Class meetings: Tuesday, Wednesday and Friday 11:30 – 12:20, 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
Recommended problems
- Ch. 0. #1, 2, 3, 5, 7, 8, 9, 11, 15, 19, 38, 59, 60.
- Ch. 2. #1, 3, 5, 12, 13, 14, 18, 20, 22, 27, 28, 35, 41, 42, 43, 44, 47.
- Ch. 3. #1, 2, 7, 8, 10, 15, 18, 19, 22, 23, 27, 33, 34, 39, 44, 45, 54, 59, 64, 68, 75, 80.
- Ch. 4. #2, 3, 8, 9, 10, 20, 24, 27, 29, 33, 35, 42, 59, 60, 64, 73, 84.
- Ch. 5. #1, 2, 3, 5, 6, 11, 12, 13, 15, 28, 34, 38, 50, 58, 66, 78.
- Ch. 6. #6, 7, 8, 9, 11, 16, 20, 30, 45, 47, 49, 53, 56.
- Ch. 7. #3, 5, 8, 10, 11, 12, 17, 24, 25, 29, 33, 40, 41, 42, 45, 47, 51.
- Ch. 29. #2, 4, 6, 8, 9, 11.
- Ch. 8. #3, 5, 6, 10, 14, 18, 20, 22, 26, 30, 31, 41, 54.
- Ch. 9. #2, 7, 11, 12, 13, 14, 18, 21, 22, 32, 39, 40, 41, 49, 50, 51, 58.
- Ch. 10. #10, 11, 12, 14, 16, 17, 20, 29, 31, 35, 36, 39, 41, 42, 51, 55, 63.
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 I (Math 2006).
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
You can use TI-83 or higher graphing calculators in class or for homework, and tests.
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 class. Late submission may not allowed. 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 December 16th (Tue), 13:30 – 16:30. 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.