Department of Mathematics

Algebra II

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Lecturer Prof. Brent Doran
Time We 13-15
Coordinator Claire Burrin

Room HG E 5
    Exercise class Mo 10-12, or Mo 15-17

Lectures start Wednesday, Feb 19

Exercise classes start Monday, Feb 17

Exercise groups

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 .

Syllabus and problem sets

Week Topics Chapters Exercises Solutions
1 (Feb 19) Quotient rings, product rings, adjoining elements 11.4-6 Ex 1
Sol 1
2 (Feb 26) Fraction fields and maximal ideals 11.7-8 Ex 2
Sol 2
3 (Mar 5) Unique factorization domains 12.2 Ex 3
Sol 3
4 (Mar 12) Factoring for integer polynomials 12.3-5 Ex 4
Sol 4
5 (Mar 19) Quadratic number fields 13.1-2 Ex 5
Sol 5
6 (Mar 26) Field extensions 13.4 ; 15.1-2 Ex 6
Sol 6
7 (April 2) Degree of field extensions, minimal polynomial 15.3-4 Ex 7
Sol 7
8 (April 9) Ruler and compass constructions 15.5 Ex 8
Sol 8
9 (April 16) Splitting fields, finite fields 15.6-15.7 Ex 9
Sol 9
10 (April 30) Primitive elements 15.8 (midterm week) ---
11 (May 7) Symmetric functions, discriminants and splitting fields 16.1-3 Ex 10
Sol 10
12 (May 14) Galois groups, isomorphisms of field extensions and fixed fields 16.4-5 Ex 11
Sol 11
13 (May 21) Galois extensions and fundamental theorem 16.6-7 Ex 12
Sol 12
14 (May 26 & 28) Applications of Galois theory 16.8-12    

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© 2016 Mathematics Department | Imprint | Disclaimer | 18 September 2014