MA20217 - Algebra 2B

Algebra 2B
Level 2

Semester 2 in 2017/18

General course information and handouts

This unit introduces ring theory and provides a thorough structure theory of linear operators on a finite dimensional vector space.

Course information

Class times and locations: The lectures take place on Wednesdays at 10:15 (EB1.1), Thursdays at 11:15 (CB1.10) and Fridays at 17:15 (EB1.1).
Tutorials begin during the week of Monday 12th February.

Weekly schedule and lecture notes

Week 1: Definition of ring, basic examples, subrings (Lecture 1, Lecture 2, Lecture 3)
Week 2: Quotient rings and ideals (Lecture 4, Lecture 5)
Week 3: Ring homomorphisms (Lecture 6, Lectures 7 and 8 cancelled)
Week 4: Applications (Lecture 9, Lecture 10)
Week 5: Primes, irreducibles, Euclidean domains, PIDs and UFDs (Lecture 11, Lecture 12 cancelled, Lecture 13)
Week 6: Polynomials over a UFD (Lectures 14 and 15 cancelled)
Week 7: Algebras and field extensions (Lecture 16, Lecture 17 and Lecture 18)
Week 8: Minimal polynomials and the Cayley-Hamilton Theorem (Lecture 19, Lecture 20, End of lecture 20 and seminar)
Week 9: Jordan normal form: the unique eigenvalue case (Lecture 21, Lecture 22, Lecture 23)
Week 10: Primary decomposition and Jordan normal form (Lecture 24, Lecture 25, Lecture 26)

Typed lecture notes for the course.

Revision lectures

There are revision lectures on Thursday 3rd and Thursday 10th May at 11:15 in CB1.10. Please email Thomas with any suggestions for topics to cover.

Revision lecture 1 Revision lecture 2

Also, during revision week some of the postgraduate tutors will give a revision session as follows:

Tutor Location Day Time Tutorial groups

Tom Crawley 8W2.13 Tuesday 12:15-13:05 1,3

Tom Crawley 1W3.30 Tuesday 15:15-16:05 7,8

Martin Prigent 8W2.20 Tuesday 15:15-16:05 2,4

Martin Prigent 8W2.13 Wednesday 13:15-14:05 6

Tom Crawley 8W2.20 Thursday 13:15-14:05 5

Please go to the tutorial with your group number if possible (or any other if not).

Homework assignments

Please submit solutions each Thursday by 3pm to the pigeonholes near the lifts on the ground floor of 4W.

Week 1 (due in week 2): Exercises 1 with solutions
Week 2 (due in week 3): Exercises 2 with solutions
Week 3 (due in week 4): Exercises 3 with solutions
Week 4 (due in week 5): Exercises 4 with solutions
Week 5 (due in week 6): Exercises 5 with solutions
Week 6 (due in week 7): Exercises 6 with solutions
Week 7 (due in week 8): Exercises 7 with solutions
Week 8 (due in week 9): Exercises 8 with solutions
Week 9 (due in week 10): Exercises 9 with solutions
Week 10 (due in week 11): Exercises 10 with solutions

Books that you might find useful

There are a few books in the library that cover some or all of the content of the course, but there are too few copies given how large the class is. For this reason, everything you need is in the typed lecture notes. Nevertheless, just in case, two of the most relevant books are:

A first course in abstract algebra by John B. Fraleigh. This covers much of the first three sections of the course on ring theory and factorisation.
Linear algebra by Serge Lang. This covers much of the final section of the course on the structure of linear operators.

Exam information and past papers

Here is some information about the exam (updated 1 May 2018):

Exam information

You'll also find it helpful to look at the past papers for this unit.

Department of Mathematical Sciences,
University of Bath, Claverton Down,
Bath BA2 7AY.

Office: 4W 3.41
Phone: 01225 386219
Email: d.m.j.calderbank at bath dot ac dot uk

Tutor	Location	Day	Time	Tutorial groups
Tom Crawley	8W2.13	Tuesday	12:15-13:05	1,3
Tom Crawley	1W3.30	Tuesday	15:15-16:05	7,8
Martin Prigent	8W2.20	Tuesday	15:15-16:05	2,4
Martin Prigent	8W2.13	Wednesday	13:15-14:05	6
Tom Crawley	8W2.20	Thursday	13:15-14:05	5

Algebra 2B Level 2

Algebra 2B
Level 2