MATH 3030 - 2012-2013

Abstract Algebra

This is the page where I post material related to the MATH 3030 course I am teaching in 2012-13.

 

  • Office hours: Monday 13:30-14:30, Wednesday 13:30-14:30, Thursday 14:30-15:30
  • Office: 251 Chase building (on the 2.5th floor - you need to take the stairs at the South end of the building.)
  • If you want to come to my office at a different time please email me:tkenney@mathstat.dal.ca
  • Midterm Exam: Wednesday 31st October, in class.
  • Here are some practice questions for the midterm examination. Here are the model solutions.
  • Here are the model solutions for the midterm examination.
  • Midyear Exam: Friday 7th December, 7:00-10:00 PM, Dalplex.
  • Here are some practice questions for the midtyear examination. Here are the model solutions.
  • Here are the model solutions for the midyear examination.
  • Textbook: Abstract Algebra (Seventh Edition) by John B. Fraleigh, published by Addison Wesley, 2003
  • Final Exam: TBA.
  • The information for the second term is at www.mathstat.dal.ca/~tkenney/3030/2012/index2.html.

    • Handouts

    Course Handout

    Planned material

    Lecture time is limited, so I plan to use it explaining concepts and giving examples, rather than reading the textbook. Therefore, to get the most out of each lecture, you should read the relevant material before the lecture. Here is the list of what I expect to cover in each lecture. This is subject to change - make sure to check regularly for changes.

    Week beginning Monday Wednesday Friday
    3rd September
  • Introduction
    •
    10th September
  • 0. Sets and Relations
    •
  • 2. Binary Operations
    •
  • 3. Isomorphism
    •
    17th September
  • 4. Groups
    •
  • 4. Groups (cont.)
  • 5. Subgroups
    •
  • 5. Subgroups (cont.)
  • 6. Cyclic Groups
    •
    24th September
  • 6. Cyclic Groups (cont.)
  • 7. Generators and Cayley Graphs
    •
  • 8. Permutation Groups
    •
  • 8. Permutation Groups (cont.)
  • 9. Orbits, Cycles and Alternating Groups
    •
    1st October
  • 9. Orbits, Cycles and Alternating Groups (cont.)
  • 10. Cosets and Lagrange's Theorem
    •
  • 10. Cosets and Lagrange's Theorem (cont.)
    •
    8th October Thanksgiving
  • 11. Direct Products and Finitely Generated Abelian Groups
    •
  • 13. Homomorphisms
    •
    15th October
  • 13. Homomorphisms (cont.)
  • 14. Factor Groups
    •
  • 14. Factor Groups (cont.)
    •
  • 15. Factor Group Computations and Simple Groups
    •
    22nd October
  • 15. Factor Group Computations and Simple Groups (cont.)
    •      		Revision Revision
    29th October Revision

    MIDTERM

    EXAMINATION
  • 18. Rings and Fields
    •
    5th November
  • 18. Rings and Fields (cont.)
  • 19. Integral Domains
    •
  • 19. Integral Domains(cont.)
    •
  • 20. Fermat's and Euler's Theorems
    •
    12th November REMEMBRANCE DAY
  • 20. Fermat's and Euler's Theorems (cont.)
    •
  • 21. The Field of Quotients of an Integral Domain
    •
    19th November
  • 21. The Field of Quotients of an Integral Domain (cont.)
    •
  • 22. Rings of Polynomials
    •
  • 22. Rings of Polynomials (cont.)
  • 23. Factorisation of Polynomials over a Field
    •
    26th November
  • 23. Factorisation of Polynomials over a Field (cont.)
  • 24. Non-commutative Examples (if time)
    •      		Revision Revision
    3rd December

    MIDYEAR

    EXAMINATION

    		 END OF LECTURES

    Homework

    Assignment 1 Due Friday 28th September. Model Solutions
    Assignment 2 Due Friday 5th October. Model Solutions
    Assignment 3 Due Friday 12th October. Model Solutions
    Assignment 4 Due Friday 19th October. Model Solutions
    Assignment 5 Due Friday 26th October. Model Solutions
    Assignment 6 Due Friday 2nd November. Model Solutions
    Assignment 7 Due Friday 16th November. Model Solutions
    Assignment 8 Due Friday 23rd November. Model Solutions
    Assignment 9 Due Friday 30th November. Model Solutions