Spring 2008 : MATH567 Abstract Algebra II

  1. General information
  2. Textbook
  3. Homework
  4. Exams
  5. Grading scheme
  6. Course syllabus

General information

Textbook

The textbook for this course is :

dummit.jpeg

David S. Dummit and Richard M. Foote "Abstract Algebra" 3rd edition, Wiley 2003.

It is available from the campus bookstore. The authors' list of errata are available online.

Homework

There will be weekly homework, set from the textbook. The homework will be announced on Wednesday on this webpage (next to the syllabus), and must be handed in the following Wednesday at the beginning of the lecture.

Exams

There will be one midterm and one final exam. The midterm will be held in ENGRG E106 and the final will be held in ENGRG E105.

If you are unable to attend any of these exams because of a legitimate reason (for example, it clashes with an exam for another course), then you must let the instructor know at least one week in advance.

Grading scheme

Course grades will be determined based on homework (50%), the midterm exam (20%), and the final exam (30%). In addition, this is a "portfolio course" for graduate students in the mathematics department: your result in the final exam alone will count towards your PhD qualification. Topics which may appear on the final exam should be drawn from this list.

Course syllabus

The syllabus below will be updated as the semester progresses.

Week

Material covered (with page numbers)

Homework

Jan 21-25
No class on Monday

Chapter 10 : Introduction to Module Theory (337-407)

  • definitions and examples
  • quotients and homomorphisms
  • generation, direct sums, free modules

Page 343, exercises 8, 11, 15.
Page 350, exercises 3, 5, 14.
Page 356, exercises 7, 10 (you may use the result of ex. 9).
Due Wednesday 30th January.

Jan 28-Feb 1

Chapter 10 : Introduction to Module Theory (337-407)

  • tensor products

Page 356, exercises 15, 18.
Page 375, exercises 5, 9, 10, 16, 17, 20.
Due Wednesday 6th February.

Feb 4-8

Chapter 10 : Introduction to Module Theory (337-407)

  • exact sequences and projective modules
Chapter 11 : Vector Spaces (408-455)
  • definitions
  • the matrix of a linear transformation
  • dual vector spaces

Page 403, exercises 3, 8, 14a.
Page 413, exercise 6.
Page 422, exercises 3, 8a, 11.
Page 435, exercise 2cd.
Due Wednesday 13th February.

Feb 11-15

Chapter 11 : Vector Spaces (408-455)

  • determinants
  • tensor, symmetric, and exterior algebras
Chapter 12 : Modules over PIDs (456-508)
  • basic theory

Page 454, exercise 7.
Page 468, exercises 2, 6, 8, 9, 11, 15, 21.
Due Wednesday 20th February.

Feb 18-22

Chapter 12 : Modules over PIDs (456-508)

  • rational and Jordan canonical forms

Page 488, exercises 4, 9(1st and 2nd matrices only), 10, 17.
Page 499, exercises 6, 9, 16, 22, 24.
Due Wednesday 27th February.

Feb 25-29

Chapter 13 : Field Theory (510-557)

  • field extensions
  • algebraic extensions
  • splitting fields and algebraic closures

Page 519, exercises 2, 3, 8.
Page 529, exercises 4, 8, 10, 14, 17.
Page 545, exercises 2, 4.
Due Wednesday 5th March.

Mar 3-7

Chapter 13 : Field Theory (510-557)

  • separable and inseparable extensions
  • cyclotomic polynomials
Chapter 14 : Galois Theory (558-654)
  • definitions

Attempt the practise exams.
We will discuss the solutions next Monday.

Mar 10-14

Revision
Midterm Exam on Tuesday 6-8pm, ENGRG E106

Page 551, exercises 2, 4, 5, 10.
Page 555, exercises 4, 5, 8, 11.
Page 566, exercises 4, 5, 7, 8.
Page 581, exercises 4, 5, 6.
Due Wednesday 23rd April.

Mar 17-21

No classes - spring break.

Mar 24-Apr 18

No classes for four weeks.

Additional problems, not to be handed in.
Page 375, exercises 3, 4 (solutions).
Page 555, exercises 14, 15, 16, 17 (solutions).
Feel free to email me to discuss the problems/solutions.

Apr 21-25

No classes on Monday and Friday.
Chapter 14 : Galois Theory (558-654)

  • the Fundamental Theorem

Page 581, exercises 9, 13, 14, 16, 27, 28.
Due Wednesday 30th April.

Apr 28-May 2

Chapter 14 : Galois Theory (558-654)

  • finite fields
  • composite and simple extensions
  • cyclotomic and abelian extensions

Page 589, exercises 5, 6, 7, 11.
Page 595, exercise 5.
Page 603, exercises 3, 8, 10.
Due Wednesday 7th May.

May 5-9

Chapter 14 : Galois Theory (558-654)

  • Galois groups of polynomials
  • solvable and radical extensions
  • insolvability of the quintic
Revision

Page 617, exercises 1, 3, 18, 20.
Due Friday 9th May.

May 12-16

Review session : Monday 2-4pm, Weber 130
Final exam : Thursday 3:40-5:40pm, ENGRG E105

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This page last modified by Justin Sawon
Monday, 05-May-2008 11:40:58 MDT
Email corrections and comments to sawon@math.colostate.edu