Math 113 (Spring 2009) Yum-Tong Siu Homework Assigned on February 17, 2009 due February 24, 2009
1
Problem 1 (from Stein & Shakarchi, p.67, #14). Let R > 1 and z0 C with |z0 | = 1. Let h(z) be a holomorphic function on cfw_ |z| < R with h (z0 ) = 0. Let
Solutions Manual for
Functions of One Complex Variable I, Second Edition 1
Copyright by Andreas Kleefeld, 2009
All Rights Reserved2
1 by
John B. Conway
updated on August, 3rd 2009
2 Last
PREFACE
Most of the exercises I solved were assigned homeworks in t
Solutions Manual for
Functions of One Complex Variable I, Second Edition 1
Copyright by Andreas Kleefeld, 2009
All Rights Reserved2
1 by
John B. Conway
updated on August, 3rd 2009
2 Last
PREFACE
Most of the exercises I solved were assigned homeworks in t
Algebra Homework
1. Find all conjugacy classes in D8.
2. Find Z(D8).
3. Find all centralizers of single elements in Sym(6).
4. Show that Sym(n) is generated by (1, 2) and (1, 2, ., n).
5. Show that if n > 2, then Z(Sym(n) = 1.
6. Show that Z(A B) = Z(A) Z
Sinusoids
CMPT 318: Lecture 3 Sinusoids
Tamara Smyth, [email protected] School of Computing Science, Simon Fraser University January 16, 2006
Sinusoids is a collective term referring to both sine and cosine functions. A sinusoid is a function of time hav
c 2010 Society for Industrial and Applied Mathematics
SIAM REVIEW
Vol. 52, No. 1, pp. 354
Numerical Methods for
Electronic Structure
Calculations of Materials
Yousef Saad
James R. Chelikowsky
Suzanne M. Shontz
Abstract. The goal of this article is to give
The two papers in this issue have to do with matrices and sparsitybut from
different points of view. Sparsity, in the rst paper, means many zero elements in the
matrix, while in the second paper it refers to many zero singular values, i.e., low rank.
The
Book Reviews
Introduction, 565
Featured Reviews: Pattern Formation and Dynamics in Nonequilibrium Systems (Michael Cross
and Henry Greenside), Edgar Knobloch, 567
Analytic Combinatorics (Philippe Flajolet and Robert Sedgewick), Robin Pemantle, 572
Numeric
Slope Word Problems
Slope Word Problems
Lesson Objective: 4.01a
Students will know how to solve word
problems using slope
Slope Word Problems
In 2005, Joe planted a tree that was 3 feet
tall. In 2010, the tree was 13 feet tall.
Assuming the growth of the
Mat 534 Algebra I Fall 2005
Solutions to Test 1
Let p be a prime number, and Fp the eld of congruence classes modulo p. In problems 15,
the group G = GL2 (Fp ) is the group of all invertible 2 2 matrices with coecients in Fp .
Remark: In the solutions, we
Mat 534 Algebra I Fall 2005
Solutions to Test 1
Let p be a prime number, and Fp the eld of congruence classes modulo p. In problems 15, the group G = GL2 (Fp ) is the group of all invertible 2 2 matrices with coecients in Fp . Remark: In the solutions, we
Problem 1 2 3 4 5
Scores
Bonus:
Total:
Mat 534 Algebra I Fall 2005
Name:
Test 1 (December 1 / 80 minutes)
1. Denote by F the subset of R consisting of all elements of the form a + b 3 2 + c 3 4, where a, b
and c are rational numbers.
(a) Verify that that
Problem 1 2 3 4 5 Scores
Bonus:
Total:
Mat 534 Algebra I Fall 2005
Name:
Test 1 (December 1 / 80 minutes)
1. Denote by F the subset of R consisting of all elements of the form a + b 3 2 + c 3 4, where a, b and c are rational numbers. (a) Verify that that
Algebra I: Solutions to selected homework problems HW1: 4. (a) Let m and n be relatively prime integers. Prove that (Z/nZ) (Z/mZ) (Z/mnZ) .
Solution: Let us prove the following more general result. Under the same assumptions on n and m, the rings Z/nZ Z/m
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT4030
Solutions for Homework 2
1. (2.1.11)
Given that
X (u, v ) = (g (u), h(u) cos v, h(u) sin v )
Computation shows that
Xu Xv = h(
So if Xu Xv = 0, h = o or
dh
du
=
dg
du
2. (2.1.16)
Given
Complex Analysis I
Math 3X03
Solutions of homework 2
(1) We claim that the sequence cfw_zn converges if and only if |z | < 1, and that
limn zn = 0 in this case.
To see this, we assume rst that |z | < 1 and show that limn |nz n | = 0.
Since |nz n | = n|z
Massachusetts Institute of Technology 6.854J/18.415J: Advanced Algorithms David Karger
Handout 8 Wednesday, October 7, 2009
Problem Set 3 Solutions
Wednesday, October 7, 2009 Problem 1. (a) Consider the (k + 1)st item inserted. Since only k buckets (at wo
Algebra 3 (2004-05) Solutions to Assignment 7
Instructor: Dr. Eyal Goren
1). How many elements of order 7 does a simple group of order 168 must have?
Solution. 168 = 23 3 7. The 7-Sylow subgroup cannot be normal and it follows that n7 = 8. Each
7-Sylow co
Fall 2009
18.314 Combinatorial Analysis
S. Assaf
Solutions to Problem Set 8
1. (2 points) Recall that a connected graph on n vertices is a tree if and only if it has n 1 edges, and in this case adding any additional edge to the graph creates a cycle. Let
MATH 418 COMPLEX VARIABLES Homework 11 Solution
Due April 26, 2001 Note: If you have any questions about the solution, or you think there are some typos/errors in the solution, please e-mail me. Ill double-check it and then reply to you. Thank you. C20. W
Solutions to Homework 21
Problem 1a: Two elements of Sn are conjugate exactly when they have the same cycle structures. Thus,
we have the following conjugacy classes in S4 :
cfw_id
cfw_(1 2), (1 3), (1 4), (2 3), (2 4), (3 4)
cfw_(1 2 3), (1 2 4), (1 3
Homework 4 Solution, Math 804 1. Use Schwartz Reflection principle to show that an analytic function f in a domain D can be analytically continued across part of its boundary D where f (or Re f ) is a constant provided the the boundary segment is analytic
Algebra I: Solutions to selected homework problems
HW1:
4. (a) Let m and n be relatively prime integers. Prove that
(Z/nZ) (Z/mZ)
(Z/mnZ) .
Solution: Let us prove the following more general result. Under the same assumptions
on n and m, the rings Z/nZ Z/m