East Texas Baptist University s4

MATHEMATICS 4305 ABSTRACT ALGEBRA EAST TEXAS BAPTIST UNIVERSITY FALL 2014

Professor: Dr. Kevin J. Reeves Office: Meadows 200C Office Phone: 923-2312 Email: [email protected] Office Hours: MW: 1:00-2:59, TTH: 10:00-11:59, 1:00-1:59

Course Description: An introduction to abstract algebra, this course focuses on fundamental concepts of basic algebraic systems; groups, subgroups, and homomorphism; and rings, ideals, integral domains, and fields. Prerequisite: Mathematics 3300 with a “C” or better.

Course Objectives: Upon successful completion of this course, the student should be able to  understand mappings and operations and how they apply in algebraic situations  give examples of algebraic objects having specified properties  compute elements of algebraic objects and construct tables of elements  understand, prove, and apply basic theorems related to algebraic structures At ETBU, we are committed to Embracing Faith, Engaging Minds and Empowering Leaders. In an effort to empower you as a leader, the following leadership objective has been established for the course:  demonstrate confidence in mathematical understanding and proofs of results

Assigned Text: Contemporary Abstract Algebra (8th Ed) by Joseph A. Gallian. (ISBN: 978-1133599708)

Attendance: Attendance is an essential requirement of this course. The 2014-2015 catalog states on pages 23-24, “Attendance at all meetings of the course for which a student is registered is expected. To be eligible to earn credit in a course, the student must attend at least 75 percent of all class meetings.” With 29 class sessions, students must attend 22 sessions, so 8 absences require a grade of “F” from the instructor. Disruptive behavior or excessive tardiness will count as a class absence. See the catalog for more details on the attendance policy. Any student who misses 2 class periods or less will receive an extra half-percent grade boost on their overall course grade (athletics and other school approved activities will not count against this number if the student notifies the instructor about the absence in advance).

Examinations and Grading Policy: The course grade will be determined by averaging the scores from 3 in class tests (accounting for 30% of the grade), homework (50%), and the comprehensive final (20%). The semester grade will be based upon the following scale: A: 90%-100%, B: 80%-89%, C: 70%-79%, D: 60%-69%, F: below 60%

Makeup Policy: Homework: Homework assignments must be turned in when they are requested. Late homework will not be graded. Tests: If you will miss an exam for any of the reasons mentioned in Item 3 under Class Attendance on pp. 23-24 of the catalog, and I am notified in advance of your absence, you will be allowed to schedule a makeup test. Students who miss one exam (and no more) for any other valid reason during the semester are allowed to replace the score on that exam with the percentage from their final exam grade. No other makeup exams will be given for any reason. This policy is not flexible. Final Exam: The final exam must be taken on the posted day and time unless you satisfy one of the reasons listed on p. 31 of the catalog and you follow the directions listed there to reschedule your exam with me.

Homework: Homework assignments will be posted on Blackboard. These assignments are generally per section, and are due the next class period after that section has been completed. Questions concerning an assignment should be asked outside of class if possible. All homework assignments may not be worth the same amount of points. The instructor reserves the right to modify this homework policy during the semester, if necessary. Academic Integrity: Section 3 of the page on Classroom Expectations addresses this fundamental aspect of classroom behavior. Also see p. 21 of the current catalog for more information on Academic Integrity.

What to expect each class period: Most, if not all class periods will have a reading assignment for students to read and focus on particular items in the reading. This MUST be done before class for in-class work to progress as planned. At the beginning of each period, the instructor will lead a brief discussion of the reading (no more than 15 minutes) to help clarify any points that are not fully understood. The in-class work will consist of groupings of 2-3 students each (assigned by the instructor and changed regularly) to work toward deepening the understanding of definitions, examples, and theorems for that day’s material. Then homework will be assigned for each student to complete (as individuals) to show how fully the student has mastered the concepts assigned. Each of these three components will have a grade assigned, with the reading component accounting for 10% toward the homework grade, in-class participation counting as another 10%, and the assigned problems counting as the remaining 30%.

Tentative Course Outline: (Note: all dates and material are tentative and subject to change as needed)

Tuesday, Aug 26 0 – Preliminaries 1 – Introduction to Groups 2 – Groups 3 – Finite Groups; Subgroups 4 – Cyclic Groups 5 – Permutation Groups Review Tuesday, Sept 23 Test I

6 – Isomorphisms 7 – Cosets and Lagrange’s Theorem 8 – External Direct Products 9 – Normal Subgroups and Factor Groups 10 – Group Homomorphisms 11 – Fundamental Theorem of Finite Abelian Groups Review Thursday, Oct 30 Test II

12 – Introduction to Rings 13 – Integral Domains 14 – Ideals and Factor Rings 15 – Ring Homomorphisms 16 – Polynomial Rings * 17 – Factorization of Polynomials * 18 – Divisibility in Integral Domains * Review Tuesday, Dec 9 Test III

(Sections marked with * will be covered if time permits)

Final Exam – Tuesday, December 16 @ 2:00-3:50

Disability Accommodation Statement: A student with a disability may request appropriate accommodations for this course by contacting the Office of Academic Success located in Marshall Hall 301, and providing the required documentation. If accommodations are approved by the Disability Accommodations Committee, the Office of Academic Success and Graduate Services will notify you and your professor of the approved accommodations. You must then discuss these accommodations with your professor. Classroom Expectations This document is part of the class syllabus, and all students are expected to carefully read it to understand their part in enhancing the learning environment. 1. It is the student’s responsibility to arrive on time for class, prepared and ready. a. Attendance is recorded during the first five minutes of the class period. If you arrive after that time (or leave early), you will be marked absent for the day, unless you discuss the situation with me and I agree to mark you present. b. Bring all necessary materials with you, including textbook, calculator, pen or (sharpened) pencil, and something to write on. c. Read ahead through whatever section of the textbook is to be discussed that day and make notes about portions you don’t understand. d. Turn off any cell phones or other devices that may cause disturbances during class time. Texting during class is not permitted. e. Make any needed trips to the rest room or water fountain before class begins. f. Come to class rested and ready to learn. If you are observed sleeping during class time you will be marked absent for the day. 2. It is the student’s responsibility to observe appropriate behavior during class time. a. No food or drink is allowed in classroom environments (with the exception of water in a clear, closeable water bottle). b. Do not carry on conversations with your fellow classmates during class. If disruptive behavior persists after being warned, you will be asked to leave the class and be marked absent for the day. c. If you have a question about something covered by the instructor, please raise your hand and get the instructor’s attention to ask your question. d. Do not disrupt your fellow student’s ability to learn during class time in any way your instructor or fellow students feel is inappropriate. Laptops may be used in class, but only to follow along with the class lectures if needed. 3. It is the student’s responsibility to promote academic honesty at all times. a. Any assignment turned in (including homework) must be your own work, and not someone else’s. Even if you and a friend work together on an assignment, what you turn in must be your own work, and not your friend’s work. b. During exams and quizzes, make sure that nearby students cannot see your paper. c. During any closed book testing environment, make sure your notes, textbook, etc are out of view of all students (including yourself). d. Observe any dress code that your instructor requires. For example, I do not allow baseball caps to obscure student’s eyes on test days. e. If a student is observed cheating on any exam, the student will receive an F for the course, and will be referred to the Academic Affairs office for disciplinary action. Note that sending or receiving electronic messages (texting) during any exam is considered cheating and will be handled as such.