Instructor: Dr. Chein
Office: 612 Computer Building
Phone: 204-7846
e-mail:
orin@math.temple.edu
Office hours (subject to change): M,W:
12:00-1:00, T: 11:30-12:15, F:
8:30-9:15
Text: Algebra, Pure and Applied, by Aigli Papantonopoulou.
Prerequisites:
Math
141 and Math 147, or permission of the instructor
Concepts
that students are expected to know as a prerequisite:
1. Equivalence
relations and their relationship to partitions
2.Mappings (functions),
including injectivity (1 to 1 -ness) and surjectivity (ontoness)
3. Elementary set theory, including Cartesian
products
4. Techniques of
proof (at least some idea of how to approach a proof of a theorem)
5. Mathematical
induction
6. Properties of the Integers (including divisibility, the Division Algorithm, the greatest common divisor, and prime numbers).
The text reviews most of these topics in Chapter
0.
I expect every student in the class
to get a Blackboard account. If you
don’t already have one, go to http://blackboard.temple.edu
and login using your astro account username and the last four digits of
your social security number as your password.
(If you don’t know your astro account user name, ask me.) Once you have done so, change your password
for security. I expect every member of
the class to check Blackboard at least once a week, preferably, daily. I plan to use blackboard for announcements,
for some homework assignments, and possibly even for some tests or
quizzes. I also hope to use it for
discussions and possibly even surveys.
You might post queries about things you didn’t understand or missed in taking
notes, and, hopefully, you will answer each other’s questions as well. You can also use this as a vehicle to
contact me.
The
Course:
This semester, we will
concentrate on Group Theory, which is covered in the first five chapters of the
book. If we can do a bit more, that
would be great, but we will play this by ear.
Next semester, we will cover rings
and fields.
Homework:
Numerous
problems will be assigned each class to be done for the following class (see
the attached problems list). Some of
these problems will be designated as "hand-in" problems, and are to
be submitted in writing or on Blackboard, as discussed below. Other homework problems will not be
collected (although you may submit them if you would like me to correct them),
but I will review some of them in class if you request that I do so. Nevertheless, it is expected that you
attempt all of the problems in a timely manner, and that you keep up with the
pace set in class. This is part of your
responsibility to yourself as a student and to whoever is paying for your
education. THE ONLY WAY TO LEARN
MATHEMATICS IS TO DO MATHEMATICS.
Writing:
Since this is a W course, you will be expected to do a substantial amount of writing. Each week (more or less) some problems will be assigned to be handed in. A list of these problems may be found on page 6, below. These problems will be graded primarily for mathematical content but organization, style, grammatical and idiomatic correctness, spelling and punctuation will affect the grade as well. The hypothetical audience for all written work will be the other students in the class. You must explain your reasoning to them and must convince them (and me) that your solution to the problem you are submitting is both correct and complete.
Some hand-in problems
are to be submitted on paper, and others are to be submitted on
Blackboard. Although I encourage
discussion of overnight problems among class members, hand-in problems must
represent your individual efforts and are not to be discussed with anyone
other than me until after they have been submitted. Breaking this rule is a serious violation of
the Student Code of Conduct and will be severely punished. (I caution you, based on past experience,
that I almost always can tell when two students have worked together or when one
has copied from the other, so I strongly advise you not to work with anyone and
not to copy anyone else's work nor allow anyone to copy yours. This warning is not intended as a challenge
but, rather, as a word to the wise.) If
you need help with a hand-in problem, come to me.
Hand-in problems will
usually be due the Monday after they are assigned. Problems listed on page 6 are considered to be assigned on the
day we cover in class the section in which they appear. This applies even if I forget to mention the
problems during class. If in doubt,
ask. Late work will not receive credit.
Page 6 also contains
rules governing the format of problems to be handed in. It is important that you carefully read
these rules. If you do not follow them,
you will lose credit.
Grading:
There will probably be
three midterm exams, each worth approximately 16% of the final grade, and a
cumulative final examination, worth approximately 22%. Grades for the written homework assignments
will be worth approximately 25%; attendance and class participation will be worth
approximately 5%.
Grades on exams will be
assigned in the following manner: Each problem will be worth a certain number
of points (which may or may not add up to a total of 100 on any one exam). Problems will be graded based on the indicated
number of points and the total of these awarded points will be computed, giving
a numerical score for the exam. These
numerical scores will then be converted into letter grades in accordance with
the following procedure: Prior to my
totaling individual scores, I will determine what I deem to be appropriate
cut-off level for each letter grade.
For example, I might decide, AOn this exam, in order to get an A-, a student
should get a total of 72 points.@ After
each student=s grade is totaled, I
may make small modifications in my predetermined cut-offs. For example, if my predetermined cut-off
score for an A- is 72 points, and if there is one student with 71 points and
the next highest point total is 54, I may decide to move the cut-off for A- to
71.
The
grade for homework will be determined similarly, except that the letter grade
will be based on the total points each student accumulates for the semester
rather than on having a letter assigned for each assignment. (Most problems assigned will be graded on a
basis of 5 points. Although I may modify this, past experience suggests that
the cut-off for an A- will be a per
problem average of 4 points out
of 5. Thus, if, for example, 22 hand-in
problems are assigned for the semester and if you get a total of 88 points,
then your homework grade will be A-.
Cut-offs for B-, C- and D- respectively will probably be 3+, 3- and 2.
[Here, + represents 1/3, and - represents 1/3 off]. )
After a letter grade is assigned to
each component of the grade, the letters will be converted to numbers according
to a scale such as the following:
A+ = 97; A = 94; A- = 90; B+ = 87; B = 84; B- = 80; C+ = 77; C = 74; C-
= 70; D+ = 67; D = 64; D- = 60; F+ = 55; F = 50. The weighted average of the components will then be computed and
reconverted to a letter grade using a slightly more liberal scale such as:
92=A; 88=A-; 85=B+; 82=B; 78=B-; 75=C+; 72=C; 68=C-; 65=D+; 60=D; 55=D-.
As an example, suppose a
student receives grades of A, B and A- on the three midterm exams, A- on the
final; A- for the homework; and C+ for attendance and class participation.
Then, using the scale above, these will be converted to 94, 84, 90, 90, 90 and
77 respectively. Using the weights
indicated above, the weighted average
would be (.16)@94 + (.16)@84 + (.16)@90 + (.22)@90
+ (.25)@90 + (.05)@77
= 89.03. This would then be
converted to a letter using the second scale.
The resulting grade for the course would be A-.
Attendance and lateness:
It is expected that you
attend class regularly and on time. I
expect this not only because I want you to share in the benefit of my
"words of wisdom" but also because a group with several members
absent no longer can function as a group.
A nationwide survey of employers indicates that in the vast majority of
cases in which an employee is fired the primary reasons for this firing are
absenteeism and tardiness.
While I do not have any
hard and fast rules such as "five absences means an automatic F", I
do take attendance, and you can be sure that excessive unexcused absence or
lateness will affect your grade.
You are also expected to
be present for each scheduled exam. If
you determine in advance that you will not be able to be present on the date of
a scheduled exam, I expect you to notify me immediately of that fact, so that
we can discuss alternate arrangements.
If a last minute emergency prevents you from being able to take a
scheduled exam, I expect you to call my office AS SOON AS POSSIBLE. (If you are ill or your car won't start, I
expect to hear from you between 8:30 and 9:15 on the morning of the exam. If you are in a coma, then when you emerge
from the coma will be soon enough, assuming that you have a doctor's note
attesting to the fact that you were in the coma!) If I am not available when you call, leave a message on my voice
mail, stating your name, the class you are in, your reason for missing the exam
and a phone number at which I can reach you later that day. If you don't follow these instructions, I am
likely to treat your absence as unexcused.
Also, since I check my e-mail more frequently than I do my phone
messages, please contact me by e-mail as well, if possible.
If we have not made
arrangements for you to take a make-up exam before the scheduled exam, you
should be prepared to take a make-up on the day you return to campus. In general, I find it difficult to compose
two exams that are truly comparable, so I prefer not to. For an excused absence, I may decide to give
a make-up or I may decide to disregard
the exam and to increase the percentages that your other exams and/or writing
grades contribute your final grade.
(This is my decision, not yours.)
Exams that are missed
due to unexcused absence will receive the grade of zero.
Students who miss more
than one exam may receive a zero for the second exam, regardless of the reason
for the absence, unless advance arrangements have been made.
Tentative examination dates:
Monday, October 7
Monday, November 4
Monday, December 2
Final examination:
Wednesday, December 18,
8:30-10:30 AM
Final comments:
What I discuss in class
is not likely to coincide exactly with what is in the text. There will be material in the text that I do
not have an opportunity to discuss in class, and there will be material that I
discuss in class which may not be in the text.
You are responsible for both.
While exams will concentrate
most heavily on what I cover in class, you are also responsible for knowing
what is contained in any sections of the text that are not specifically
excluded. (This includes material
discussed in all assigned exercises.)
I suggest the following
routine for this course (as well as for any other mathematics course you may
take):
1. Try to read the next scheduled section of
the text BEFORE it is covered in class.
It is not necessary that you understand it completely, but try to get an
idea of what it is about and where any difficulties you may have in
understanding it lie.
2. Pay attention in class and try to take as
careful notes as you can. ASK QUESTIONS
about material you do not understand.
3. AFTER class, reread the text and your notes,
and try to fill in any gaps that may exist in your notes. Make a list of items you do not understand
and ASK about them during the following class or during my office hours.
4. Attempt all of the assigned problems. Answers or solutions to some of the problems
are contained at the back of the book; but do not rely on this as a crutch. If you need to consult the answers to guide
you through some problems, that is OK; but, if you find that you have to
"massage" most of your work to get the answers in the back of the
book, then it is time to make an appointment to see me. No solutions or answers will be available to
guide you when it comes time to take a test.
Overnight assignments (homework to be done and
discussed in class and on the bulletin board but not collected):
Section 0.1, page 6: # 1-15, 18
Section 0.2, pages 9-10: # 1-4, 7, 10, 12, 13
Section 0.3, pages 22-24: # 2, 4, 6, 8, 10, read
11, 12, 13, 18, 22, 23, 24, 32, 34
Section 0.4, page 30: # 1-14, 16
Section 0.5, pages 35-36: # 1, 2, 5-12, 15, 16,
19-21
Section 1.1, pages 48-49: # 1-9, 14, 15, 17, 19,
21, 25, 26, read 27, 29
Section 1.2, pages 54-55: # 2, 4-7, 11, 12, 14,
16-19, 21, 22, 25, 33, 35, 36
Section 1.3, pages 60-62: # 1-7, 9, 11, 19, 21,
23
Section 1.4, pages 71-73: # 3, 4, 6-8, 10-13,
16-18, 20, 21, 23, 31, 33-37
Section 2.1, pages 78-80: # 1-8, 11, 14-16,
18-21, 25, 28, 39
Section 2.2, pages 86-88: # 1-3, 5-11, 13, 14,
16, 17, 23-26, 31, 32, 36-38, 40-43, 46
Section 2.3, pages 92-93: # 1-6, 8-13, read 15,
20-25, read 27
Section 2.4, pages 100-101: # 1-8, 10, 11,
15-19, 24, 26, 28, 29
Section 2.5, pages 106-107: # 1-3, 5, 6, 9-12,
14-19, read 20-22
Section 3.1, page 112: TBA
Section 3.2, page 115: TBA
Section 3.3, pages 120-122: TBA
Section 3.4, pages 129-130: TBA
Section 4.1, pages 136-137: TBA
Section 4.2, pages 140-141: TBA
Section 4.3, pages 147-148: TBA
Section 4.4, pages 152-153: TBA
Section 4.5, pages 158-159: TBA
Section 4.6, pages 164-165: TBA
Section 4.7, pages 170-171: TBA
Section 5.1, pages 177-178: TBA
Section 5.2, page 183: TBA
Section 5.3, pages187-189: TBA
If time permits
Section 6.1, pages 197-198: TBA
Section 6.2, pages201-202: TBA
Section 6.3, pages 208-209: TBA
Section 7.1, pages 214-215: TBA
Section 7.2, pages 222-224: TBA
Section 7.3, pages 230-231: TBA
*: For problems marked Aread@, it is not necessary to
do the problem. Just read it for
general interest and, if it concludes by proving a theorem, know the statement
of the theorem (but not the proof).
Hand-in assignments:
Instructions for written work:
1. Each problem is to begin on a new page.
2. You are to write on one side of the page
only, leaving ample blank space for me to write comments.
3. Pages of a problem
may be stapled or clipped together.
However, different problems are NOT to be stapled to each other.
4. Your name is to
appear on the top of the first page of each problem, and your name or initials
are to appear at the top of each subsequent page.
5. Everything you write
is to be in grammatically and idiomatically correct English. This does not mean that you may not use
equations and other forms of mathematical shorthand. What is does mean is that, when read aloud, everything you
write, including equations etc., should read as complete and correct
sentences. (Thus, it is important to
know how to pronounce an equation in English.)
Transitions and paragraph formation are also important considerations.
6. Although there is no specific requirement to
this effect, word processed or typed work is preferred, with work written in
blue or black pen preferable to work done in pencil, even though you may have
to cross out rather than erase mistakes.
Work done in red will not be accepted. In any case, all work submitted must be clearly legible.
Section 0.1, page 6:
Section 0.2, pages 9-10:
Section 0.3, pages
22-24:
Section 0.4, page 30:
Section 0.5, pages
35-36:
Section 1.1, pages
48-49: # 11, 18, 22 (all three on
Blackboard) [Note for exponents, use ^;
that is, 3^2 = 9.]
Section 1.2, pages
54-55: # 24, 29, 32 (all three on
blackboard)
Section 1.3, pages
60-62: # 17, 20 (both on blackboard)
[Note: Use _ for subscripts;
that is, x_1 means xsub1.]
Section 1.4, pages
71-73: # 26, 29, 38, 39 (all four on paper)
Section 2.1, pages
78-80: # 9, 10. 13, 17, 22, 37 (all on Blackboard)
Section 2.2, pages
86-88: # 4 (justify your answer), 19, 20, 22, 34, 36 (on Blackboard or paper, as you see fit)
[Note: Use \phi if you cannot make j; use Z for the
integers.]
Section 2.3, pages
92-93: # 7, 14 (paper), 16, 18, 26, 28, 29 (Blackboard) [Note, if you can’t figure how
to make the symbol
for a normal subgroup, then use <|
.]
Section 2.4, pages
100-101: # 20 (Blackboard), 22 (paper), 23 (Blackboard), 25 (Blackboard),
27
(either) – extra credit
Section 2.5, pages
106-107: # 4, 7, 8 (all on Blackboard)
Section 3.1, page 112:
TBA
Section 3.2, page 115:
TBA
Section 3.3, pages
120-122: TBA
Section 3.4, pages
129-130: TBA
Section 4.1, pages
136-137: TBA
Section 4.2, pages
140-141: TBA
Section 4.3, pages
147-148: TBA
Section 4.4, pages
152-153: TBA
Section 4.5, pages
158-159: TBA
Section 4.6, pages
164-165: TBA
Section 4.7, pages
170-171: TBA
Section 5.1, pages
177-178: TBA
Section 5.2, page 183:
TBA
Section 5.3,
pages187-189: TBA
If time permits
Section 6.1, pages
197-198: TBA
Section 6.2,
pages201-202: TBA
Section 6.3, pages
208-209: TBA
Section 7.1, pages
214-215: TBA
Section 7.2, pages
222-224: TBA
Section 7.3, pages
230-231: TBA