MA 410 SYLLABUS, Spring 2014

Course Objectives:  Beginning with the natural numbers, the integers and rational numbers are developed.  This is followed by an introduction to rings and fields and the development of polynomials over the integers, rational numbers, and general rings and integral domains.  In addition to gaining an understanding of these mathematical structures, students will improve their skills at constructing and writing mathematical proofs and developing examples and counter-examples. 

Class Schedule:  Tuesday, Thursday 6 – 7:15 p.m., Howard Hall 211

Attendance Requirement:  Class participation is a significant part of your grade.  Up to three absences will be excused when you are not scheduled to give a presentation, but absences on presentation days require a substantiated excuse.  If you must miss an examination, you MUST let me know BEFORE the examination (by voice-mail or e-mail) or you automatically receive a grade of 0.  You must then be in direct contact with me prior to the next class to schedule a make-up examination.

Last date to Withdraw with automatic assignment of "W" grade:  March 31, 2014.

Statement on Academic Honesty:  Whenever you have had assistance with a problem, or worked with any other student, you must acknowledge who you worked with at the beginning of the solution to the problem.  In courses for mathematics majors, I often get too much whole-class homework.  If I get two papers which are identical (and so clearly haven’t been written up separately) or where the errors are identical but joint work isn’t acknowledged, I will give both students a 0 for that homework assignment, and for the second such incident, will report it to the University Disciplinary Committee.
Examination Rules:  No student is permitted to have at his or her desk any books or papers that are not given out or expressly permitted by the instructor.  Possession of such material will be regarded as evidence of intent to use the information dishonestly.  No communication between students during the examination is permitted.  If there are questions, or if there is a need for additional material, the instructor should be asked.  In accordance with the academic honesty policy of Monmouth University each exam will contain the following pledge:
"I, ____________________________, certify that I have read the above rules for examinations, and that I have abided by them. By signing, I affirm that I have neither given nor received aid during this examination, and I understand that violation of this affirmation may result in suspension or expulsion from Monmouth University."

Statement on Special Accomodations:  Students with disabilities who need special accommodations for this class are encouraged to meet with me or the appropriate disability service provider on campus as soon as possible.  In order to receive accommodations, students must be registered with the appropriate disability service provider on campus as set forth in the student handbook and must follow the University procedure for self-disclosure, which is stated in the University Guide to Services and Accomodations for Students with Disabilities.  Students will not be afforded any special accommodations for academic work completed prior to the disclosure of the disability, nor will they be afforded any special accommodations prior to the completion of the documentation process with the appropriate disability office.

Notes to Students:  You are expected to read the section for the day prior to class, and, when it is a new section, write at least two questions over the section.  Homework from that section is due at the following class, unless I specify that some may be postponed one period.  Rewrites are due the class after they're returned to you.  I've assigned very few problems that have answers at the back of the text; however, usually looking at one just before or just after the one assigned, and how the book did it, will often help.

MA 314 is a prerequisite for this course.  We will be using material from MA314 very heavily in the course, especially an understanding of arithmetic modulo n.  You need to be able to add and multiply (mod n) and to understand that two integers that differ by a multiple of n are effectively the same number (they’re congruent (mod n)).  We will be making heavy use of the theorems in chapters 1 (especially the Euclidean algorithm and following it back up to solve diophantine equations, and theorems 1.12-1.14), 3 (especially theorem 3.24, how to actually find those solutions, and the theorems leading up to it), and 4 of the MA314 text (and some use of chapter 2).  So if you went home over Christmas break and forgot all that material, do some very serious review!  I don’t want blank stares when I mention these facts.

Note on written presentations:  Your written presentations are to be written up individually in Word, and submitted via the Presentations dropbox.  You are to use Word's Equation Editor (you need to be in Word 2007) to write your equations.
 

 Additional 6.2 problem: (a) List all principal ideals in Z₁₂ (b) For each ideal I in part (a), write out the addition and multiplication tables of Z₁₂/I.  
(c) Show that each of the new rings you wrote out the tables for in part (b) is isomorphic to one of these rings: 0, Z₂, Z₃, Z₄, Z₆, Z₁₂.