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Math 451: Abstract Algebra I (Fall 2017)
Contents
Syllabus
Download the course syllabus here. The syllabus contains essential information about the course (textbook, prerequisites, course description, material covered, etc.).
Note: This is the syllabus for Abstract Algebra I and Abstract Algebra II. Math 451 only covers Abstract Algebra I.
Textbook
The official textbook for this course is: A first course in Abstract Algebra (7th edition), authored by John B. Fraleigh, published by Pearson. See this link for the full reference.
Class time and location & Office hours
Class time and location:
Monday: 2:303:50pm, Hill Hall 202
Wednesday: 1:002:20pm, Hill Hall 202
Office hours:
Monday: 1:152:15pm, Smith Hall 308
Wednesday: 2:303:30pm, Smith Hall 308
Course policies
Grading policy
Your overall grade for the course will be a precise combination of:
 Your global quiz grade $G_1$. There will be about 9 quizzes in the semester. Each quiz grade will be automatically scaled to a grade /100, and at the end all the quiz grades, dropping the lowest two, will be averaged to a global quiz grade.
 Your global midterm grade $G_2$. There will be two midterm exams, whose grades will be automatically scaled to grades /100, and then averaged to a global midterm grade.
 Your final exam grade $G_3$. There will be one final exam, whose grade will also be automatically scaled to a grade /100.
The formula for your overall grade $G$ for the course will be: $G = c_1 G_1 + c_2 G_2 + c_3 G_3$, where the coefficients $c_1$, $c_2$ and $c_3$ will be around $c_1 = 35\%$, $c_2 = 30\%$ and $c_3 = 35\%$. These coefficients may be subject to marginal change.
Finally, you will be assigned a letter grade for the course depending only on your overall grade $G$, according to the following table:
Overall grade  Letter grade 

90% ≤ G ≤ 100%  A 
80% ≤ G < 90%  B+ 
70% ≤ G < 80%  B 
60% ≤ G < 70%  C+ 
50% ≤ G < 60%  C 
40% ≤ G < 50%  D 
0% ≤ G < 40%  F 
Note: There will be no exceptions to the grading policy described above.
Attendance & Excused absence policy
Attendance is mandatory: you are required to attend every class.
If you must miss a class for a legitimate reason, you are required to inform me as soon as possible and provide documentation for your absence. If you miss a midterm exam, there will not be automatically a makeup exam if the reason of absence is not serious or the notice is too short. There will be no makeup quizzes, even if you miss a quiz with a valid reason of absence.
Textbook vs Lecture notes
Although we will follow the outline of the textbook very closely, your lecture notes should always be your primary source of information. You can only be expected to know the contents of the lectures, unless you are explicitely asked to review specific segments of the textbook. Nevertheless, the textbook is a great secondary source of information and will be the main source of problems, which are of the utmost importance.
Calculator
You will never need to use a calculator in this course. Calculators will not be allowed during quizzes or exams.
General advice
Our goal is to provide all the resources necessary for you to succeed and learn great mathematics in the process, regardless of your background coming in. Nevertheless, you may find this course very challenging. Attending every class is absolutely necessary to meet the challenge but in no way will it be sufficient. The key to your success rests on yourself: it will require hard work, including hours of study, lots of problem solving, and your active involvement in learning both in and outside of the classroom. Of course, you will be assisted in your efforts, and I encourage you to reach me as often as you need.
Contact
My email is brice@loustau.eu. I encourage you to write with any questions.
My office is 308 in Smith Hall. You are welcome during office hours (see above), you may also see me outside of office hours by appointment (first send me an email).
Course schedule
For general important dates in the semester, see the academic calendar here.
Refer to the course schedule below very regularly. It contains among other things the homework assignments and the past quizzes and exams.
This course schedule is only tentative: it is very much subject to change. Always refer to last version online, and make sure that you refresh the page.
Date  Topic  Homework assignment  Special 

Wed 09/05 
Discussion of course policies Introduction to the course 0. Sets and relations 
First day of class  
Mon 09/11  0. Sets and relations  Review lecture notes  
Tue 09/12      Last day to drop a course without a "W" grade 
Wed 09/13 
Functions Chapter I: Groups and Subgroups 1. Introduction and examples 
Review Lecture notes Section 0. Exercises 118, 2336 

Mon 09/18  1. Introduction and examples 
Review Lecture notes Section 0. Exercises 118, 2336 
Quiz #1 
Wed 09/20  1. Introduction and examples  Review Lecture notes  
Mon 09/25  2. Binary structures 
Review Lecture notes Exercises given in class Section 1 Exercises 127, 3941 
Quiz #2 Quiz #2 Makeup 
Wed 09/27  2. Binary structures  Review Lecture notes  
Mon 10/02 
2. Binary structures 
Review Lecture notes Exercise given in class Section 2 All Exercises 
Quiz #3 
Wed 10/04 
2. Binary structures Monoids and inverses 
Review Lecture notes Exercises given in class 

Mon 10/09  (3.) Morphisms of binary structures. 
Review Lecture notes Homework problems 
Quiz #4 
Wed 10/11 
4. Groups 
Review Lecture notes Exercises given in class Section 3 Exercises 115, 33 

Mon 10/16    List of topics 
EXAM #1 EXAM #1 Solutions 
Wed 10/18 
4. Groups 5. Subgroups 
Review Lecture notes 

Mon 10/23 
5. Subgroups 6. Cyclic groups 
Review Lecture notes Section 4 Exercises 110, 1119, 23, 2837, 41 Homework problems 1, 2, 3 given in class 
No quiz 
Wed 10/25 
66. Cyclic groups 
Review Lecture notes Homework problems given in class Section 5 Exercises 143, 47, 49, (50), 51, 52, 53 

Mon 10/30 
8. Groups of permutations 
Review Lecture notes Section 6 Exercises 17, 1921, 3041, 4547, (48, 49, 50) 
Quiz #5 Quiz #5 Solutions 
Wed 11/01  9. Orbits, Cycles and the alternating group 
Review Lecture notes Homework problems given in class Section 8 Exercises 19, (10), 1113, 18, 20, 4041, (4947), 48, 52 

Mon 11/06 
10. Cosets and the theorem of Lagrange 11. Direct products and finitely generated abelian groups 
Review Lecture notes Homework problems given in class Section 9 Exercises 13, 713, 23, 24, 29, 30, 33, 36 
Quiz #6 Quiz #6 Solutions 
Wed 11/08 
11. Direct products 13. Group homomorphisms 
Review Lecture notes Homework problem given in class Section 10 Exercises 1, 2, 6, 7, 15, 16, 2634, 40 

Mon 11/13 
Review Lecture notes Homework problem given in class Section 11 Exercises 46, 47, 49, 54 List of topics 
EXAM #2 EXAM #2 Solutions 

Wed 11/15 
13. Group homomorphisms 14. Factor groups 
Review Lecture notes  
Mon 11/20  14. Factor groups 
Review Lecture notes Homework problem given in class Section 13 Exercises 1, 2, 3, 6, 7, 8, 13, 14, 19, 22, 28, 29, 47, 48, 49, 51 
No quiz 
Wed 11/22      Class cancelled follows a Friday schedule 
    Thanksgiving recess 11/23  11/26 

Mon 11/27  18. Rings and fields 
Review Lecture notes Homework given in class 
Quiz #7 Quiz #7 Solutions 
Wed 11/29 
18. Rings and fields 19. Integral domains 
Review Lecture notes Homework problems 1, 2, 3 given in class Section 18 Exercises 14, 713, 20, 22, 2728, 38, 44, 5556 

Mon 12/04 
19. Integral domains 22. Ring of polynomials 
Review Lecture notes Section 18 Exercises 120, 22, 2728, 3133, 35, 38, 40, 49, 5456 
Quiz #8 Quiz #8 Solutions 
Wed 12/06  23. Factorization of polynomials over a field 
Review Lecture notes Section 19 Exercises 111, 14, 19, 29 Section 22 Exercises 16, 20, 24, 2930 

Mon 12/11  23. Factorization of polynomials over a field 
Review Lecture notes Section 22 Exercises 710, 1215 Section 23 Exercises 14, 911, 14, (2730), 36 
Quiz #9 Quiz #9 Solutions 
Wed 12/13  Review session 
Review Lecture notes Homework problem given in class Section 23 Exercises 1215, 27, 29 

Mon 12/18  FINAL EXAM  List of topics 
FINAL EXAM Time: 3:00  6:00pm Location: Hill 202 