Fall 2010 Syllabus

Math 415 Abstract Algebra (3 hours)

 

Instructor:  William Harris                                                     Office:  120 ASC

Email:  wharris@georgetowncollege.edu                                Phone:  863-7921

Instructor’s Web Site:  spider.georgetowncollege.edu/mpc/harris

Author’s Web Site:  www.d.umn.edu/~jgallian

Text Web Site:  college.cengage.com/mathematics/gallian/abstract_algebra/6e/students/index.html

Course Web Site:  https://scholar.georgetowncollege.edu

 

Office Hours:  10:00-10:30 MWF; 1:30-2:30 MWF; 1:00-2:00 TR; also by appt.

 

Course Description:  A theoretical development of basic algebraic structures, with an emphasis on group theory.  Topics include cyclic groups, Lagrange’s Theorem, quotient groups and homomorphisms.  Rings, integral domains, and fields are introduced.

 

Prerequisites:  MAT 225 and MAT 301.

 

Text:  Gallian, Joseph A., Contemporary Abstract Algebra, 6th ed., Houghton Mifflin, 2006.

 

Course Objectives:  In this class, successful students will:

--demonstrate basic content knowledge of group theory, including subgroups, cyclic groups, permutation

   groups, cosets, normal subgroups, homomorphisms and isomorphisms, on homework and exams;

--apply problem-solving skills on computational problems to arrive at correct solutions on

   homework and exams;

--employ analytical reasoning skills in selecting and correctly applying an appropriate technique to

   prove statements on homework and exams;

--employ written communication skills to effectively and precisely convey proofs of statements on

   homework and exams.

 

 

Requirements of Course:  Students will be asked to complete a variety of assignments.  Many will be homework assignments to be completed individually, but there will be other types, as well.  Some assignments may require group work.  Some assignments may be on-line.  There will be two examinations and a comprehensive final.  I’d like to give the exams out-of-class, in the evening, and allow you two hours to complete it.  The rationale for this is to give you plenty of time to thoughtfully consider the questions. At the moment, I’m targeting Tuesday, October 5 and Thursday, November 18.  The final is scheduled for Friday, December 10, at 9am.

 

Course Outline:  We will cover topics from Chapters 0 through 13 of the text.  Additional material will be introduced if time permits.

 

Evaluation:

            Assignments:                                       40%

            Exams:                                                 40%

            Comprehensive Final:                          20%

 

I would expect grades to be assigned according to the following scale: 

A:  91-100;  A/B:  88 up to 91;  B: 81 up to 88;  B/C:  78 up to 81; 

C:  70 up to 78;  D: 60 up to 70;  F:  below 60.  

I reserve the right to adjust this scale slightly at the end of the semester.

 

Attendance:  Daily attendance is expected.  I’ll be chatting with you if there are problems.

 

 

 

 

Bibliography:

Dubinsky, Ed, and Leron, Uri, Learning Abstract Algebra with ISETL, Springer-Verlag, 1994.

 

Dummit, David S. and Foote, Richard M., Abstract Algebra, 2nd ed., Prentice Hall, 1999.

 

Fraleigh, John B., A First Course in Abstract Algebra, 7th ed., Addison Wesley, 2003.

 

Hibbard, Allen C., and Levasseur, Kenneth M., Exploring Abstract Algebra with Mathematica, Springer, 1999.