Math 31: Topics in Algebra
Winter, 2003
Instructor: David Little
Lecture: MWF 10:00-11:05, Gerry 104
X-period: Th 12:00-12:50, Gerry 104
 Office: Bradley 411
Office Hours: MWF 2:00-3:30
Phone: (603) 646-2960
E-mail:david.little@dartmouth.edu


General Info/
Announcements
  • 2/21/03 - The final exam will be held Thursday, March 13, 8:00-10:00am in Gerry 104.
  • 2/21/03 - Class will meet next Thursday during the x-hour.
  • 2/13/03 - Second midterm exam will be held Monday, Feb. 24 from 7:00 to 9:00 pm in Bradley 105.
  • 1/22/03 - First midterm exam will be held on Friday, Jan. 31.
  • 1/6/03 - Welcome to the class website for Math 31 - Topics in Algebra
  • 1/6/03 - Course Syllabus
    * The above files require Adobe's Acrobat Reader.

    • Homework
    Problems
    Due Date Date Assigned Chapter Topics Covered Problems
    1/13 Mon. 1/6 0 Division Algorithm, GCD, Euclidean Algorithm, Modular Arithmetic p23-24: 3,4,8,11,16
    Wed. 1/8 0,1 Equivalence Relations, Dihedral Group p23-25: 14,46
    p37: 2,6
    Fri. 1/10 0,2 Functions, Binary Operators
    1/23 Mon. 1/13 2 Examples and properties of groups p54-56: 5, 12, 14, 26, 36
    Wed. 1/15 3 Subgroups p67-69: 4, 8, 10, 23, 25, 29
    Thur. 1/16 Proof Techniques - Mathematical Induction
    Fri. 1/17 3 Subgroups
    1/29 Wed. 1/22 4 Cyclic Groups p69-71: 30, 50d,54
    p82-83: 10,24,40
    Thur. 1/23 4 Cyclic Groups
    Fri. 1/24 RSA - An application of group theory
    Mon. 1/27 The Euler-Fermat Theorem for RSA
    Wed. 1/29 5 Permutation Groups
    2/14 Mon. 2/3 5,6 Permutation Groups and Isomorphisms p111-114: 4, 9, 16, 19, 20, 28, 44, 50, 51
    Wed. 2/5 6 Isomorphisms p 130-132: 4, 5, 22, 24, 25, 41
    2/21 Mon. 2/10 7 Cosets and Lagrange's Theorem p145-148: 1, 8, 14, 17, 18, 31, 46
    Wed. 2/12 7 Lagrange's Theorem and Counting Necklaces
    Thur. 2/13 9 Normal Subgroups
    Fri. 2/14 9 Factor Groups p186-190: 4, 12, 15, 25, 41, 60
    Mon. 2/17 10 Homomorphisms p205-206: 3, 6, 10, 14
    2/28 Wed. 2/19 11 Direct Products and Finite Abelian Groups
    Fri. 2/21 11, 12 Fundamental Theorem of Finite Abelian Groups, Intro to Rings p219-220: 2, 7, 9, 12, 18
    Mon. 2/24 12, 13 Rings and Integral Domains p235-237: 2, 19, 28, 33, 42
    3/7 Wed. 2/26 13, 14 Fields & Ideals p247-249: 8, 13, 14, 16, 35, 48
    Thurs. 2/27 14 Ideals And Factor Rings p261-262: 10, 12, 26, 31
    Fri. 2/28 15, 16 Ring Homomorphisms & Polynomial Rings p291-292: 12, 15, 24, 31
    Mon. 3/3 16 Polynomial Rings
    -/- Wed. 3/5 17 Factorization of Polynomials p307-309: 6, 8, 12, 14, 24, 25
    Fri. 3/7 23 Geometric Constructions