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MA 312 Abstract Algebraic Structures
Smith, Charlie L.


Mission Statement: The mission of Park University, an entrepreneurial institution of learning, is to provide access to academic excellence, which will prepare learners to think critically, communicate effectively and engage in lifelong learning while serving a global community.

Vision Statement: Park University will be a renowned international leader in providing innovative educational opportunities for learners within the global society.

Course

MA 312 Abstract Algebraic Structures

Semester

SP 2007 HO

Faculty

Smith, Dr. Charlie L.

Title

Associate Professor of Mathematics, and Department Chair of Mathematics

Office Location

SC 308

Office Hours

MW 2:00-4:00 p.m.; TR 9:00-11:30 a.m.; F 2:00-3:00 p.m.; Or by Special Appointment

Daytime Phone

(816) 584-6261

E-Mail

charlie.smith@park.edu

Semester Dates

January 16, 2007 - May 8, 2007

Class Days

--T-R--

Class Time

1:00 - 2:15 PM in SC 307

Prerequisites

MA 212 and MA 301

Credit Hours

3


Textbook:

Dan Saracino.  Abstract Algebra: A First Course.  Prospect Heights, IL.  Waveland Press, 1992.

Additional Resources:

McAfee Memorial Library - Online information, links, electronic databases and the Online catalog. Contact the library for further assistance via email or at 800-270-4347.
Career Counseling - The Career Development Center (CDC) provides services for all stages of career development.  The mission of the CDC is to provide the career planning tools to ensure a lifetime of career success.
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Resources for Current Students - A great place to look for all kinds of information http://www.park.edu/Current/.


Course Description:
A study of several algebraic systems from a postulational viewpoint. Systems studied include groups, rings, integral domains, and fields. PREREQUISITES: MA 212 and MA 301. 3:0:3

Educational Philosophy:

Mathematics is my lifelong passion and obsession.  In the classroom, I try to convey my enthusiasm and excitement for mathematics; I emphasize its pristine beauty and logical structure.  Students are required to work a substantial number of homework problems in order to learn the material.  Typically two major tests are given each semester. Material is presented in lecture format; students are encouraged to interrupt to ask questions.

Learning Outcomes:
  Core Learning Outcomes

  1. Define the concept of a group; distinguish between nonabelian and abelian groups and recognize examples and nonexamples of each
  2. State the fundamental theorems of groups and use them to prove additional results.
  3. Apply the properties of exponents in computation and proof
  4. Define the order of a group element and apply the concept to exercises
  5. Define a cyclic group and apply the concept to exercises
  6. Define and utilize the properties of subgroups
  7. Demonstrate basic properties of symmetric groups and apply to exercises
  8. Define the concepts of equivalence relations and cosets and apply to appropriate exercises
  9. Apply LaGrange's Theorem and its corollaries to appropriate exercises
  10. Define and utilize the concept of a normal subgroup
  11. Define and apply the concept of homomorphism to appropriate exercises


Core Assessment:
  • Periodic assignments
  • Quizzes
  • Tests

Class Assessment:

Frequent homework assignments   60%
Midterm examination                     15%
Final Examination                           25%
                                                    100%
 
Testing Dates:  Midterm, Tuesday, March 6, 2007 from 1:00 - 2:15 p.m.
                        Final, Tuesday, May 8, 2007 from 1:00 - 3:00 p.m.

Grading:

85 - 100%   A
70 - 84%     B
60 - 69%     C
50 - 59%     D

Late Submission of Course Materials:

Homework assignments MUST be turned in on the announced due date. LATE PAPERS WILL NOT BE ACCEPTED. You will either turn in an assignment on the date that it is due, or you will not turn it in at all. An assignment MUST be received by class time on the announced due date. If it is not received by this time, then a score of ZERO will be recorded for that assignment. NO EXCEPTIONS. NO EXCUSES. Athletes who are traveling out of town with a Park University team must turn in the assignment BEFORE DEPARTURE. 
 
PLEASE take each TEST on the day that it is scheduled.  Any make-up test given will be significantly more difficult than the origianl test.  The instrucotr may deny this option depending upon circumstances.  Once taken and recorded, your test score is final and cannot be changed.

Classroom Rules of Conduct:

Expectations (What are the things that the student needs to do in order to succeed in this course?)
1. Regular attendance is essential.
2. PLEASE bring your textbook to every class session.
3. Listen carefully and pay attention.
4. Take thorough, accurate class notes. For better retention, review your notes as soon as possible after each class session. Review your notes regularly throughout the semester.
5. VOCABULARY, TERMINOLOGY,  and NOTATION are extremely important in learning mathematics.
6. ASK QUESTIONS DURING CLASS whenever you need more explanation.
7. Read your textbook over and over until you understand the material completely.
8. Consult with the instructor if you are having ANY DIFFICULTY WHATSOEVER.  That’s why they pay me the big bucks.
 
Responsibility

 

     The student is entirely responsible for obtaining and learning any material missed because of absence.  Get handouts and assignments from the instructor.  Get class notes from another student in the class.
Calculator

     The student will probably find it useful to have a scientific calculator for computational purposes. 

Miscellaneous

     What material are you responsible for understanding? EVERYTHING. Of course, it would be impossible for you to reproduce everything or demonstrate total knowledge on homework and tests, but you are expected to strive for excellence in everything that we cover, so that you will be prepared for anything.  As mathematics majors, any effort on your part less than this cannot be considered satisfactory.

 

     The instructor reserves the right to make changes in the syllabus due to time constraints, speed of coverage, or other factors.

Course Topic/Dates/Assignments:
Reading Assignments  

 

Read chapters from the textbook as assigned. You may have to read a chapter several times until you understand the material completely.
Testing
All tests will be CLOSED REFERENCE tests, meaning that you are NOT allowed to use the textbook, personal class notes, or handouts. However, calculators are permitted. PLEASE take each test on the day that it is scheduled. Any make-up test given will be significantly more difficult than the original test. The instructor may deny this option depending upon circumstances. Once taken and recorded, your test score is final and cannot be changed.
Topics/Assignments:
Sets and Inductions
Chapter 1 Binary Operations
Chapter 2 Groups
Chapter 3 Fundamental Group Theorems
Chapter 4 Powers of an Element, Cyclic Group
Chapter 5 Subgroups
Chapter 6 Direct Products
Chapter 7 Functions
Chapter 8 Symmetric Groups
Chapter 9 Equivalence Relations, Cosets
Chapter 10 Counting the Elements of a Finite Group
Chapter 11 Normal Subgroups
Chapter 12 Homomorphisms
Chapter 13 Homomorphisms and Normal Subgroups
Chapter 14 Direct Products and Finite Abelian Groups (OPTIONAL)
Chapter 15 Sylow Theorems (OPTIONAL)
Chapter 16 Rings
Chapter 17 Subrings, Ideals, and Quotient Rings
Chapter 18 Ring Homomorphisms
Chapter 19 Polynomials
Chapter 20 Polynomials to Fields
Chapter 21 Unique Factorization Domains
 

 

Academic Honesty:
Academic integrity is the foundation of the academic community. Because each student has the primary responsibility for being academically honest, students are advised to read and understand all sections of this policy relating to standards of conduct and academic life.   Park University 2006-2007 Undergraduate Catalog Page 87-89

Plagiarism:
Plagiarism involves the use of quotations without quotation marks, the use of quotations without indication of the source, the use of another's idea without acknowledging the source, the submission of a paper, laboratory report, project, or class assignment (any portion of such) prepared by another person, or incorrect paraphrasing. Park University 2006-2007 Undergraduate Catalog Page 87

Attendance Policy:
Instructors are required to maintain attendance records and to report absences via the online attendance reporting system.

  1. The instructor may excuse absences for valid reasons, but missed work must be made up within the semester/term of enrollment.
  2. Work missed through unexcused absences must also be made up within the semester/term of enrollment, but unexcused absences may carry further penalties.
  3. In the event of two consecutive weeks of unexcused absences in a semester/term of enrollment, the student will be administratively withdrawn, resulting in a grade of "W".
  4. A "Contract for Incomplete" will not be issued to a student who has unexcused or excessive absences recorded for a course.
  5. Students receiving Military Tuition Assistance or Veterans Administration educational benefits must not exceed three unexcused absences in the semester/term of enrollment. Excessive absences will be reported to the appropriate agency and may result in a monetary penalty to the student.
  6. Report of a "F" grade (attendance or academic) resulting from excessive absence for those students who are receiving financial assistance from agencies not mentioned in item 5 above will be reported to the appropriate agency.

Park University 2006-2007 Undergraduate Catalog Page 89-90

Disability Guidelines:
Park University is committed to meeting the needs of all students that meet the criteria for special assistance. These guidelines are designed to supply directions to students concerning the information necessary to accomplish this goal. It is Park University's policy to comply fully with federal and state law, including Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, regarding students with disabilities. In the case of any inconsistency between these guidelines and federal and/or state law, the provisions of the law will apply. Additional information concerning Park University's policies and procedures related to disability can be found on the Park University web page: http://www.park.edu/disability .

Copyright:

This material is protected by copyright and can not be reused without author permission.

Last Updated:2/20/2007 12:16:08 PM