This page contains the program of the course: lectures and problem sessions. 

Lecturer and examiner: Per Salberger.

Schedule

The schedule of the course is in TimeEdit. 

Lectures

The lectures will take place Tuesday 8-10 and Thursday 13-15. The first Tuesday January 21^th there will also be a lecture 10-12. 

The lectures are based on the same sections in Durbin's book as the recommened exercises below.

Textbook

J.R. Durbin: Modern Algebra, An Introduction, John Wiley & Sons, version 5 or 6.

Note that the sections 53, 54, 55 in the fifth edition are moved to sections 56, 57, 58 in the sixth edition!

 

Problem sessions The problem sessions are held on  Tuesday 10-12 and Friday 10-12, beginning January 19^th. The problems will be chosen from the list of recommended exercises below. These are all important, and more than half of them will be discussed during the problem sessions.

There will be two groups; one in English with Douglas Molin as group leader and one in Swedish with Per Salberger as group leader.

 

Recommended exercises

The exercises below are selected from the sixth edition of Durbin’s book . These exercises may also be found in the fifth edition and usually with the same numerotation. The exceptions are listed with a V for the numbers in the fifth edition.   A star * indicates that the exercise is considered more challenging. Please try to do as many exercises as possible before the days indicated for them!

 

Days	Exercises
Jan 24	3.1-3.8, 3.13, 3.24, 4.1, 4.2, 5.1-5.12, 5.17, 6.1-6.3, 6.5, 6.9.
Jan 28 and Jan 31	7.1, 7.2, 7.13, 7.14, 7.22*-7.24*, 9.5-9.8 , 10.1-10.3 , 10.13 , 10.25, 10.26, 11.3, 11.13-11.17*, 12.7 , 12.20 , 12.21. 13.5, 13.6, 13.7, 13.9
Feb 4 and Feb 7	13.19*, 13.20, 13.21, 14.3-14.7, 14.9, 14.18, 14.25, 14.14, 14.23, 14.24, 14.31, 14.32, 14.33, 14.34, 15.24*, 16.2, 16.5, 16.7, 16.15, 17.2, 17.4, 17.7, 17.10, 17.12, 17.24, 17.25, 17.27, 17.30, 17.32.
Feb 11 and Feb 14	15.7, 15.9, 15.12, 15.17-15.19, 15.21, 17.14, 17.15*, 18.11*-18.14, 19.1, 19.2-19.5, 19.7, 19.14, 19.15, 19.21=V19.19, 19.22=V19.20, 19.23=V19.21, 19.27=V19.25, 19.32=V19.30, 19.34=V19.32, 21.5-21.10, 21.15-21.18, 21.26-21.28*, 21.34, 21.35.
Feb 18 and Feb 21	22.1, 22.2, 22.6, 22.12, 22.14, determine the quotient groups: (a) 4Z/12Z (b) R#/R>0 , 23.2, 23.4, 23,12, 23.12, 23.13, V23.20*, 56.5= V53.5, 56.6= V53.6, 56.8= V53.8, 56.9= V53.9, 57.5= V54.5, 57.13= V54.13, 58.1= V55.1, 58.2=V55.2, 58.7= V55.7.
Feb 26 and Feb 28	25.1, 25.4, 25.5, 25.7, 25.21, 26.1-26.9, 26.13, 26.18, 26.23*, 27.20*, 27.21, 27.23, 34.6, 34.8, 35.4-35.6, 35.9, 35.12, 35.13, 35.18, 36.1, 36.9, 36.11, 36.12, 36.22*-36.24*, 37.2-37.5, 37.8.
Feb 4 and March 7	38.1-38.4, 38.9, 38.12-38.15, 38.18*-38.20*, 38.22, 38.24*, show that any R-ideal I which contains an invertertible element is equal to R, 39.1-39.4, 39.7, 39.8*-39.10*, 39.12*, 41.2,41.3, 41.12, 42.4, show that any field of characteristic 0 contains a subfield isomorphic to Q, determine the minimal polynomials for √2+√3 and i=√-1 over Q, 40.6-40.10, 50.3=V45.3, 50.4=V45.4, 50.5=V45.5.
March 11 and March 14	43.1= V44.1, 43.18= V44.18, 30.3, 30.8, 35.14. Let a≠0 and f(x) be a polynomial such that f(xn) is divisible by (x-a). Show that f(xn) is also even divisible by (xn -an).

Solutions to some exercises: Solution to the exercise on Cube.docx

Douglas' handwritten notes in English for the exercise sessions (uploaded 3/3) : Douglas notes (Session 1-13).pdf 

Examination

For the exams 2017-19, click here. MMG500 Mar 2017.pdf, MMG500 Jun 2017.pdf

MMG500 Aug 2017.pdf, MMG500 Mar 2018.pdf, MMG500 Jun 2018.pdf

MMG500 Aug 2018.pdf, MMG500 Mar 2019.pdf,  Exam MMG500 Jun 2019.pdf,

Exam MMG500 Aug 2019.pdf

For solutions of exams in 2019, click here. 

Solutions MMG500 Mar 2019.pdf,  Solutions MMG500 June 2019.pdf, 

Solutions MMG500 Aug 2019 corrected.pdf 

 

The dates, times and places for the exams are in the student portal (Links to an external site.).

Use of AI tools

[The extent to which and how AI tools may be used and how their use is to be reported are specified here. This is particularly important for examinations such as assignments and quizzes. If it is only a written exam, this may be sufficient: “During your studies, you are free to use AI tools to support your learning. During the exam, the use of any kind of AI tools is not allowed.” ] 

Examination procedures

In Chalmers Student Portal (Links to an external site.) you can read about when exams are given and what rules apply to exams at Chalmers. In addition to that, there is a schedule (Links to an external site.) when exams are given for courses at the University of Gothenburg. Before the exam, it is important that you sign up for the examination. You sign up through Ladok (Links to an external site.).  At the exam, you should be able to show valid identification. After the exam has been graded, you can see your results in Ladok.

At the annual (regular) examination: 

When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office (Links to an external site.). Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination: 
Exams are reviewed and retrieved at the Mathematical Sciences Student office (Links to an external site.). Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Course evaluation

At the beginning of the course, at least two student representatives should have been appointed to carry out the course evaluation together with the teachers. The evaluation takes place through conversations between teachers and student representatives during the course and at a meeting after the end of the course when the survey result is discussed and a report is written. Guidelines for Course evaluation (Links to an external site.) in Chalmers student portal.

Student representatives

The following students have been appointed:

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