MATH 0430Introduction to Abstract Algebraic Systems2091 INSTRUCTOR Dr. Elayne ArringtonOffice: 608 Thackeray HallOffice Hours: MTuWThF 2:00-3:30 pm (or by appointment )Telephone: 412-624-8337 or 8375 (Math Office)fax: 412-624-8397e-mail: [email protected] SCHEDULE This course meets Tu and Th from 4:00-5:15 p.m.COURSE WEBSITEhttp://www.math.pitt.edu/~earr COURSE DESCRIPTIONThis course introduces the student to abstract algebraic concepts: rings, integraldomains, fields, integers, rational numbers, real and complex numbers andpolynomials. Many examples will be presented during class and in the homework.The students are expected to improve their proof-writing techniques.COURSE GOALS This course will familiarize the students with several basic algebraic structures. Thestudents will be able form new structures from these basic structures. The course will provide students with the opportunity to develop and practicecommunication skills and work in groups or teams while using course concepts.The course will provide student with the opportunity to improve communicationskills by writing solutions to many problems in the form commonly accepted inmathematical journals.The course will provide students with the opportunity to improve presentationskills by participating in a special project.TEXTBOOK The textbook for Math 0430 is Abstract Algebra; An Introduction, second editionby Thomas W. Hungerford. We will cover most topics in chapters 1 through 6. Itis important that the student reads the section(s) to be covered before theappropriate lecture.Prerequisites: The material in Appendices A through D.ATTENDANCE Although class attendance is not specified as a factor in determining the coursegrade, the student is expected to attend all classes and he or she is responsible forall assignments and material covered in class, and all announcements or changesmade in class, whether present or not.HOMEWORK Homework is an essential part of the course and will be regularly assigned andgraded. It is important that the student improve her/his proof-writing techniquethrough the homework. Fifty (50) problems worth ten (10) points each will beassigned during the session. The solutions to the problems are to be written in theforms of proofs, as presented in the textbook and in class. Each assignment is dueat the beginning of the appropriate class. Solutions will be provided when thehomework is collected and no late homework will be accepted. The highest 35scores will be counted for the homework grade.EXAMINATIONS Two class-long examinations will be given.SPECIAL PROJECT Each student will participate in a special team-project that uses concepts learnedearly in the course. Working in groups of three, students will complete the projectand give a 10-12-minute presentation on the project in class.Arrington Math 0430 2091FINAL EXAMINATIONThere will be a two-hour comprehensive final examination on the last day of class.COURSE GRADE The course grade will be based solely on the student’s performance on thehomework, the exams, the special project, and the final exam. The homework willcomprise 35% of the grade, each exam will count for 15% of the grade, the specialproject will count for 10% of the grade, and the final exam will count for 25% ofthe course grade.STUDENTS WITH DISABILITIESA student with a disability for which he or she is requesting an accommodation, isencouraged to contact both the instructor and the Office of Disability Resourcesand Services, 216 William Pitt Union (412) 648-7890 as early in the term aspossible.ACADEMIC INTEGRITYCheating/plagiarism will not be tolerated. Students suspected of violating theUniversity of Pittsburgh Policy on Academic Integrity will incur a minimumsanction of a zero score for the quiz, exam or paper in question. Additionalsanctions may be imposed, depending on the severity of the infraction. Students maywork together or use library resources to do homework, but each student must write his orher own solutions independently. Copying solutions from other students will be consideredcheating, and handled accordingly. CLASSROOM CONDUCTAll students are expected to report to class on time, refrain from individualconversation during class, turn cell phones and pagers off or to “vibrate”, and showrespect for fellow students and faculty.DEADLINES Add/drop period ends: Friday, September 5Monitored withdrawal ends: Friday, October 17Arrington Math 0430 2091MATH 0430Introduction to Abstract Algebraic SystemsTentative Course Schedule (2091)Date # Lecture Topic Text Reading DueTu, Aug. 26 1 The Division Algorithm 1.1Th, Aug. 28 2 Divisibility 1.2Tu, Sept.2 3 Primes and Unique Factorization 1.3Th, Sept.4 4 Primality Testing. 1.4 Homework #1Tu, Sept.9 5 Congruence and Congruence Classes 2.1 SP(a)Th, Sept.11 6 Modular Arithmetic 2.2 Homework #2Tu, Sept.16 7The Structure of Ζp When p is Prime.2.3Th, Sept.18 8 Definition and Examples of Rings 3.1 Homework #3Tu, Sept.23 9 Definition and Examples of Rings 3.1 SP(b)Th, Sept.25 10 Basic Properties of Rings 3.2 Homework #4Tu, Sept. 30 11 Isomorphisms and Homomorphisms 3.3 SP(c)Th, Oct. 2 12 Isomorphisms and Homomorphisms 3.3 Homework #5Tu, Oct. 7 13 ReviewTh, Oct. 9 14 Exam #1Tu, Oct. 14 No Class (Fall Holiday)Th, Oct. 16 15 Polynomial Arithmetic and the Division Algorithm4.1Tu, Oct. 21 16 Divisibility in F[X] 4.2 Th, Oct. 23 17 Irreducibles and Unique Factorization 4.3 Homework #6Tu, Oct. 28 18 Polynomial Functions, Roots, and Reduciblity4.4 SP(d)Th, Oct. 30 19 Congruence in F[X] and Congruence Classes5.1 Homework #7Tu, Nov. 4 20 Congruence-Class Arithmetic; 5.2Th, Nov. 6 21 The Structure of F[X]/(p(x)) When p(x) is Irreducible5.3 Homework #8SP(e)Tu, Nov. 11 22 ReviewTh, Nov. 13 23 Examination #2 Tu, Nov. 18 24 SP(f)Th, Nov. 20 25 Ideals and Congruence 6.1Tu, Nov. 25 26 Quotient Rings and Homomorphisms 6.2Th, Nov. 27 No Class (Thanksgiving)Arrington Math 0430 2091Tu, Dec. 2 27 The Structure of R/I When I Is Prime or Maximal6.3 Homework #9Th, Dec. 4 28 Homework #10Tu, Dec. 9 29 ReviewTh, Dec. 11 30 Final ExaminationArrington Math 0430 2091Math 0430Introduction to Abstract Algebraic Systems2091 HomeworkHomework problems should be written on 8½- by 11- inch paper with no ragged edges.The first sheet should