Fall 2016 – Math 3005, Abstract Algebra I

Class meetings: Tuesday and Friday 1:00 – 2:15, JMH 406
Instructor: Han-Bom Moon
Office: JMH 418
E-mail: hmoon8@fordham.edu
Course webpage: http://fordham.blackboard.com
Office hours: Wednesday 12:30 – 2:30 or by appointment
Text: Abstract Algebra: An Introduction, 3rd ed. Thomas Hungerford, ISBN: 978111156924

Recommended problems

    • Sec. 1.1. #2, 7, 9.
    • Sec. 1.2. #1, 3, 5, 13, 15, 17, 25, 27, 31.
    • Sec. 1.3. #1, 5, 15, 17, 23, 27.
    • Sec. 2.1. #1, 3, 5, 7, 9, 11, 15, 17, 21.
    • Sec. 2.2. #1, 3, 5, 11, 13, 15.
    • Sec. 2.3. #1, 2, 3, 5, 7, 9, 11, 17.
    • Sec. 3.1. #5, 9, 13, 15, 19, 23, 27, 31, 35, 39, 43.
    • Sec. 3.2. #1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 29, 31, 33, 35, 41, 43.
    • Sec. 3.3. #1, 3, 9, 11, 13, 15, 17, 23, 27, 29, 31, 37, 41.
    • Sec. 4.1. #1, 3, 5, 7, 9, 11, 13, 19.
    • Sec. 4.2. #1, 3, 5, 7, 15.
    • Sec. 4.3. #1, 3, 5, 7, 9, 11, 13, 15, 21, 23.
    • Sec. 4.4. #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 31.
    • Sec. 5.1. #1, 3, 5, 7, 9, 11, 13.
    • Sec. 5.2. #1, 3, 5, 7, 9, 13.
    • Sec. 5.3. #1, 3, 5, 7, 9.
    • Sec. 6.1. #1, 3, 9, 11, 13, 17, 21, 23, 25, 27, 29, 31, 35, 43.
    • Sec. 6.2. #1, 3, 5, 9, 17, 19, 21, 23, 25, 30, 31.
    • Sec. 14.1. #5, 9, 11, 13.
    • Sec. 14.3. #1, 3, 5, 6.
    • Sec. 7.1. #1, 3, 7, 9, 11, 13, 23, 25, 27, 31, 33, 35.
    • Sec. 7.2. #1, 3, 5, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29.
    • Sec. 7.3. #1, 5, 7, 11, 15, 17, 19, 23, 27, 33, 35, 37, 39, 43, 45, 47, 53, 57.
    • Sec. 7.4. #1, 5, 9, 11, 13, 15, 19, 21, 25, 29, 31, 33, 39, 53, 55, 57.
    • Sec. 7.5. #1, 3, 5, 7, 9, 11, 13, 19, 21, 27, 31, 35, 36, 39, 41.
    • Sec. 8.1. #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 31, 32, 33, 35, 37, 39, 41.
    • Sec. 8.2. #3, 5, 7, 9, 15, 17, 21, 35.
    • Sec. 8.3. #1, 3, 5, 7, 9, 11, 15, 17, 21, 25, 27, 29, 33.
    • Sec. 8.4. #1, 3, 5, 7, 9, 11, 13, 19, 21, 25, 31, 35, 39.

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 notions of rings and groups, their properties and structures, and applications.

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 x 20 %
Final 30 %

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 and final exam schedule, which will depend on the course progress, will be announced later. 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.

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