.N.Herstein, covers some more
advanced topics and includes difficult problems.
The most ambitious students will have the option of learning
more by presenting a project, individually chosen by the
instructor, on selected topics of
Herstein’s book (or maybe on some additional problems from the
textbook of Gilbert and Nicholson).
The grade of the project will be 200 points and will replace the
score of the final exam. This option will be granted only to the
students who plan to to do
graduate work in Math and pass the first two tests with grade A.
The project can be presented orally or in writing, depending on
its nature, but this must be
done before the final exam (better before the end of classes).
Makeup exams will not be given. If you have an excused
absence for an exam, the grade will be replaced by 1/2 of the
average of the other two exam
grades.
If you have taken all three exams, the lowest grade will count for
half. Excused absences will be given only for valid medical
reasons, University business,
or appearances in court.
Excused homework will not be used in computing the final
grade. Any unexcused absences on exams (including the final)
or unexcused late homework will
be counted as zero.
Any student with a valid reason to be excused from an exam
must contact before the exam or immediately after, either by
email or by phone, and present
documentation at the next class session attended.
Any student who needs to be excused for a religious observance
should let me know as soon as possible, but in any case no later
than the end of the schedule
adjustment period.
Homework: Homework problems from the text are listed
below. Homework will be due each Tuesday and will be on
everything covered the previous week.
Selected problems will be discussed in class - after the
homework is collected, if they are assigned problems.
Note that many of the odd numbered problems are done at the
back of the book. Try doing the odd numbered problems without
looking.
For the even numbered problems, if you are stuck, try looking at
the answer to an odd numbered problem that is similar.
Grading: A total of 550 points is available in the course:
Three hour exams (100 points, lowest counts half)
Final
Homework
Total
250
200
100
550
The schedule of exams follows:
Thursday,
October 3
Test I
Tuesday,
November Test II
5
Tuesday,
Test
November
III
28
Friday,
December
20 (1:303:30)
Final
A tentative schedule of homework follows. There may be
changes made as the semester progresses. In particularsome
homework problems
may be dropped if the load turns out to be too heavy for the
majority of the class.
In this case, those students who will submit correct solutions
to the full homework set listed here will receive a bonus
score.
Homework Assignments
The following homework is to be handed in, except those of the
odd-numbered problems that are solved at the end of the book
(but are listed here just because they are
needed or useful to solve some of the even-numbered ones).
Some of these problems are trivial (in green in this list): mistakes
in their answers will be penalized.
Some require ingenuity (in red): mistakes will be tolerated, and
correct answers will be a bonus. Among these are two problems
recurrent in several chapters, that ask to
Prove the second and third isomorphism theorems for various
algebraic structures: the students who are not able to find the
proofs can read it in most books in Algebra,
and are welcome to do so.
Each assignment is due the Tuesday following the completion of
the chapter.
Page Problems
Chapter
71
3
2, 4, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 38,
42, 44, 48, 56, 60, 62, 64, 68, 72, 74, 78,
86, 89
Chapter
100
4
2, 4, 6, 8, 10, 12, 14,
15, 16, 18, 22, 30, 34,
36, 38, 40, 42, 43, 44,
48, 50, 54, 63
Chapter
121
5
6, 8, 23, 24, 28, 30,
35
Chapter
176
8
2, 4, 6, 8, 10, 12, 16,
20, 24, 30, 32, 34, 36,
38, 40, 41, 42, 43, 44,
48, 51, 52, 54, 56
Chapter
201
9
2, 4, 6, 8, 10, 12, 14,
18, 20, 22, 26, 28, 34,
38, 40, 42, 44, 46, 48,
50, 52, 53, 56, 58, 59,
62, 65, 67, 68
Chapter
214
10
2, 4, 6, 8, 12, 14, 16,
18, 19, 20, 21, 22, 25,
26, 30, 31, 34, 36, 38,
40, 44, 48, 50, 52, 54,
56, 57, 58, 60, 65
Chapter
232
11
2, 6, 14, 18, 20, 26,
28, 34, 36,38, 41, 44,
60
Chapter 288
14
2, 6, 10, 12, 14, 20
Tentative Schedule of Lectures
Math 4031 Section 0201 Fall 2013 Sections 02** University of
Maryland, College Park
The following course schedule is tentative, subject to change as
necessary.
In fact, the pace will depend very much on the difficulties that
the class will have on each subject.
If the proposed schedule is too hard for the class, then we shall
slow down and drop Chpter 14, “Error-correcting Codes”.
Day
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Tues
Thurs
Date
3Sep
5Sep
10Sep
12Sep
17Sep
19Sep
24Sep
26Sep
1Oct
3Oct
8Oct
10Oct
15Oct
17Oct
22Oct
24Oct
29Oct
31Oct
5Nov
7Nov
Section
Pages.
3.1-3.4
47-62
3.5-3.8,
4.1
63-78
Review
71-75 and previous material
4.2-4.4
78-91
4.5-4.8,
91-99
Review
5.1-5.3
5.4-5.5
Review
of
Practice
Test 1
100-103 and previous material
104-111
111-120
71-75, 100-103, 121-123, 176-179,
Old exams: _Resources_ at
www.math.umd.edu/undergraduate
Exam 1
8.1-8.3
155-164
8.4-8.6
164-172
8.7,
Review
172-179
9.1-9.2
9.3-9.5
9.6-9.7
Review
Review
of
Practice
Test 2
180-187
187-195
195-200
201-203 and previous material
176-179, 201-203, Old exams:
_Resources_ at
www.math.umd.edu/undergraduate
Exam 2
10.110.3
204-210
Tues
Thurs
Tues
Thurs
Tues
Tues
Thurs
Tues
Thurs
Friday
12Nov
14Nov
19Nov
21Nov
26Nov
3Dec
5Dec
10Dec
12Dec
20Dec
10.4,
Review
11.111.2
11.311.4
Review
210-217
218-225
225-232
233-235
Review
of
Practice
Test 3
Exam 3
14.114.3
14.414.5
14.6,
Review
264-276
276-284
284-292
Final
Exam
Academic Dishonesty:
Please consult the following website regarding university policy
on academic dishonesty: http://www.shc.umd.edu/code.html.
You should be familiar with the University's policies on
Academic Integrity, including the Honor Pledge.
Any instances of academic dishonesty on worksheets, quizzes, or
exams will be vigorously prosecuted.
Behavior in class:
Of course students should better pay attention all the time to
what the instructor teaches, and avoid to chat on the Internet or
read their email instead.
But some types of behaviors are considered inacceptable: those
who create any type of distraction and confusion in the audience,
distracting others students who are
trying to learn.
This includes making noise, talking loudly with other students,
whispering repeatedly, talking on the phone. Going out of the
classroom is some sort of distraction,
but of course it may be necessary sometimes. Going out and back
in more than once, for instance to make phone calls, is severely
discouraged.
As explained above, changes in the program are possible, maybe
even likely. This page will be kept up-to-date as changes are
made.
You are responsible for checking these
updates.
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