Home Page for Math 701: Graduate Algebra

Textbook: Abstract Algebra,  3rd edition, David Dummit and Richard Foote, Wiley.
Course objective: To gain an overwiew of the fundamental algebraic structures: groups, rings, modules (fields and vector spaces), with an appreciation of the analogies and the differences between them, and maybe a sense of where they arise in other parts of mathematics.

Other recommended texts:
Algebra, Thomas Hungerford, GTM 73, Springer.
Algebra, Serge Lang, Addison Wesley.
Basic Algebra I, Nathan Jacobson, Freeman.

Instructor: Dr. D. Haskell, HH316, ext.27244
Course meeting time: TWF 9:30 - 10:20
E-mail: haskell@math.mcmaster.ca
Office hours: M 13:00-14:00, W, F 11:00-12:00

Course requirements, in brief (consult the course information sheet  for more detailed information).
Homework: 70%
Takehome Final: 30%

ANNOUNCEMENTS
 The course is meeting in HH410 from now on.

Homework

Homework 1, due Tuesday September 21 in class.
    p41 23   
    p48 6, 13
    p232 26, 28
    p343 5, 8, 9, 10, 12

Homework 2, due Tuesday September 28 in class.
    p40: 19
    p101: 10
    p247: 12, 17, 34
    p350: 9, 10

Homework 3, due FRIDAY October 8, in class
    p220: 3, 6
    p256: 7, 18
    p356: 9, 10, 11

Homework 4, due TUESDAY October 12, in class
    p727: 12, 15(a)(b)

REVISED Homework 5, due Tuesday October 26, in class
    p278: 8
    p283: 6
    p292: 1, 5
    p298: 8
    p311: 1, 6

Homework 6, due Tuesday November 2, in class
    p.414: 10, 14
    p422: 10
    p435: 4, 5

Homework 7, due Tuesday November 9, in class
    p.469: 5
    p.499: 1
    p.147: 19

Homework 8, due Tuesday November 23, in class
    p.198: 6, 25, 31

Homework 9, due Tuesday November 30, in class (might be supplemented)
    Homework 9 pdf file

Homework 10, due before December 17.
   Homework 10 pdf file

Planned course schedule (subject to revision):  readings and problems refer to the textbook by Dummit and Foote, except where otherwise noted.
 


Dates
  Topics  Reading
Sept 6-10
Week 0 		Introduction; review definitions of groups, rings, modules
 Chapter 1, 7.1, 7.2, 10.1
Sept 13-17
Week 1
 Examples, substructures. Homomorphisms, structure of kernels, quotient structures, Chapter 2
Chapter 3, 7.3, 10.2
Sept 20-24
Week 2
 Isomorphism theorems. Generators, universal properties of free structures  2.4, 6.3, 7.4, 10.3
Sept 27- Oct 1
Week 3
 More advanced theory: rings
properties of ideal, rings of fractions, chinese remainder theorem
  7.4, 7.5, 7.6
Oct 4-8
Week 4
 more on rings
euclidean domains, principal ideal domains, unique factorisation domains		 Chapter 8
Oct 11-15
Week 5
 Polynomial rings
 Chapter 9
Oct 18-22
Week 6
 More advanced theory: modules
modules over a field (= vector space)
 10.4, 11.1, 11.2
Oct 25-29
Week 7
 more on modules
structure theory of module over a PID, application to fg abelian groups
 Chapter 12
Nov 1-5
Week 8
 More advanced theory: groups
Sylow theorems, semidirect products
 4.5, 5.5
Nov 8-12
Week 9
 more on groups
composition series, p-groups, nilpotent and solvable groups
 6.1
Nov 15-19
Week 10
 commutative algebra
 Chapter 15
Nov 22-26
Week 11
Chapter 16
Nov 29-Dec 3
Week 12