
Fall 2014
Lectures:

MWF 
11:00 AM11:50 AM 
PETER 102 (Peterson Hall) 

WF 
4:00 PM5:00 PM 
APM 7230 

Discussion session information:

A01


M

6:00 PM6:50 PM


APM 2301

Zonglin Jiang

zojiangucsd edu

A02


M

7:00 PM7:50 PM


APM 2301

Zonglin Jiang

zojiangucsd edu


TA's office hour information:

Zonglin Jiang;

M 4:005:30 pm; T 122:30 pm;

APM 6414.



General information
 Title: Abstract Algebra I: Introduction to Group Theory.
 Credit Hours: 4.
 Prerequisite: Math 109 or Math 31CH. Math 20F is also important as linear transformations provide us a rich set of examples.
 Catalog Description: First course in a rigorous threequarter introduction to the methods and basic structures of higher algebra.
In this course, we study basics of group theory.

Book
 John A. Beachy, William D. Blair, Abstract Algebra (3rd edition), Published by Waveland Press, 2006.
 We will cover Chapters 1, 2, 3, and parts of 7.
 There are lots of interesting books on group theory. I like the following books:
 P. B. Bhattacharya, S. K. Jain, S. R. Nagpaul, Basic abstract algebra. (It has nice problem sets.)
 Joseph Rotman, An introduction to the Theory of Groups. (It is an advanced book, full of interesting topics.
Towards the end, some of the connections of group theory and topology is explored.)

Schedule
This is a tentative schedule for the course. If necessary, it
may change.

Homework
 Homework will be assigned in the assignment section of this page.
 Homework are due on Wednesdays at 5:00 pm. You should drop your homework assignment in the homework dropbox in the basement of the APM building
 Late homework is not accepted.
 There will be 9 problem sets. Your cumulative homework grade will be based on the best 8 of the 9.
 Selected problems on the each assignment will be graded.
 Style:
 A messy and disorganized homework might
get no points.
 The upper right corner of each assignment
must include:
 Your name (last name first).
 Your discussion session (e.g. C01,etc.).
 Homework assignment number.
 Fullsized notebook papers should be used.
 All pages should be stapled together.
 Problems should be written in the same
order as the assignment list. Omitted problems should still appear in
the correct order.
 As a math major, sooner or later you have to learn how to use LaTex. I really encourage you to use Latex to type your solutions.
 A good portion of the exams will be
based on the weekly problem sets. So it is extremely important for you to make sure that
you understand each one of them.
 You can work on the problems with your classmates, but you have to write down your own version. Copying from other's solutions is
not accepted and is considered cheating.
 Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment.
You are responsible for material in the assigned reading whether or not it is discussed in the lecture.
 Homework will be returned in the discussion sections.

Grade
 Your weighted score is the best of
 Homework 20%+ midterm exam I 20%+ midterm exam II 20%+
Final 40%
 Homework 20%+ The best of midterm exams 20%+ Final 60%

You must pass the final examination in order to pass the course.
 Your letter grade is determined by your weighted score using the best of the following methods:

A+ 
A 
A 
B+ 
B 
B 
C+ 
C 
C 
97 
93 
90 
87 
83 
80 
77 
73 
70 
 Based on a curve where the median
corresponds to the cutoff B/C+.

If more than 90% of the students fill out the
CAPE questioner at the end of the quarter, all the students get one additional point towards their weighted score.

Regrade
 Homework and midterm exams will be returned in the discussion sections.
 If you wish to have your homework or exam regraded, you must return it immediately to your TA.
 Regrade requests will not be considered once the homework or exam leaves the room.
 If you do not retrieve your homework or exam during discussion section, you must arrange to pick it up from your TA within
one week after it was returned in order for any regrade request to be considered.

Further information
 There is no makeup exam.
 Keep all of your returned homework and exams. If there is any mistake in the recording of your scores, you will need the original
assignment in order for us to make a change.
 No notes, textbooks, calculators and electronic devices are allowed during exams.
 You must bring a blue book to the exam.
 Academic Dishonesty: Academic dishonesty is considered a serious offense at UCSD.
Students caught cheating will face an administrative sanction which may include suspension or expulsion
from the university. It is in your best interest to maintain your academic integrity.

Exams.
 The first exam:
 Topics: All the topics that are
discussed in the class and in the book about Sections 1.11.4 and 3.1.
 Questions are fairly similar to the
homework assignments and the examples discussed in the class. Make sure
that you know how to solve anyone of them.
 Practice: besides going through your
homework assignments, examples presented in the class and problems in
the relevant chapters of your book, you can use the following practice exams: (it will be posted later)
 You will need a blue book.
 Here is the first exam.
 The second exam:
 Topics: Here is a list of the main relevant topics.
 Questions are fairly similar to the homework assignments and the examples discussed in the class. Make sure
that you know how to solve anyone of them.
 Practice: go through your
homework assignments, examples presented in the class and problems in
the relevant chapters of your book. You can find practice exams here:
 You will need a blue book.
 Here is the second exam.
 The final exam:
 Time: December 16, 11:30am2:30pm.
 Location: Peter 102.
 It is your responsibility to ensure that you do not have a schedule conflict involving the final examination.
You should not enroll in this class if you cannot sit for the final examination at its scheduled time.
 Topics: All the topics that are discussed in the class and in the book.
 Questions are fairly similar to the homework assignments and the examples discussed in the class. Make sure
that you know how to solve anyone of them.
 Practice: besides going through your
homework assignments, examples presented in the class and problems in
the relevant chapters of your book, you can use problem set number 10 and Brian Longo's set of problems.
 You will need a blue book.
 As it is stated above, in the worst case scenario the median of the weighted scores corresponds to
the B/C+ cutoff.

Lectures
Here are some of the notes that I prepare before each lecture!
 These notes should not be your primary source of study.
 As you can see, most of the times, I prepare a bit more. And so there is a a repetition in topics discussed in the files.
 These are unpolished notes that I prepare to know what I would like to discuss during the lectures. So they might have several
grammatical errors.
 With all of their deficiencies I believe you might find them useful and that is why I am sharing them with you!
 Let me know if you have spotted a mistake.
 Here is the first lecture: Introduction to Group Theory; Several Examples.
 Here is the second lecture: Division algorithm.
 Here is the third lecture: Subgroups of Z.
 Here is the forth lecture: aZ+bZ=gcd(a,b)Z.
 Here is the fifth lecture: Fundamental Theorem of Arithmetic.
 Here is the sixth lecture: Power of p in n and its applications.
 Here is the seventh and eighth lectures: Basics of congruence.
 Here is the ninth and tenth lectures: Chinese Remainder Theorem and Units.
 Here is the summary of three lectures: group, subgroup criteria, subgroup generated by a set.
 Here is the fourteenth lecture: order of an element and cyclic groups.
 Here is a rough outline of the rest of the lectures in this quarter.
 Here is the fifteenth lecture: group action.
 Here is the sixteenth lecture: orbits, cosets, Lagrange theorem.
 Here is the seventeenth lecture: bijection between orbits and left cosets, actions of a cyclic group.
 Here is the eighteenth lecture: cyclic decomposition of permutations
 Here is the nineteenth lecture: basic formulas; any permutation is a product of transpositions
 Here is the twentieth lecture: odd and even permutations; order of a permutation; alternating group and its index in the symmetric group.
 Here is the twenty first lecture: group homomorphism; several examples.
 Here is the twenty second lecture: group homomorphism; basic properties; image and kernel; normal subgroup.
 Here is the twenty third lecture: factor group; the first isomorphism theorem.
 Here is the twenty fourth lecture: the first isomorphism theorem.
 Here is the twenty fifth lecture: isomorphism theorems.
 Here is the twenty sixth lecture: Cauchy's theorem and pgroups.
 Here is the twenty seventh lecture: Cauchy's theorem and groups of order pq.
 Here is the twenty eighth lecture: dihedral group, groups of order 2p, etc.

Assignments
The list of homework assignments are subject to revision during the quarter.
Please check this page regularly for updates. (Do not forget to refresh your page!)

Homework 1 (Due October 15)
 Here is the first problem set.

Homework 2 (Due October 22)
 Here is the second problem set.

Homework 3 (Due October 29)
 Here is the third problem set.

Homework 4 (Due November 5)
 Here is the forth problem set.

Homework 5 (Due November 12)
 Here is the forth problem set.

Homework 6 (Due November 19)
 Here is the sixth problem set.

Homework 7 (Due November 26)
 Here is the seventh problem set.

Homework 8 (Due December 3)
 Here is the eighth problem set.

Homework 9 (Due December 10)
 Here is the ninth problem set.

Homework 10 (NOT Due)
 Here is the tenth problem set. Most of these are discussed either during the lecture or in my office hour.
 Here is a set of problems prepared by Brian Longo. You might find them useful. I would like to thank Brian for sharing this with me.
