MATH 404 - ABSTRACT ALGEBRA: GROUPS, RINGS, AND FIELDS

North Carolina Wesleyan College

SECTION 01, 3 CREDIT HOURS,  Spring, 2000

Tuesday and Thursday, 11:20-12:50pm

INSTRUCTOR: Dr. Carol Lawrence

OFFICE 114, Braswell

OFFICE HOURS  TTH 9:30-10:15am, WF 9:10-10:15am, or by apt.

OFFICE PHONE (252) 985-5183 (call for an appointment)

OFFICE FAX (252) 985-5235

BUILDING AND ROOM PC 274

WEB SITE http://faculty.ncwc.edu/clawrence

EMAIL: clawrence@wesnet.ncwc.edu

TEXT: A First Course in Abstract Algebra, Sixth Edition, John B. Fraleigh, Addison Wesley Longman, 1999.

PREREQUISITE: Placement or MAT 122, 250, and junior standing.

COURSE DESCRIPTION: Integers and equivalence relations, groups, rings, integral domains, fields.  (writing intensive)

OBJECTIVES OF THE COURSE: In general, the course is designed to develop an understanding of the language of modern algebra, i.e. terminology, concepts, and methods specifically related to groups, rings, and fields. The student will become cognizant of the general procedure for developing the theory of an algebraic system from the axioms of that system as related to groups, rings, and fields. Due to the emphasis on writing in this course, the student will become further acquainted with the notion of proof by continuing to develop the abilities to recognize, understand, and construct proofs.

OUTCOMES OF THE COURSE: Specifically, the student will develop a basic understanding of abstract algebra terms within the context of groups, rings, and fields. The student will be able to recognize, analyze, and construct proofs within this context. The student will demonstrate his/her understanding of a specific abstract algebra concept be developing a paper and presentation and assigned topic.

TEACHING METHODS: Concepts will be presented by methods of lecture, group discussion, and group presentations. Instructor/student and student/student interaction is encouraged.

ATTENDANCE: Punctual attendance is required. Attendance is 5% of your grade.The College attendance policy as stated on page 61 of the catalog will be strictly enforced. No more than two absences are allowed. Three tardies count as an absence.Two homework grades will be dropped for all students that stay within the three absences limit. There will be no make-up tests or exam for unexcused absences. Make-up daily assignments should be turned in by the next class period after the absence occurred. The instructor should be notified in advance of excused absences due to college approved events.
 
GRADING:
Paper and Presentation
25%
Homework
10% 
Tests
45% 
Attendance
5% 
Final Exam
15% 

I will assign homework each class period. A 10 point grading scale will be used.

FINAL EXAM — Monday, May 9, 11:00-1:00pm

CHEATING AND PLAGIARISM: A scholar is characterized by his/her honesty and fairness. Therefore, a scholar neither gives nor receives "information illicitly with intent to deceive the instructor in his or her effort to grade fairly any academic work" (NCWC Catalog, p. 64). Also, a scholar does not take credit for someone's work without giving credit to the creator. The violation of these principles is academic dishonesty and will not be tolerated. The instructor will adhere strictly to the plagiarism and cheating policy as stated in the catalog on pages 64-65.


MATH 404: ABSTRACT ALGEBRA:  GROUPS, RINGS, AND FIELDS


 
DATE CHAPTER /SECTION TOPIC
2/1  0.1 Mathematics and Proofs
0.2
Sets and Relations (Functions, Modular Arithmetic)
2/3
0.2
Sets and Relations (Equivalence Relations)
2/8
0.2, 0.4
Matrix Algebra
2/10
1.1
Binary Operations
2/15
1.2
Isomorphic Binary Structures
2/17
1.3
Groups
2/22
1.3
Groups (continued)
2/24 Test 1
2/29
1.4
Subgroups
3/2
1.5
Cyclic Groups and Generators
3/7
1.5
Cayley Digraphs
3/9
2.1
Groups of Permutations
3/21
2.2
Orbits, Cycles and the Alternating Groups
3/23
2.2
Plane Isometries
3/28
2.3
Cosets and the Theorem of Lagrange
3/30 Test 2
4/4
2.4
Direct Products and Finitely Generated Abelian Groups
4/6
2.5
Binary Linear Codes
4/11
3.1
Homomorphisms
4/13
3.1
Homomorphisms continued
4/18 Test 3
4/20
3.2
Factor Groups
4/25
5.1
Rings and Fields
4/27
5.1
Rings and Fields continued
5/2
5.2
Integral Domains
5/4
5.2
Integral Domains continued
5/9 Final Exam