UNIVERSITY OF WAIKATO
Department of Mathematics
MATH310-10A – Modern Algebra- 2010
Paper Outline
A new summary of the notes sections 1-9 is
linked here. It includes a club on showing in a PID every irreducible is prime and not the unique factorization thm on a PID. The test today will cover all definitions and theorem statements, but no proofs other than those marked with a "club" symbol. The same applies to the Rings and Fields section B of the examination, but there will also be exercise/assignment syle questions in this.
The test will be in class time on Thursday 3rd June. It will cover "bookwork" from the work covered in sets 1 through 9 of the notes. Two sample tests from 2004 and from 2009 are linked here.
The Examination will be to do 6 questions out of 8 with 2 at least from section A (Groups) and at least 2 from section B (Rings and Fields). The paper from 2009 is linked here. We will go over the Rings and Fields questions in class on Friday noon.
Rationale:
The application of algebraic structures called rings and fields is widespread in mathematics and its applications. Unlike groups, which "measure" symmetry, these structures are found everywhere.
Details of the paper content:
See the CMS Undergraduate Handbook for 2010.
Bibliography:
There are a number of texts but I will refer to Joseph A. Gallian's "Contemporary Abstract Algebra" which has good coverage, lots of examples and exercises, and interesting historical notes. There are currently 3 unsold copies in Bennetts. However you may wish to use the excellent online textbook, "Abstract Algebra: Theory and Applications" by Thomas W. Judson, 14th February 2009, available at
this link.
Lecturer
- Professor Kevin Broughan, Office G3.22,
Tel 838-4423, email kab@waikato.ac.nz
Office Hours: Normally Thursdays, 3.10-5.00 p.m. in G3.22 during the teaching weeks.
Lecture timetable:
- Monday 1.10pm - in G3.33 (tutorial)
- Tuesday 4.10pm in S1.03,
- Thursday noon- in S1.03,
- Friday noon- in KG.11.
The paper outline
This is linked here.
On-line lecture notes:
The on-line lecture notes will be attached here as they are produced:
Background Reading and exercises
- Rings: Read Gallian Ch 12, 13, do page 234 (7th ed page 242) #3,6,7,13,17,19. Judson Section 14.1, 14.2, do page 250 #1,2,3.
- Integral domains: Read Gallian Ch 13, do page 246 (7th ed page 255) # 3,5,7,9,11,13,25,37,39,51. Judson Section 14.4, do page 251 # 4,5,7,8,9,11,12.
- Prime and maximal ideals: Read Gallian Ch 14 do page 260 (7th ed page 269) #5, 6(a), 7, 10,11,13(a),37,51. Read Judson Section 14.4, do page 252 # 16,19,20,27,28,30.
- Homomorphisms of rings: Read Gallian Ch 15, do page 278 (7th ed page 287)#5,11,12,13,15,21,41,44,51.
- Rings of polynomials: Read Gallian Ch 16, do page 290 (7th ed page 300) # 1,3,11,17,18.
- From now on all references are to the 7th edition:
- Factorization: continue with Gallian Ch 16, do page 301 # 21,23,24,25,29,31,33,38-41,45,47,49.
- Irreducibility: read Gallian Ch 17, do page 316 # 3,4,5(c)(d), 11,12,13,15.
- PID's and Euclidean domains: read Gallian Ch 18, do page 335 # 3,5,8,11,14,17,21,31,35.
- Vector spaces: read Gallian Ch 19, do page 349 # 5,7,8,9,10,13,19,22.
- Field extensions: read Gallian Ch 20, do page 366 # 1,3,5,7,8,9,10,13,17,18.
- Primitive elements and the dimension theorem: Gallian Ch 21, do page 378 # 5,8,13,14,15,16,18,23,24.
- Same topic, Gallian Ch 21, do page 380 # 33-37,39,40.
Assignments
Four regular marked assignments worth a total of 25% of the internal assessment,
will be handed out at the lecture on Friday and should be handed in through the slot marked 310 under
the Mathematics Office reception counter (G3.19) by the following Friday. Late assignments will be penalized.
- Assignment 1 questions,
solutions,
- Assignment 2 questions,
solutions,
- Assignment 3 questions,
solutions,
- Assignment 4 questions,
solutions.
Dates and values of the Assignments and the test:
- Assignment 1: Out Friday 30th April, back Friday 7th May, value 6%,
- Assignment 2: Out Friday 7th May, back Friday 14th May, value 6%,
- Assignment 3: Out Friday 14th May, back Friday 21st May, value 6%,
- Assignment 4: Out Friday 21st May, back Monday 31st, value 7%,
- Test: Thursday 3rd June in class commencing noon, value 25%.
Kevin Broughan
3rd June 2010