- 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: MW 3:30-4:30pm, MSCS 405
- Textbook:
*Algebra*by Serge Lang, Revised 3rd Edition, Springer GTM 211 (2005) - Prerequisites: Modern Algebra II or equivalent
- Course Web Page: http://www.math.okstate.edu/~mschulze/teaching/12S-MATH5623
- OSU Syllabus Attachment: http://academicaffairs.okstate.edu/images/documents/sylatspr.pdf

- Field Theory: Algebraic extensions, algebraic closure, normal, separable and inseparable extensions, finite fields. (All of Ch. 5.)
- Galois Theory: Galois extensions, norm and trace, cyclic extensions, solvability, cyclotomic extensions, X
^{n}-a=0. (Ch. 6, §1-9.) - Ring extensions: Integral ring extensions and Galois extensions. (Ch. 7, §1-2.)
- Matrices and linear transformations: Rank, determinants, duals, bilinear forms, minimal polynomial, Jordan and rational form. (Ch. 13, §1-6; Ch. 14.)
- Multilinear algebra: Tensor products, alternating and symmetric algebras. (Ch. 16, §1-2, 5, 8; Ch. 19, §1.)
- Homological algebra (time permitting): Complexes, homology, derived functors. (Ch. 20, §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 | 01/09 | V.1 | Finite and Algebraic Field Extensions | ||

2 | 01/11 | V.2 | Algebraic Closure | ||

3 | 01/13 | V.3 | Normal Extensions | Homework 1 | 01/18 |

01/16 | University Holiday | ||||

4 9 | 01/18 | V.4 | Separable Extensions Primitive Elements and Homework Solutions | ||

5 | 01/20 | V.5 | Finite Fields | Homework 2 | 01/25 |

6 | 01/23 | V.6 | Inseparable Extensions | ||

7 10 | 01/25 | VI.1 | Galois Extensions Homework Solutions | ||

8 | 01/27 | VI.2 | Examples and Applications | Homework 3 | 02/06 |

(9) | 01/30 | No class (replaced by afternoon session 01/18) | |||

(10) | 02/01 | No class (replaced by afternoon session 01/25) | |||

(11) | 02/03 | No class (replaced by morning session 02/15) | Homework 4 | 02/08 | |

12 | 02/06 | VI.3 | Roots of Unity | ||

13 | 02/08 | VI.5 | Norm and Trace | ||

14 | 02/10 | Review for Exam 1 | |||

11 15 | 02/13 | VI.6 - | Cyclic ExtensionsExam 1 | Homework 5 | 02/20 |

16 46 | 02/15 | VI.7,9 - | Solvable Extensions, Galois Group of X^{n}-aHomework Solutions | ||

17 | 02/17 | VIII.1 | Integral Extensions | ||

18 | 02/20 | VIII.1 | Integral Extensions | ||

19 | 02/22 | VIII.1 | Integral Extensions | ||

20 | 02/24 | XVI.1 | Tensor Product | Homework 6 | 02/29 |

21 | 02/27 | XVI.2+4 | Properties of Tensor Product | ||

22 | 02/29 | XVI.2+Ex.11 | Properties of Tensor Product | ||

23 | 03/02 | XVI.3 | Flatness | ||

24 | 03/05 | XVI.Ex.11+XX.5 | Homotopies of Morphisms of Complexes | Homework 7 | 03/12 |

25 | 03/07 | XX.5+XVI.3 | Free Resolutions and Tor-Functor | ||

26 | 03/09 | XVI.5-8 | Tensor Product of Algebras, Symmetric Products | ||

27 | 03/12 | XIII.4 | Determinants | ||

28 | 03/14 | XIII.4 | Determinants | ||

29 | 03/16 | XIII.4 | Determinants | ||

03/19 | Spring Break | ||||

03/21 | Spring Break | ||||

03/23 | Spring Break | ||||

30 | 03/26 | Exam 2 | |||

31 | 03/28 | XIX.1 | Alternating Products | ||

32 | 03/30 | XIX.1 | Alternating Products | ||

33 | 04/02 | XIX.2 | Fitting Ideals | Homework 8 | 04/09 |

34 | 04/04 | XIX.2 | Fitting Ideals | ||

35 | 04/06 | XIX.3 | Derivations | ||

36 | 04/09 | XIX.3 | Universal Derivation | ||

37 | 04/11 | XIX.Ex.6-8 | Properties of Universal Derivations | Homework 9 | 04/16 |

38 | 04/13 | XX.1 | Complexes | ||

39 | 04/16 | XX.2 | Homology Sequence | ||

40 | 04/18 | XX.3 | Euler Characteristic | ||

41 | 04/20 | XX.3 | Grothendieck Group | ||

42 | 04/23 | XX.4 | Injective Modules | ||

43 | 04/25 | XX.5-6,Ex.27 | Derived Functors, Ext^{1} and Extensions | ||

44 | 04/27 | XX.6 | F-acyclic Resolutions | ||

45 | 05/02 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.