MATH 414: ABSTRACT ALGEBRA

Course Prerequisites: Minimum grade of C in Math 240 (Discrete Math)

Course Description: An introduction to abstract mathematical structures, principally groups and rings. This is an advanced mathematics course, with an emphasis on understanding abstract structures, and reading and writing mathematical proofs.

Course Objectives: Upon completion of this course, the student should be able to

1. Write mathematical proofs and reason abstractly in exploring properties of groups and rings.
2. Use the division algorithm, Euclidean algorithm, and modular arithmetic in computations and proofs about the integers.
3. Define, construct examples of, and explore properties of groups, including symmetry groups, permutation groups and cyclic groups.
4. Determine subgroups and factor groups of finite groups.
5. Determine, use and apply homomorphisms between groups.
6. Define and construct examples of rings, including integral domains and polynomial rings.

Text: Algebra, Pure & Applied by Papantonopoulou (Prentice Hall).

Attendance Policy: Attendance is absolutely essential to success in this class. You are expected to attend every class; please notify the professor if you know you are going to be absent. All exams must be taken at the scheduled time, and assignments will not be accepted late.

Student Disability Policy: If you have any documented special educational needs, you are encouraged to work with the Cushing Center for Counseling and Academic Support to prepare a written request for the accommodations you need in this course. To receive accommodations in this course, the professor must receive a written request from CCAS at the beginning of the course, or as soon as the disability is diagnosed.

College Policies: Please note that all college policies pertaining to academic dishonesty, drop/add procedures, and grade appeal should be followed by students enrolled in this class. Consult the undergraduate college catalog or ask the professor if you have questions about these policies.

Teaching Methods: In order to succeed in this course, you need to be an active participant in learning – both in class and out of class. Class time will be spent on lecture as well as discussion of homework problems and some group work. To actively participate in class, you need to prepare by reading the textbook and doing all assigned homework before class (homework will be assigned each class period, to be discussed the following period). You should be prepared to discuss your homework (including presenting your solutions to the class) at each class meeting. You are encouraged to work together with other students and to ask questions and seek help from the professor, both in and out of class.

Grading and Testing Procedures: Your grade will be calculated from your grades on weekly assignments, three exams and a final exam, using the scheme

Weekly Assignments	50 %
Exams 1 - 2	30 %
Final	20 %.

Assignments will be due at the beginning of class on Fridays, according to the attached schedule. Instructions for each assignment will be given in advance. Since a major component of this course is training in correct mathematical writing, you are expected to write neat, clear, mathematically correct solutions to the assigned problems.

There will exams on September 28 and November 2 and a final on Wednesday, December 12. These exams will each have two parts – a take-home part, and an in-class part.

Letter grades will be assigned using the grade cut-offs:
93 A
90 A-
87 B+
83 B
80 B-
77 C+
73 C
70 C-
67 D+
63 D
60 D-
0 F