
Lecturer 
Prof. Brent Doran 
Time 
We 1315 
Coordinator 
Claire Burrin 
Room 
HG E 5 
Exercise class  Mo 1012, or Mo 1517 
Lectures start Wednesday, Feb 19
Exercise classes start Monday, Feb 17
HG E 21 
Alexandru Sava 
Mo 1012 
HG E 33.1 
Beatrice Pozzetti 
Mo 1012 
HG F 26.3 
Pedro Vieira 
Mo 1012 
HG G 26.1 
Wenying Gan 
Mo 1012 
CLA E 4 
Humberto Silva Naves 
Mo 1517 
The exercise classes resume with the first Monday of the semester and will review the material on rings covered in December  rings, ring homomorphisms, ideals. Throughout the semester, there will be examples presented during the exercise sessions that complement the content of the Wednesday lectures. This is exam material ! Participation to the exercise sessions is thus strongly recommended.
As last semester, there is no testat, and you are free to test yourself with the weekly problem sets (also strongly recommended for obvious reasons) and hand in your solutions for further comments and corrections if you wish so. New problem sets will be published here at the middle of every week. You can hand in your solutions the Wednesday of the following week (the boxes are still in J 68). Please don't forget to register for an exercise class on mystudies.
The lectures will follow closely Artin's Algebra, 2nd edition. The relevant chapters for this semester will be 11 (Rings), 12 (Factoring), 13 (Quadratic Number Fields), 15 (Fields) and 16 (Galois Theory). See the syllabus below for the precise references.
The midterm will take place on Monday, May 5th during the exercise sessions, and covers all the material of this semester up to the Easter holidays. As always, this is an open book exam, is not compulsory, but could boost your final algebra grade, if well done. Here is the midterm and its solutions.
On Monday, May 26, there will be instead of your exercise class an additional lecture. The reserved classroom is HG D7.2.
There will be several Ferienpräsenzen organised by the department in June and July. You can find all dates and registration links at http://www.math.ethz.ch/~gruppe1/ .
Week  Topics  Chapters  Exercises  Solutions 
1 (Feb 19)  Quotient rings, product rings, adjoining elements  11.46 
Ex 1 
Sol 1 
2 (Feb 26)  Fraction fields and maximal ideals  11.78 
Ex 2 
Sol 2 
3 (Mar 5)  Unique factorization domains  12.2 
Ex 3 
Sol 3 
4 (Mar 12)  Factoring for integer polynomials  12.35 
Ex 4 
Sol 4 
5 (Mar 19)  Quadratic number fields  13.12 
Ex 5 
Sol 5 
6 (Mar 26)  Field extensions  13.4 ; 15.12 
Ex 6 
Sol 6 
7 (April 2)  Degree of field extensions, minimal polynomial  15.34 
Ex 7 
Sol 7 
8 (April 9)  Ruler and compass constructions  15.5 
Ex 8 
Sol 8 
9 (April 16)  Splitting fields, finite fields  15.615.7 
Ex 9 
Sol 9 
10 (April 30)  Primitive elements  15.8  (midterm week)   
11 (May 7)  Symmetric functions, discriminants and splitting fields  16.13 
Ex 10 
Sol 10 
12 (May 14)  Galois groups, isomorphisms of field extensions and fixed fields  16.45 
Ex 11 
Sol 11 
13 (May 21)  Galois extensions and fundamental theorem  16.67 
Ex 12 
Sol 12 
14 (May 26 & 28)  Applications of Galois theory  16.812 
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