- Instructor: Dr. Mathias Schulze
- E-mail: mschulze@math.okstate.edu
- Phone: (405) 744-5773
- Office: MSCS 406
- Office Hours: MWF 11:30am-12:20pm and by appointment

- Class Meeting: MWF 9:30-10:20am, CLB 322
- Problem Session: M 2:30-4:00pm, MS 405
- Textbook:
*Algebra*by Serge Lang, Revised 3rd Edition, Springer GTM 211 (2005) - Prerequisites: Modern Algebra I or equivalent
- Course Web Page: http://www.math.okstate.edu/~mschulze/teaching/11F-MATH5613
- OSU Syllabus Attachment: http://academicaffairs.okstate.edu/faculty-a-staff/47-syllabus-fall

- Group Theory: Review of basic group theory, Group actions, permutation groups, semi-direct products, Sylow Theorems, finitely generated abelian groups, inverse limit, free groups. (All of Ch. 1.)
- Ring Theory: Polynomial and group rings, localization, PIDâ€™s, factorial domains and euclidean domains. (All of Ch. 2.)
- Modules: Hom, direct sums and products, projective and injective modules, free modules, vector spaces, modules over a PID, direct and inverse limits. (Ch. 3, §1-7, 10.)
- Polynomials: Polynomials over a FD, irreduciblility criteria, noetherian rings, Hilbert basis theorem. (Ch. 4, §1-6.)

You are expected to attend class on a regular basis and participate in class discussion. You are responsible for knowing the material covered in class and that in the corresponding sections in your textbook.

Homework assignments and due dates will appear in the course schedule. Turn in your solutions at the end of the lecture at the given due date. Late submissions will not be accepted.

There will be 2 midterm exams and a final exam, but no quizzes. 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.

The contributions to your clourse score will be weighted as follows.

Homework | Midterm Exams | Final Exam | |

Course Grade | 30% | 2 x 20% | 30% |

6-Weeks Grade | 50% | 1 x 50% | 0% |

Your total/6-weeks score will be truncated to an integer percentage and determines your course/6-weeks letter grade as follows.

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.

Your starting points are the textbook and the lecture. I recommend that you at least skim through upcoming sections of the textbook at home before they are covered in class. If you have time to read in depth, try to isolate what you do not understand and be prepared to ask questions in class.

Do not hesitate to ask questions. There are no stupid questions. On the contrary, asking the right question is often an important step toward the solution of a problem.

The importance of working on example problems can not be overemphasized. Work on the homework assignments intensively. If you find time, pick additional problems from the textbook, from other algebra textbooks, or from the Archive of Doctoral Exams in Algebra.

Discussion is crucial for learning abstract concepts. 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 is to explain to someone else. However keep in mind that in exams you are on your own, so please try solving the homework problems yourself first before you seek help.

It is essential to work contstantly to keep up with the class. As a rule of thumb, I suggest to study at least two hours per hour of class time. Contact me immediately if you get the feeling that you fell behind.

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 | Textbook Sections |
Subject | Homework Assignment |
Due Date |
---|---|---|---|---|---|

1 | 08/22 | I.1-2 | Groups, Subgroups, Homomorphisms | ||

2 | 08/24 | I.2-3 | Cosets, Index Formula, Factor Group, Exact Sequences | ||

3 | 08/26 | I.3 | Homomorphism Theorems, Semidirect Products | Homework 1 | 08/31 |

4 | 08/29 | I.3-4 | Solvability, Cyclic Groups | ||

5 | 08/31 | I.4-5 | Cyclic Groups (ctd), Group Actions | ||

6 | 09/02 | I.5 | Group Actions (ctd), Symmetric Groups | Homework 2 | 09/07 |

- | 09/05 | - | University Holiday | ||

7 | 09/07 | I.5-6 | Alternating Groups, p-Groups | ||

8 | 09/09 | I.6 | Sylow's Theorem | Homework 3 | 09/14 |

9 | 09/12 | I.6 | Applications of Sylow Theory | ||

10 | 09/14 | I.6 | Applications of Sylow Theory (ctd) | ||

11 | 09/16 | I.7 | Direct Sums and Free Abelian Groups | Homework 4 | 09/21 |

12 | 09/19 | I.8 | Finitely Generated Abelian Groups | ||

13 | 09/21 | I.9 | Dual Groups | ||

14 | 09/23 | I.10 | Inverse Limits | Homework 5 | 09/28 |

15 | 09/26 | I.11 | Categories and Functors | ||

16 | 09/28 | I.11 | Categories and Functors (ctd) | ||

17 | 09/30 | I.1-11 | Exam 1 | Homework 6 | 10/05 |

18 | 10/03 | I.12 | Coproducts and Free Groups | ||

19 | 10/05 | II.1 | Rings and Modules | ||

20 | 10/07 | II.2 | Commutative Rings | Homework 7 | 10/12 |

21 | 10/10 | II.2-3 | Prime Ideals and Polynomial Rings | ||

22 | 10/12 | II.3 | (Semi)group Rings | ||

- | 10/14 | - | Students' Fall Break (No Classes) | Homework 8 | 10/19 |

23 | 10/17 | II.4 | Localization | ||

24 | 10/19 | II.4-5 | Localization Examples, Euclidean Domains | ||

25 | 10/21 | II.5 | Factorial Rings | Homework 9 | 10/26 |

26 | 10/24 | Comp. Exam Problems | |||

27 | 10/26 | III.1-2 | Algebras, Modules | ||

28 | 10/28 | III.3-4 | (Co-)Products, Free and Projective Modules | ||

29 | 10/31 | III.4-6 | A Projective Non-Free Module, Vector Spaces, Dual Modules | ||

30 | 11/02 | III.6 | Dual Modules (ctd) | ||

31 | 11/04 | III.7 | Modules over PIDs | Homework 10 | 11/11 |

32 | 11/07 | III.8-9 | Euler-Poincaré Maps, Snake-, 4-, 5, 9-Lemma | ||

33 | 11/09 | III.10 | Direct and Inverse Limits | ||

34 | 11/11 | III.10 | Limits (ctd), Filtrations and Graded Rings | ||

35 | 11/14 | II.1-III.10 | Exam 2 | Homework 11 | 11/21 |

36 | 11/16 | IV.1 | Polynomials vs. Polynomial Functions | ||

37 | 11/18 | IV.2 | Polynomials over Factorial Rings | ||

38 | 11/21 | IV.3 | Irreducibility Criteria | Homework 12 | 12/05 |

- | 11/23 | - | First day of students' Thanksgiving break (No Classes) | ||

- | 11/25 | - | University holiday | ||

39 | 11/28 | - | No Class Meeting (replaced by afternoon meeting) | ||

40 | 11/30 | - | No Class Meeting (replaced by afternoon meeting) | ||

41 | 12/02 | - | No Class Meeting (replaced by afternoon meeting) | ||

42 | 12/05 | IV.4 | Hilbert's Theorem | ||

43 | 12/07 | IV.5 | Filtrations, Grading and Strict Maps, Partial Fractions | ||

44 | 12/09 | IV.6 | Symmetric Polynomials | ||

45 | 12/12 8:00-9:50am | . | Final Exam |

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.