More actions; September 17
This material is covered in Chapter 5 and sections 6.1, 6.2
1
Vocabularycontinued
1. Orbit
2. Transitive
3. Isotropy subgroup of a point.
4. The relationship between isotrop
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Continuation of Intro to rings, modules, ideals
October 15
This material is covered in sections 10.1-10.4
1
Ideals
Recall denition of ideal (left, right, two-sided) and of quotient rings.
Recall:
Ex
Linear Equations, Matrices, and algebraic systems of various sorts;
intro to groups
September 3, 2009
1
Systems of Linear Equations:
This material is covered in Artins Chapter 1, sections 1-3
It is ha
Conjugacy, Class Equations, Examples
(Computations in GL2 and the Symmetric Groups)
September 22
This material is (more than) covered in sections 6.2. 6.6, 5.7, 5.8, 4.4
1
Vocabulary Review
Orbit, Tra
More Presentations; Homework due October 15; Intro to rings
October 8
Much of this material is covered in sections 6.7. 6.8, 10.1-10.4
1
Presentations
Let x1 , x2 , . . . , xn be n symbols and F := Fn
Intro to rings, modules, ideals
October 13
This material is covered in sections 10.1-10.4
1
Rings
Denition of rings: recall the conventions, a ring being an associative ring. Discuss rings with
unity,
Groups; isomorphisms; examples; more examples
September 8, 2009
1
Groups
This material is covered in Artins Chapter 2, section 1
A group G is a set with a composition law, i.e., a mapping m : G G G (f
The Symmetric Groups; Quotient groups
September 24
This material is (more than) covered in sections 6.2. 6.6, 5.7, 5.8, 4.4
1
The group Sn
Cycles of length , Transpositions.
Disjoint cycles commute.
Permutations and actions
(September 15)
1
Reading assignment
Read section 4 of Chapter 1 of Artin (pp. 24-28). The material well do in class today is covered
in 5.8 and 6.1.
2
Permutation Groups
Denit
More Quotient groups; Products; . . .
September 29
1
Quotient Groups
1. Denition (Section 2.10)
2. First Isomorphism Theorem Recall
3. Even permutations versus odd permutations. The alternating group