Syllabus

Course title/number, number of credit hours Course Title: Modern Algebra Term: Summer 1, 2016 Classroom location: SC 178 MW4:45-6:20pm Is this an online course: Yes ___ or No _x__ Credit hours 3 CRN( optional): 82653 Course number: MAS 4301 001

Course prerequisites or corequisites Course number MAD 2104 Prerequisites Course Title: Discrete Mathematics Permission of the instructor is required: Yes ___ or No _x__

Instructor contact information Instructor: Frederick Hoffman Office: SE 212A Office Hours: MW 3:15-4:15pm Office Phone: (561) 297-3345 E-mail Address: [email protected]

Course description Description: Elementary number theory. Groups, rings and ideals, polynomials, and fields.

Objectives, Learning Outcome Goals: Upon successful completion of the course the student will be familiar with definitions, properties and theorems about the integers, groups, rings and fields. Students will learn to write and present correct statements of mathematical definitions, theorems and proofs. Students will learn to read and master proofs, and to generalize and apply the results to solve problems. Students will learn to produce their own proofs. Students will present proofs and problem solutions to the class. The topical outline indicates the approximate schedule for class presentations and discussions of exercises. The lectures will tend to be ahead of the readings, and the instructor will indicate what the students are to read on their own. This course is a modified guided discovery (or Moore Method) course. Students will be guided by the text and the lectures, but are not supposed to use other texts or internet sources to find solutions. Students may work independently or in groups.

We shall attempt to cover most of the first 26 chapters of the text, following the author’s order of presentation, with one slight change. Your purpose is to learn the basic ideas of modern algebra, and develop your ability to read, create and present proofs. I consider the exercises to be an integral part of the text; please read all of the sets listed. The ones I indicated with asterisks are those that seemed to me to be more important or more interesting. Students will be asked to present some of these in class, and to turn in a few of them—with ample notice. Individual students, or small groups of students may pre-select sets of problems to work on and present, by arrangement with the instructor. The following statement pertains to this section of MAS 4301 This course was developed out of an FAU Curriculum Grant Program, designed to support integrating research and inquiry ideas and activities into course assignments, and engaging students in the process of discovery as part of FAU’s Quality Enhancement Plan (QEP) program: Distinction through Discovery. As part of this course, some of your work samples may be collected to evaluate the effectiveness of the Distinction through Discovery program. For more information about the QEP, please visit http//www.fau.edu/qep/

The schedule refers to the homework; the lectures will run ahead. Course topical outline Date Topics HW Assignments May Operations/ Why Abstract Algebra 2/A, B, C; 16 May Definition of Groups/ Elementary 3/A,B,C*,F*,G*; 18 Properties 4/B,C*,D,E*,F*,G*

May Subgroups/ Functions 5/A,,C,D*,E*,F*,H*;6/C,D,E,G* 23 May25 Permutation Groups/ Finite 7/A,B,C,D*,F*,G*;8/A,B,C,D,E*, Permutations F* Jun1 9/A,B,C,D,G* Isomorphism (including part of ch. 14) Jun 6 The Integers/ Factoring into Primes 21/A,B*,C,E,F*;22/A,B*,C*,D*,E *,F* Jun 8 Order of Elements 10/A*,B,C,D,E*,F,G* Jun 13 Cyclic Groups 11/A,B,*,C*,D,E* Jun 15 Test 1 Jun 20 Partitions, Equivalence 12/ A,B,C,D*

Jun 22 Counting Cosets 13/ A,B,C*,D*,E,F*,G*,H*,I*,K Jun 27 Homomorphisms 14/ A,B,C*,D,E*,F*,G,H*,I* Jun 29 Quotient Groups 15/ A,B,C*,D*,E*,F,G*,H Jul 6 Fundamental Theorem 16/ A,B,C,D*,E,F*,G*,H,I*,J*,K*,L*, M,N,O,P,Q Jul 11 Rings 17/ A,B,C,D,E,F,G,H*,I*,J* Jul 13 Ideals and Homomorphisms 18/ A,B,C*,D*,E,F*,G,H,I Jul 18 Quotient Rings 19/ A,B,C*,F* Jul 20 Integral Domains 20/ A,B*,C*,D,E*,F* Jul 25 Rings of Polynomials 24/ A,B,C,D*,E,F,G,,J Jul 27 Factoring Polynomials 25/ A,B,C*,D*,E*,F*,G* Aug 1 Substitution 26/ A*,B,C,D*,E,F*,G,H*,I* Aug 3 Final Examination (two parts) Included course topics are subject to reasonable changes at the discretion of the instructor.

Course evaluation method Class participation and homework: 35% Test 1 25% Comprehensive Final Exam: 40%

Course grading scale Cumulative performance Grade ≥90 A 87-89 A- 83-86 B+ 80-82 B 77-79 B- 73-76 C+ 60-72 C 50-59 D <50 F

Policy on attendance, makeup tests and incompletes Regular attendance is required, including active involvement in all class sessions and professional conduct in class. If announcements are made in class, students are assumed to be aware of the announcements. Students are responsible for arranging to make up work missed because of legitimate class absence, such as illness, family emergencies, military obligation, court-imposed legal obligations, or participation in university-approved activities. It is the student's responsibility to notify the instructor prior to any anticipated absence, and within 24 hours after an unanticipated absence. Makeup tests and exams will be given only under circumstances which coincide with university policy (see link below under attendance). If you miss a test or exam, you must provide a written, verifiable excuse, if possible in advance of the scheduled exam. For unforeseen absences, you must notify the instructor within 24 hours. http://www.fau.edu/academic/registrar/catalog/academics.php#policiesall Incompletes are only given according to University policy.

Calculators and other electronics

Students may use electronic textbooks during class; no other use of cellphones, tablets or computers is permitted; cellphones must be silenced. If you are using an online form of the Pinter text, or your notes, please let me know; otherwise put your electronics away.

Required text Pinter, C. C. A Book of Abstract Algebra, Second edition. Dover (1990) (2010 republication)

Classroom Etiquette Please refer to the FAU Code of Conduct available at http://www.fau.edu/regulations/chapter4/4.007_Student_Code_of_Conduct.pdf.

Honor Code

Students at Florida Atlantic University are expected to maintain the highest ethical standards. Academic dishonesty is considered a serious breach of these ethical standards, because it interferes with the university mission to provide a high quality education in which no student enjoys an unfair advantage over any other. Academic dishonesty is also destructive of the university community, which is grounded in a system of mutual trust and places high value on personal integrity and individual responsibility. Harsh penalties are associated with academic dishonesty. For more information, see University Regulation 4.001 at http://www.fau.edu/ctl/4.001_Code_of_Academic_Integrity.pdf

FAU Accessibility Services

In compliance with the Americans with Disabilities Act (ADA), students who require special accommodation due to a disability to properly execute coursework must register with FAU Student Accessibility services (SAS) and follow all SAS procedures. In Boca Raton, SU 133 (561-297-3880); in Davie, MOD 1 (954-236-1222); in Jupiter, SR 117 (561-799-8585); or at the Treasure Coast, CO 128 (772-873-3305). ASA website at http://www.fau.edu/sas/