MATH 367 (Spring 2011)

2010 - 11 Spring

MATH 367: Abstract Algebra


Announcements:
  • Final exam contents are: Chapter 2 (except 2.8), Chapter 3, Chapter 4 (plus prime ideals and UFD's), Sections 5.1, 5.3 and 5.5.
  • The second midterm will be on 17 May 2011, Tuesday at 17.40. Contents: All of Chapter 4, prime ideals, UFD's, Section 5.1.
  • From 11 April on, we meet on Wednesdays, instead of Tuesdays. There is no change in time and classroom.
  • The first exam will be on 30 March 2011, Wednesday at 17.40. Contents: Sections 2.1-2.7, 2.9, 2.10, 3.1.
  • On Mondays we are meeting in M-102.
  • Note the change in the schedule: Monday 12.40-13.30 M-13, Tuesday 15.40-17.30 M-103, Friday 14.40-16.30 M-13 (recitation hour)
  • The first lecture will be on 21 February, Monday.

    Prerequisite Course: Math 116

    Textbook: Abstract Algebra by I. N. Herstein, Third Edition, Prentice Hall, 1996.

    Other Books:

  • "Contemporary Abstract Algebra" by J. A. Gallian, D. C. Heath and Company, 1994.
  • "Algebra: Abstract and Concrete" by F. M. Goodman, Prentice Hall, 1998.
  • "A First Course in Abstract Algebra" by J. J. Rotman, Prentice Hall, 2000.
  • "A First Course in Abstract Algebra" by J. B. Fraleigh, Addison-Wesley.
  • "Fundamentals of Abstract Algebra" by D. S. Malik, J. N. Mordeson, M. K. Sen, McGraw-Hill, 1997.
  • "Abstract Algebra" by Dummit and Foote, Prentice Hall, 1991.


    Office Hours:
    Ay�e Berkman: Monday 8.40-9.30 and 13.40-14.30
    Arzu Zabun: Tuesday 13.40-15.30 (until 23 April)
    Ayberk Zeytin: Anytime (after 23 April)


    Grading:
    Two midterm exams (30 points each) and a final exam (40 points).


    Done in the class:
    Week 1: Motivation for groups and examples. Subgroups, cyclic groups.
    Week 2: Equivalence relations, partitioning. Congruence modulo a subgroup, left and right cosets. Lagrange's Theorem and its corollaries.
    Week 3: Examples of homomorphisms and isomorphisms. Cayley's Theorem. Kernels. Normal subgroups.
    Week 4: Quotient groups. Homomorphism Theorems.
    Week 5: Direct Products. Classification of finite abelian groups.
    Week 6: More on permutations. Review. Exam 1.
    Week 7: Even/odd permutations. Class Equation. Sylow Theorems. (End of group theory!)
    Week 8: Definitions and examples of rings, integral domains, division rings, fields. Ideals and ring homomorphisms.
    Week 9: Prime and maximal ideals. Polynomial rings.
    Week 10: Maximal ideals in F[x]. Irreducibility criteria for polynomials over rationals.
    Week 11: Field of quotients. Examples of fields. Field extensions.
    Week 12: Algebraic elements. Minimal Polynomials.
    Week 13: Review. Exam 2.
    Week 14: Three impossible constructions.


    Suggested Exercise:

    Some warm-up exercises from Chapter 1: 1.1, 2.13, 3.10, 3.25, 3.26, 3.30, 3.31, 7.22, 7.25.

    Section 2.1: 1(e,f), 3, 4, 9, 13, 18, 21, 23, 24, 26, 27.
    Section 2.2: 2.
    Section 2.3: 1, 4, 5, 7, 11, 19, 20, 21, 26, 29, 30.
    Section 2.4: 5, 12, 13, 16, 17, 18, 27, 29, 30.
    Section 2.5: 1, 6, 9, 13, 14, 17, 20, 24, 28, 29c, 36.
    Section 2.6: 8, 11, 12, 13, 15, 17, 18.
    Section 2.7: 2, 4, 5, 6, 7.
    Section 2.9: 1, 2, 3, 4, 5.
    Section 2.10: All
    Section 3.2: 15, 16, 17, 20, 22, 23, 24, 25.
    Section 3.3: 1, 2, 3, 5, 8.
    Section 2.11: 2, 3, 5, 9, 15, 20.
    Section 4.1: 2, 3, 9, 13b, 15, 20, 21, 28, 30.
    Section 4.2: 2, 3, 4.
    Section 4.3: 2, 6, 12, 19, 20, 21, 23, 24.
    Section 4.4: See the exercise sheet.
    Section 4.5: 1, 8, 9, 12, 16, 20.
    Section 4.6: 3, 6, 8, 9, 13.
    Section 4.7: Fill out the details in the proof of Theorem 4.7.1.
    Section 5.1: 1, 7, 8, 9, 10.
    Section 5.3: 1, 5, 7, 12, 14.


    Last updated on 30 May 2011.