# Abstract Algebra Gallian Homework Assignments

Class meetings: Tuesday, Wednesday and Friday 09:30 – 10:20, JMH 406

Instructor: Han-Bom Moon

Office: JMH 418

E-mail: hmoon8 at fordham dot edu

Course webpage: http://my.fordham.edu

Office hours: Tuesday, Wednesday 13:00 – 14:30, or by appointment

Text: Contemporary Abstract Algebra, 8th ed., J. Gallian, ISBN 978-1133599708

#### Solutions

#### Recommended problems

- Ch. 0. #1, 2, 5, 7, 8, 9, 11, 19, 28, 38.
- Ch. 2. #1, 2, 3, 4, 7, 9, 10, 18, 20, 27, 28, 29, 30, 31, 33, 34, 36, 40, 43, 44, 53, 54.
- Ch. 3. #1, 8, 10, 20, 21, 23, 25, 27, 28, 33, 37, 39, 59, 62, 67, 73, 75, 77, 80.
- Ch. 4. #2, 7, 8, 15, 20, 23, 24, 28, 34, 35, 37, 42, 43, 60, 65, 71, 73, 84.
- Ch. 5. #5, 8, 16, 24, 38, 45, 49, 50, 51, 52, 58, 78.
- Ch. 6. #6, 7, 8, 9, 11, 16, 20, 30, 45, 47, 49, 53, 56.
- Ch. 7. #3, 5, 14, 16, 17, 22, 24, 25, 28, 33, 40, 47, 62.
- Ch. 8. #3, 8, 10, 13, 14, 19, 22, 29, 41, 45.
- Ch. 9. #3, 7, 13, 23, 30, 37, 40, 50, 56, 57, 59, 62, 66.
- Ch. 10. #4, 8, 10, 11, 15, 24, 31, 36, 54, 55, 63, 58.
- Ch. 29. #7, 8, 9.

#### Course objective

The aim of this course is twofold. First of all, we will study how to prove mathematical statements rigorously in the context of algebra. Secondly, we study basic algebraic notion of groups. The topics include definitions and properties of groups, subgroups, normality, homomorphisms, and applications to counting and geometry.

#### Prerequisite

The basic knowledge on Discrete Mathematics (Math 2001) and Linear Algebra (Math 2006) is helpful, but I will explain relevant preliminaries during the lecture.

#### Grading

I will grade on a curve. Final grades will be computed according to the following breakdown:

Participation | 5 % |

Homework | 25 % |

Midterm Exams | 2 × 15 % |

Final Exam | 40 % |

#### Calculator or computer

No calculator is allowed.

#### Homework

There is no way to learn mathematics without solving lots of exercise problems by yourself. Homework will be assigned weekly on the course webpage. It will be collected on Friday, before the class starts. I highly recommend you to work in groups and help each other. But do not copy directly. You must understand how to solve the problems.

#### Additional materials

It is always advisable to work as many additional problems from the book as you have time for. In each week I will post on the course webpage a list of recommended problems. You don’t need to submit solutions of all recommended problems, but studying them will be very helpful to improve your mathematical writing skill. Also, I will post model solutions of homework and tests. Check the course webpage regularly.

#### Test

There will be two midterm tests and a cumulative final exam. The midterm exam schedule, which will depend on the course progress, will be announced later. The final exam will be on May 7th (Wed), 9:30 – 12:30. The final is cumulative, but may slightly emphasize material covered between the second midterm exam and the last day of class. Make up exams will not be given unless you have a documented reason.

#### Attendance

Coming to every class during the official academic term is required. Attendance will be taken intermittently. This will be included in the “participation” portion of your grade.

#### Academic integrity

As a Fordham University student, you have agreed to abide by the University’s academic integrity policy. All academic work must meet the standards described in here. Lack of knowledge of the academic integrity policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic integrity policy should be directed to the instructor.

#### Disclaimer

The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary.

Back

### Instructor

Prof. Peter Sin

### Time and Location

MWF 6, Little 217

### Office Hours:

MWF 1.55-2.45pm Little 432, and by appointment.

### Description and Goals

This course is an introduction to the ideas of higher algebra, concentrating mainly on the theory of groups, with some theory of rings. Group theory is the mathematical study of symmetry. Students will become acquainted with the axiomatic approach. Many examples of groups will be used to illustrate the abstract concepts. Students will learn to read mathematics slowly and critically and, in so doing, will develop the ability to write careful accurate proofs of their own.

### Textbook

Contemporary Abstract Algebra, 7th ed., by Joseph A. Gallian (Brooks/Cole Cengage learning).

You can also use the 8th edition. The homework problem numbers refer to the 7th ed, but

you can find the corresponding 8th ed. numbers in this pdf file(Thanks to Jose Bigio).

### Software

Some examples and exercises in the text make use of GAP.

GAP is a free, top quality, open source package available for Windows, Mac OS X and Unix variants (including Linux). It can be downloaded from http://www.gap-system.org

It is not a course requirement to install and use GAP, but you will find it a good test of your understanding to try to explain the course material to a machine!

### Course Calendar

MAS4301-Calendar

### Exam Solutions

### Homework

The list of homework problems appears below. You should try to solve all of the assigned problems. I will select certain problems to be written up carefully and turned in for grading. You may discuss ideas to solve homework problems with your classmates, but the written work turned in for grading must be entirely your own.

If you have the 8th edition of the text, click here for the mapping of problem numbers.

Ch.1: 1,2,3,4,5,12,13,16.

Ch.2: 1,2,3,5,7,15,16,20,25,35,36.

Ch.3: 1,2,6,9,14,15,18,20,22.

Ch.4: 2,4,7,11,18,31,37,42.

Ch.5: 1,2,3,4,5,7,19,21,26,59.

Ch.6: 1,2,5,7,8,14,18,27,32,34.

Ch.7: 1,2,8,11,12,15,16,17,23 (harder) ,50 (harder).

Ch.8: 1,4,5,12,13,33,46.

Ch.9: 1,2,4,7,9,10,20,37,45,49.

Ch.10: 2,3,4,7,8,9,14,16,29,49,50.

Ch.11: 3,9,15,16.

Ch.12: 1,2,3,4,6.

### Final Grades

There will be 3 tests each worth 30 points and homework assignments worth 10 points in total. The dates of the tests are given in the course calendar. No make-up exams will be given except for documented special reasons such as medical emergencies. Exams can be rearranged for student athletes only if I am notified at least four weeks in advance.

### Grading Scale

**Grades: A=90-100, B+=85-89, B=80-84, B-=75-79, C+=70-74, C=65-69,C-=60-64, D=50-59, E=0-49**

The UF regulations on grades are here: https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx

### Attendance and Late Policy

To be successful you should always come to class *and* read the book by yourself.

The UF policy on attendance is here: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx

### Special accommodations

Students requesting classroom accommodation must first register with the Dean of Student Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the instructor when requesting accommodation.

### Honor Code

UF students are bound by The Honor Pledge which states, “We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code.

On all work submitted for credit by students at the University of Florida, the following pledge is either

required or implied: “On my honor, I have neither given nor received unauthorized aid in doing this

assignment.”

The Honor Code (http://www.dso.ufl.edu/sccr/process/student-conduct-honor-code/)

specifies a number of behaviors that are in violation of this code and the possible sanctions.

Furthermore, you are obliged to report any condition that facilitates academic misconduct to appropriate

personnel. If you have any questions or concerns, please consult with the instructor of this class.

### Course Evaluations

Students are expected to provide feedback on the quality of instruction in this course based on 10 criteria. These evaluations are conducted online at https://evaluations.ufl.edu. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https://evaluations.ufl.edu/results/.

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