Quiz Number 1
Group 1 North of Newark
Thamer AbuDiak
Reynald Benoit
Jose Lopez
Rosele Lynn
Dave Neal
Deyanira Pena
Professor Kenneth D. Lawerence
New Jersey Inst. Of Tech
Problems Assigned
Ragsdale
2.13, 2.16, 2.20
3.10, 3.13, 3.16, 3.21, 3.24, 3.28, 3.41
The 17 types of wallpaper groups. A discrete subgroup G Isom(R2 )
whose translational part L is a lattice is called a wallpaper group. There are
17 types of these. They can be classified according to their point groups.
One might think that the point grou
Nilpotent groups. The class of nilpotent groups is the smallest class of
groups containing the abelian groups and with the property that G is nilpotent if G/Z(G) is nilpotent. For example, S3 is not nilpotent (its center is
trivial) but D8 is nilpotent (t
8
Trace and determinant
The trace and determinant can be approach in many different ways: using
bases, using eigenvalues, and using alternating forms. It is useful to understand all approaches and their interrelations.
Trace. Let V be a finite-dimensional
The only stage where exactness is not obvious is surjectivity to Ker T n V /Vn1 .
To prove this we use the fact that T n1(Vn1 ) = T n (Vn1 ), i.e. the image of
T i |Vn1 stabilizes after n 1 iterations.
Suppose [v] Ker T n |V /Vn1 . Since dim V /Vn1 = 1, t
Riddle. What is the next term in the sequence
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59?
(Ans: 60.)
Burnside counting theorem. We now return to the setting of G acting
on a set S. If the action of G on S is not necessarily transitive,
Example. The trefoil group can be simplified to 2 generators, one relation.
Invariance of G(K).
Theorem 14.5 Equivalent projections of a knot (or link) give isomorphic
groups G(K).
Proof. We must check the Reidemeister moves. (I) A loop gives ha, b : aa =
MGAB02 Case Assignment 2016 Winter
Due Date : March 20, 2015
Paul Carter opened up Carter Electronics Inc. (Carter) many years ago in Guelph, Ontario. Carter
specializes in offering home electronics, software support, music and video games to the local
co
CGA-CANADA
ADVANCED CORPORATE FINANCE [FN2] EXAMINATION
December 2010
Marks
Time: 4 Hours
Notes:
1.
2.
3.
12
Questions 1 and 2 are multiple choice. For these questions, select the best answer for each of the unrelated items. Answer each of these
items in
CGA-CANADA
FINANCE 2 EXAMINATION
March 2007
Marks
Time: 4 Hours
Notes:
1.
2.
3.
Questions 1 and 2 are multiple choice. For these questions, select the best answer for each of the unrelated items. Answer each of these
items in your examination booklet by g
Chapter 8 Inventory Error
QUESTION
Buy More Co. reported the following amounts in its financial statements:
(a) Goods available for sale
(b) Cost of Goods Sold
(c) Net Income
(d) Total Current Assets
(e) Shareholders' Equity
Financial Statement for Year E
CGA-CANADA
FINANCE 2 EXAMINATION
March 2006
Marks
Time: 4 Hours
Notes:
1.
2.
3.
Questions 1 and 2 are multiple choice. For these questions, select the best answer for each of the unrelated items. Answer each of these
items in your examination booklet by g
CGA-CANADA
ADVANCED EXTERNAL AUDITING [AU2] EXAMINATION
March 2011
Marks
30
Time: 4 Hours
Question 1
Select the best answer for each of the following unrelated items. Answer each of these items in your
examination booklet by giving the number of your choi
3. It is normalized so that det(e1 , . . . , en ) = 1. (Volume of a cube).
From these properties one easily deduces the behavior of the determinant
under elementary operations:
1. The determinant is unchanged if a multiple of one vector is added to
anothe
The row rank and the column rank of a matrix are equal. This is clear
when the matrix of T is a projection of Rn onto Ri ; it then follows from the
Corollary above, by invariance of both quantities under composition with
automorphisms.
We will later see a
Functoriality. If T : V W then we have a natural map T : V W .
If S : V V and T : W W , then we get a map S T : V W V W
satisfying
(S T )(v w) = S(v) T (w).
Reciprocal polynomials. Let us say the reciprocal of a monic, degree
n polynomial p(t) = tn + a1