**Fall 2010 Syllabus**

**Math 415 Abstract Algebra (3 hours)**

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**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

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**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__,
6^{th} 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.

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**Bibliography:**

Dubinsky, Ed, and Leron, Uri,
__Learning Abstract Algebra with ISETL__, Springer-Verlag, 1994.

Dummit, David S. and Foote,
Richard M., __Abstract Algebra__, 2^{nd} ed., Prentice Hall, 1999.

Fraleigh, John B., __A First
Course in Abstract Algebra__, 7^{th} ed., Addison Wesley, 2003.

Hibbard, Allen C., and Levasseur,
Kenneth M., __Exploring Abstract Algebra with Mathematica__,
Springer, 1999.