MAT 333-01, Abstract Algebra, Fall 2005

MW 5:30--6:45, EAC 501
INSTRUCTOR: Sean Sather-Wagstaff
OFFICE: NSM A119
PHONE: 243.3396
EMAIL: ssather at csudh.edu

COURSE DOCUMENTS:

• Printable version of this syllabus
• Course survey
• Syllabus questions
• Group project information

PREREQUISITES: Students must have earned at least a "C" in a course equivalent to MAT 271, Foundations of Higher Mathematics, before enrolling in this course. A semester of linear algebra (MAT 331) is recommended but not required.

OFFICE HOURS: M 11:30 AM--12:30 PM and 4:15--5:15 PM, W 8:45--9:45 AM and 4:15--5:15 PM, and by appointment

AMP workshop: Tu,Th 2-4 pm in SBS D215

USEFULE WEBPAGES:

• Course webpage
• Instructor webpage
• Math department webpage
• Blackboard
• CSUDH webpage
• SRR webpage on academic integrity
• Instructor evaluation webpage--coming soon

REQUIRED TEXT: Abstract Algebra, An Introduction (2nd edition), by Thomas W. Hungerford.

COURSE DESCRIPTION: The theory of groups, rings, ideals, integral domains, fields and related results. MAT 333 meets for three hours of lecture per week.

OBJECTIVES: After completing MAT 333 the student should be able to

• state definitions of basic concepts (e.g., congruence, groups, rings, integral domains, fields, subrings, homomorphism, ideal)
• understand and use the Euclidean algorithm
• understand and use modular arithmetic and the Chinese remainder theorem
• state major theorems (e.g., the division algorithm, the unique factorization theorem, the remainder theorem, the factor theorem, the first, second, and third isomorphism theorems, classification of cyclic groups, Cayley's theorem) and be able to identify the structures to which each theorem applies (e.g. the integers, integral domains, polynomial rings k[x] where k is a field, groups, etc.)
• find examples of objects that satisfy given algebraic properties (a noncommutative ring, a commutative ring but not an integral domain, etc)
• determine whether a given conjecture is true or false, then prove or disprove it, constructing examples where appropriate
• prove that two rings or groups are, or are not, isomorphic
• prove that a given set is, or is not, a subring (subgroup, subfield, ...) of a given ring (group, field,...)
• prove that congruence classes (or cosets) in a set S do, or do not, inherit given properties from S
• write proofs of other simple propositions using basic definitions and theorems
• use the techniques of abstract algebra to solve applied problems, as appropriate.

EXPECTED OUTCOMES: Students should be able to demonstrate through written assignments and exams that they have achieved the objectives of MAT 333.

METHOD OF EVALUATING OUTCOMES: Evaluations are based on weekly homework assignments, attendance and participation, one (1) group project, three (3) midterm examinations, and one (1) comprehensive final examination covering students' understanding of topics covered in MAT 333.

HOMEWORK: I will assign homework on a weekly basis. Exercises will be assigned in class on Wednesdays and solutions will be due at the beginning of class on the following Wednesday. Each section of homework will be worth the same amount. Late homework will only be accepted under extreme circumstances. If you have a conflict with any of the homework due dates, make alternative arrangements with me beforehand.

Students are encouraged to work on assignments in small groups, but each member of the class is required to turn in a neatly written, organized set of solutions. Students will receive no credit for solutions with no work or justification. I reserve the right to deduct points for messy papers.

ATTENDANCE: While attendance is not explicitly required, it is worth 5\% of your grade. In addition, your presence, attention, and participation in lecture will greatly help your performance in this class. For these reasons, I will take attendance each class period. Officially excused absences will not be counted against you, but you must document such situations with me personally.

GROUP PROJECT: Working in small groups, students will investigate a special topic in abstract algebra with the analysis and conclusions submitted as a typewritten report. Project choices include parts of Sections 1.4, 13.1, and 13.2, and Chapter 12 in the text. More information on the projects will be made available by the beginning of October. Late projects will only be accepted under extreme circumstances. If you have a conflict with any of the project due dates, make alternative arrangements with me beforehand.

EXAMS: Midterm exams will be taken in class and will last 75 minutes. The final examination will be comprehensive and will last 2 hours. Make-up exams will only be allowed under extreme circumstances. If you have a conflict with any of the exam dates, make alternative arrangements with me beforehand.

PORTFOLIO: At the end of the semester, I will ask you to submit a portfolio for the course, consisting of the exams and homeworks that you have submitted.

Weights for evaluation items are summarized in the following table.

Homework:	15%
Attendance and participation:	5%
Draft of Group Project:	5%
Final Version of Group Project:	5%
Midterms:	15% each
Final Exam:	25%

I will update your grades throughout the semester at the university Blackboard site. Final grades will be assigned according to the following percentages.

		A	93-100%	A-	90-92.9%
B+	87-89.9%	B	83-86.9%	B-	80-82.9%
C+	77-79.9%	C	73-76.9%	C-	70-72.9%
		D	60-69.9%
		F	0-59.9%

TENTATIVE SCHEDULE: I reserve the right to make reasonable changes to the schedule if I find it necessary.

Labor Day holiday:	Mon 05 Sep
Add/drop deadline:	Thu 15 Sep
Exam 1:	Wed 28 Sep
Exam 2:	Wed 02 Nov
Group project draft due:	Wed 09 Nov
``Serious and compelling reason'' d/w deadline:	Thu 17 Nov
Thanksgiving holiday:	Thu 24 Nov -- Sat 26 Nov
Exam 3:	Mon 05 Dec
``Serious accident/illness'' d/w deadline:	Thu 08 Dec
Group project final version due:	Wed 07 Dec
Final Exam:	Wed 14 Dec 5:30-7:30 PM

LECTURE NOTES: Clear and thorough course notes will provide you with a basis for your preparations for homework assignments and exams. You are responsible for taking notes during class, as I will not be posting my lecture notes online.

WORKLOAD: You should plan to spend 6--9 hours per week working on this course outside lecture.

ANNOUNCEMENTS: Periodically, I will send course announcements to your csudh.edu email account. It is your responsibility to check this email account regularly.

QUESTIONS: If something I say or write in lecture is unclear, raise your hand and ask a question. I will try to clarify the point I am making.

GROUP STUDY: Find at least one person in the class with whom you can study. Not only does this help you study better, but also, in the event you miss a lecture, you can get the notes and assignments from this person. Finally, this will help you when it comes time to form groups for the project.

TEXT READING: Read the relevant sections of the text book before lecture. Even if you don't understand everything, seeing it once before I present it will help you follow lecture considerably.

OFFICE HOURS: Come to my office hours for help. This gives me the opportunity to focus on specific problems you may be having and to explain things in a more personal manner. If the scheduled times are bad for you, make an appointment with me.

INSTRUCTOR FEEDBACK: Soon there will be a link to an anonymous evaluation form where students can submit comments or suggestions for me at any time during the semester.

ADA: The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for this course.

ACADEMIC INTEGRITY: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

COURSE OUTLINE:

1. ARITHMETIC IN THE INTEGERS: The Division algorithm. Divisibility. Primes and Unique Factorization.

2. CONGRUENCE IN THE INTEGERS AND MODULAR ARITHMETIC: Congruence and Congruence Classes. Modular arithmetic.

3. RINGS: Definitions, Examples, and Properties of Rings. Subrings, Integral Domains, and Fields. Isomorphisms and Homomorphisms.

4. ARITHMETIC IN POLYNOMIAL RINGS F[x]: Division Algorithm and Divisibility in F[x]. Irreducibles and Unique Factorization. Polynomial Functions, Roots, and Reducibility. Irreducibility in Polynomial Rings over the Rationals, Reals, and Complex Fields.

5. CONGRUENCE IN F[x]: Congruence-Class Arithmetic in F[x]. The Structure of F[x]/(p(x)) when p(x) is Irreducible.

6. IDEALS AND QUOTIENT RINGS: Ideals and Congruence. Quotient Rings and Homomorphisms. The Structure of R/I when $I$ is Prime or Maximal.

7. GROUPS: Definitions, Examples, and Properties of Groups. Subgroups. Isomorphisms and Homomorphisms.

DUE DATE	SECTION	EXERCISES
08.31	Course survey
09.07	1.1	4, 5, 7
09.07	Syllabus questions
09.14	1.2	6, 8, 10, 16
09.21	1.2	15(d), 25, 26
09.21	1.3	4, 6, 11(a)
10.05	2.1	1, 2(a), 5, 6, 17
10.12	2.1	11, 12, 21, 26
10.19	2.2	2(c),5(a),7,9(a)
10.19	2.3	1(a,b),2(a,b),6,7(a),13
10.26	3.1	5(b,d),10,13(a),18,29
11.16	3.2	6, 11, 16, 17
11.16	3.2	28, 29, 36; (37 extra credit)
11.23	3.3	7, 8, 10(a, b), 13
11.23	3.3	27, 28, 33(b,e)
11.30	4.1	1(a,d), 5(a,c), 6(a,b), 11, 16
11.30	4.2	3, 5(a), 6(a)

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