Attendance will be checked at the beginning of each class meeting, but it does not affect your grade. However you are responsible to know the material covered in class and that in the corresponding sections of your textbook.
Working on example problems is the key to understand abstract concepts. Therefore there will be a homework assignment for each lecture in the course schedule. You turn in your solutions at the end of the lecture at the given due date. If there is no class meeting that day, you put your solutions in the drop box at the math office MS401 before noon. Make sure that you write your and my name and the course and section number on the front page. Late submissions will not be accepted. Your homework score is part of your final grade. Example solutions for selected problems will be posted in the solutions section after the due date. Feel free to ask me for solutions for specific problems that you could not solve.
Be prepared for 5-minutes in-class quizzes that count toward your final grade. These quizzes will not be announced and there are no make-up quizzes. Books, notes, and electronic devices are not permitted during quizzes.
There will be 3 midterm exams and a final exam which contribute to your final grade. Each exam will be announced in class and appear online in the course schedule. Make-up exams will be given only under exceptional circumstances and if you contact me in advance. Books, notes, and electronic devices are not permitted during exams. Example solutions for the exams can be found in the solutions section after each exam.
To gain credit your answers must be clearly presented. Your work must show how you proceeded to find the answer or why your answer is correct. Scratch work should be clearly separated from what is to be graded.
The contributions to your total score will be weighted as follows.
| Contribution | Homework + Quizzes | Midterm Exams | Final Exam |
|---|---|---|---|
| Weight (final grade) | 20% | 3 x 20% | 20% |
| Weight (6-weeks grade) | 50% | 1 x 50% | 0% |
Your total score will be truncated to an integer percentage and determines your final grade as follows.
| Total Score | 0-59% | 60-69% | 70-79% | 80-89% | 90-100% |
|---|---|---|---|---|---|
| Letter Grade | F | D | C | B | A |
Curving may be applied in form of a linear adjustment to all scores on a particular exam. I reserve the right to decide borderline cases based on class attendance and subjective impressions such as effort and conscientiousness.
Your starting points are the textbook and the lecture. It is easier to follow the lecture if you have seen the material before and presented from a slightly different point of view. I strongly recommend that you read each section in your textbook at home before it is covered in class. Try to isolate what you do not understand and be prepared to ask questions during the lecture.
Do not hesitate to ask questions. If something is unclear to you in class, just ask. You can be sure that many of the other students have the same question but do not dare to ask. If you let me know what your problems are, I can adapt the lecture and make it easier for you to follow. There are no stupid questions. On the contrary, asking the right question is often an important step in the process of solving a problem.
The importance of working on example problems can not be overemphasized. Try to work on the homework problems intensively and pick additional similar problems from your textbook.
Discussion is crucial to understand mathematics. I strongly encourage you to discuss both the material covered in class and your solutions of the homework problems with other students. The best way to check your own understanding of a subject is to explain it to someone else.
Ideally you solve the homework problems on your own, or working with other students. If you realize that you do not understand the homework problems, seek help immediately. With a backlog of not understood material it extremely difficult to catch up with the class again.
Free tutoring and other services for this and similar mathematics courses are provided by the Mathematics Learning Resource Center (MLRC). For more information, see http://www.math.okstate.edu/mlrc.
You are always welcome to see me in my office hour, or contact me by email if you have any questions or problems. If my office hours do not fit your schedule, please contact me by email for an appointment.
The following course schedule is preliminary.
| Class Meeting |
Date | Sections from Textbook |
Subject | Homework Assignment |
Due Date |
|---|---|---|---|---|---|
| 1 | 08/23 | 1.1 | Group Axioms and Examples | 1abd,2abd,6bde,7,14,25 | 08/25 |
| 2 | 08/25 | 1.2 | Dihedral Groups | 1a,2,3,7,9,17 | 08/27 |
| 3 | 08/27 | 1.3 | Symmetric Groups | 4,7,11,20 | 08/30 |
| 4 | 08/30 | 1.4 1.5 | Matric Groups The Quaternion Group | 7,8,10 1,3 | 09/01 |
| 5 | 09/01 | 1.6 | Homomorphisms and Isomorphisms | 2,7,13,14,18 | 09/03 |
| 6 | 09/03 | 1.6 1.7 | continued Group Actions | ||
| - | 09/06 | - | University Holiday | - | - |
| 7 | 09/08 | 1.7 | continued | 4,5,10a,13,14 | 09/10 |
| 8 | 09/10 | 2.1 | Subgroups | ||
| 9 | 09/13 | 2.2 | Centralizers and Normalizers, Stabilizers and Kernels | 2,4,5,9,10 | 09/15 |
| 10 | 09/15 | 2.3 | Cyclic Groups and Cyclic Subgroups | 1,5,8,12b,13b,18 | 09/20 |
| 11 | 09/17 | Review for Exam 1 | |||
| 12 | 09/20 | Exam 1 | |||
| 13 | 09/22 | 2.4 | Subgroups generated by Subsets of a Group | 8,9,10,11,12 | 09/24 |
| 14 | 09/24 | 2.4 2.5 | continued The lattice of Subgroups of a Group | ||
| 15 | 09/27 | 3.1 | Definitions and Examples | 1,5,6,9,11,12 | 09/29 |
| 16 | 09/29 | 3.1 | Examples | ||
| 17 | 10/01 | 3.2 | More on Cosets and Lagrange's Theorem | 8,9,10,22 | 10/04 |
| 18 | 10/04 | 3.3 | The Isomorphism Theorems | 3,4,7,9 | 10/06 |
| 19 | 10/06 | 3.4 | Composition Series and the Hölder Program | ||
| 20 | 10/08 | 3.5 | Transpositions and the Alternating Group | 3,5,6,7,10,17 | 10/13 |
| 21 | 10/11 | 4.1 | Group Actions and Permutation Representations | ||
| 22 | 10/13 | 4.1 | Cycle Decompositions and Examples | ||
| - | 10/15 | - | Students' Fall Break | - | - |
| 23 | 10/18 | 4.2 | Cayley's Theorem and Group Action on Cosets | 2,4,8,10 | 10/20 |
| 24 | 10/20 | 4.3 | Groups Acting on Themselves by Conjugation | 3c,6,13,27,29 | 10/22 |
| 25 | 10/22 | Review for Exam 2 | |||
| 26 | 10/25 | Examples | |||
| 27 | 10/27 | Exam 2 (Solutions) | |||
| 28 | 10/29 | 4.4 | Automorphisms of Groups | 1,2,3,11,18 | 11/01 |
| 29 | 11/01 | 4.5 | Sylow's Theorem | 1,3,9,13,18,19,30 | 11/08 |
| 30 | 11/03 | 4.5 | Continued | ||
| 31 | 11/04 | 4.5 | Continued | ||
| 32 | 11/08 | 5.1 | Direct Products | 10,11,12,18 | 11/10 |
| 33 | 11/10 | 5.2 | The Fundamental Theorem of Finitely Generated Abelian Groups | 2a,3a,7 | 11/19 |
| 34 | 11/12 | 5.4 | Recognizing Direct Products | 5,11,14 | 11/19 |
| 35 | 11/15 | 5.4 | Continued | ||
| 36 | 11/17 | 5.5 | Semidirect Products | ||
| 37 | 11/19 | 5.5 | Continued | ||
| 38 | 11/22 | 5.5 | Continued | ||
| - | 11/24 | - | Students' Thanksgiving Break | - | - |
| - | 11/26 | - | University Holiday | - | - |
| 39 | 11/29 | 6.1 | p-Groups | ||
| 40 | 12/01 | Exam 3 | |||
| 41 | 12/03 | 6.1 | Nilpotent Groups | ||
| 42 | 12/06 | 6.1 | Continued | ||
| 43 | 12/08 | 6.1 | Solvable Groups | ||
| 44 | 12/10 | 6.1 | Proof of the Fundamental Theorem of Finite Abelian Groups | ||
| 45 | 12/17 | Final Exam (take-home) | 6.1.3, 6.1.4, 6.1.8, 6.1.12, 5.5.7, 5.5.20, 4.5.32, 4.5.40 | 9:50am MS401 (mailbox) |
I will respect OSU's commitment to academic integrity and uphold the values of honesty and responsibility that preserve our academic community. For more information, see http://academicintegrity.okstate.edu.
This syllabus may be subject to future changes and it is your responsibility to be informed. Any change of the syllabus will be announced in class and appear online.