Math 421/551
Modern Algebra I
Course description: Introduction to the theory of groups, rings, integral domains, and fields.
Prerequisites: Math 322 and Math 292, or permission of department head.
Text: Contemporary Abstract Algebra by Joseph A. Gallian, 6th edition, Houghton Mifflin.
For details about your instructor's contact information, office hours, and policies, go to www.faculty.mcneese.edu and access your instructor's website.
Objectives
The student will be able to
- prove statements involving familiar number systems as well as abstract algebraic structures using a variety of techniques, including direct and indirect argument, and mathematical induction;
- understand the algebraic properties of groups through the exploration of examples from familiar number systems, modular groups, matrices, and permutation groups;
- demonstrate knowledge of subgroups and direct products of groups;
- demonstrate knowledge of normal subgroups and factor groups;
- compare group structures using the concepts of homomorphism and isomorphism.
Course material
Course material will include the following topics:
| Topic | Chpt. |
|---|---|
| Preliminaries | Ch. 0 |
| Introduction to groups | Ch. 1 |
| Groups | Ch. 2 |
| Finite groups; subgroups | Ch. 3 |
| Cyclic groups | Ch. 4 |
| Permutation groups | Ch. 5 |
| Isomorphisms | Ch. 6 |
| Cosets and Lagrange's Theorem | Ch. 7 |
| External direct products | Ch. 8 |
| Normal subgroups and factor groups | Ch. 9 |
| Group homomorphisms | Ch. 10 |
| Introduction to rings | Ch. 12 |
| Introduction to integral domains and fields | Ch. 13 |
Topics and applications may be added or deleted at the discretion of the instructor. In particular, topics from Chapter O will be covered as needed.
Graduate students will be required to do independent reading, study, and/or presentations.
Assessment
The Semester score for the course will be calculated by using the weights (%) indicated below:
| Weight (%) | |||
|---|---|---|---|
| 75% | Semester average | Tests | ______ % |
| Assignments | ______ % | ||
| _________ | ______ % | ||
| 25% | Final exam grade |
The Semester letter grade in the course will be assigned according to the scale below:
| Semester grade | Semester score |
|---|---|
| 90–100 | A |
| 80–89 | B |
| 70–79 | C |
| 60–69 | D |
| 0–59 | F |
Notes:
- In cases of an excused absence, the instructor reserves the right to reweight the final exam in lieu of a make-up test.
- In the case where a student's score on his final exam indicates exceptional achievement above and beyond that indicated by the semester average, the instructor reserves the right to reweight the value of the final exam in computing the semester grade.
Please read the Department's Attendance Policy.
Instructor's office hours
can be found on the MSU web site at
http://www.faculty.mcneese.edu
Click on individual instructor to view their web page.
Or navigate from MSU Home Page; select Faculty & Staff, select Faculty Web Server.
Students should visit the MSU web page at
http://www.mcneese.edu/policy/diversity.htm
for information about diversity awareness and sexual harassment policies and
procedures, as well as the Americans with Disabilities Act.
Students should also visit the MSU web page at
http://www.mcneese.edu/integrity
for information on the Academic Integrity Policy.
ANY STUDENT WITH A DISABILITY IS ENCOURAGED TO CONTACT THE OFFICE OF SERVICES FOR STUDENTS WITH DISABILITIES IN DREW HALL, ROOM 200, VOICE (337) 475-5916, HEARING IMPAIRED (337) 475-5722. IT IS EACH STUDENT'S RESPONSIBILITY TO REGISTER WITH THE OFFICE OF SERVICES FOR STUDENTS WITH DISABILITIES WHEN REQUESTING A REASONABLE ACCOMMODATION.
One week of summer school is equivalent to 2 ½ weeks of Fall or Spring classes
DMCS
Location:
Kirkman Hall, Beauregard Drive
Mail:
Box 92340, MSU, Lake Charles, LA 70609
Phone:
(337) 475–5788,
Fax:
(337) 475–5799
e-Mail:
sbradley@mcneese.edu
