Math 01.340 Modern Algebra I
Syllabus
Dr. Abdul Hassen
Office: Robinson Hall, Mathematics Department 229E
Phone (856) 256-4500 ext 3888. e-mail: hassen@rowan.edu
Office Hours: MW 9:25 – 10:40; W 5:30 - 6:15, and by appointment
Prerequisite: Math 03.150 Discrete Mathematics, Math 01.210 Linear Algebra, and Phil 09.130 Introduction to Symbolic Logic
Text: Gilbert and Gilbert, Elements of Modern Algebra, 7th Edition; Publisher: Brooks/Cole
Course Description: This course includes: the introductory
theory of groups, rings, integral domains, and fields. Also included are
homomorphisms and isomorphisms, subgroups, kernels, rings and ideals, and
polynomial rings. At the option of the instructor, computer use can be
required.
OBJECTIVES: This course is designed to begin the student's development in the area of abstract algebra and mathematical reasoning.
1. Fundamentals
Logic; Sets; Relations; Functions; Equivalence relations, Equivalence classes
2. The Integers
Mathematical Inductions; Prime Factorization and GCD; Modulo Arithmetic
3. Groups
Definition and examples; Basic Group Theorems; Subgroups; Cyclic Groups; Homomorphisms and Isomorphisms;
4. More on Groups
Permutation Groups, Cayley’s Theorem; Normal subgroups; Quotient groups; Homomorphisms and Isomorphisms
5. Rings, Integral Domains, and Fields
Definition and Examples; Integral Domains and Fields; Field of Quotients;
6. More on Rings
Ideals and Quotient Rings; Ring Homomorphisms; Prime and Maximal Ideals
Grading Policy: Your final grades will be determined by your results on three tests and homework assignments, and class participation. Thus attendance will be very important. The dates for each test will be announced in class two weeks before the test date. The materials covered in the four tests will be as follows:
Test 1 (25% of the total grade) covers all sections of Chapters 1 and 2
Test 2 (30% of the total grade) covers Chapter 3 and 4
Test 3 (25% of the total grade) covers Chapters 5 and 6
20% of your grade will be from homework assignments. A letter grade assignment will be as follows:
A(A-) = 90 to 100 B(-,+) = 80 to 89 C(-,+) = 70 to 79 D(-,+) = 55 to 69 F = 0 to 54
Homework: The homework problems will be posted on the Blackboard page of the course.
Attendance Policy: Attendance is mandatory. An attendance sheet will be passed around at the beginning of each class period. Please write your signature next to your printed name on the list. If you are absent/tardy from a class, you must submit a note requesting that the absence/tardiness be excused by the next class meeting. Each student is allowed a total of three unexcused absences/tardies (combined). If you miss a class, it is your responsibility to study the section(s) covered and do the homework.
If you are absent the day of a regularly scheduled test, a grade of zero is automatically recorded as your test score. You will be permitted to make up this zero only when you can confirm that you were absent for reasons beyond your control. In such cases, you must telephone 256-4500 extension 3888 (or send me an e-mail) and leave a message including your name and telephone number, the reason for your absence and the date you anticipate returning. Students who fail to leave the above information will be assigned the grade of zero for that test.
Academic Honesty: Cheating on a
test or assignment seriously undermines the integrity of the academic system
and will not be tolerated. If I determine that a student has cheated, I
will assign the grade of F for this course and send a letter to this effect to
his advisor. Although a student is not cheating, he or she is expected to
refrain from actions that could be suspicious. Using common sense on your
part should avoid unnecessary embarrassment.
You may visit the website http://www.rowan.edu/provost/policies/AcademicIntegrity.htm for more information on Academic Integrity policy at Rowan University.
Classroom rules:
· Students will abide by Rowan's student code of conduct and policy on
academic honesty (p. 19 and p. 28 of Rowan 1999-2000 undergraduate catalog,
respectively). Improper behavior will not be tolerated.
· Students are not permitted to leave the classroom during class period except
for emergencies or unless prior arrangements have been made with the
instructor. Please use the restrooms before class begins.
Students with Disabilities and Special Needs:
Please speak with me as early in the semester as possible so that we can make
appropriate accommodations for you. If necessary, you can also contact the
Office of Special Services.
Questions in Class: The best time
to ask questions is during class. Many times students fear that their questions
will seem foolish, while in fact, many others also have the same
question. I urge you to ask your questions during class. If you have
questions that were not answered in class, you may stop by my office during my
office hours.