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 holom
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
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
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
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c 2010 Society for Industrial and Applied Mathematics
SIAM REVIEW
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Mat 534 Algebra I Fall 2005
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Let p be a prime number, and Fp the eld of congruence classes modulo p. In problems 15,
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Mat 534 Algebra I Fall 2005
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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 matri
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Mat 534 Algebra I Fall 2005
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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
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Solution: Let us prove the following more general result. Un
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
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(1) We claim that the sequence cfw_zn converges if and only if |z | < 1, and that
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To see this, we assume rst that |z | <
Massachusetts Institute of Technology 6.854J/18.415J: Advanced Algorithms David Karger
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Problem 1a: Two elements of Sn are conjugate exactly when they have the same cycle structures. Thus,
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cfw_id
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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
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. Un
Math 113 (Spring 2009) Yum-Tong Siu Solutions of Problems of Math 113 Final Examination May 20, 2009, 9:15 a.m. - 12:15 p.m. Science Center A Total Number of Points = 200
1
Problem 1. Evaluate the fol
Math 113 (Spring 2009) Yum-Tong Siu Solution of Homework Assigned on January 29, 2009 due February 5, 2009
1
Problem 1 (from Stein & Shakarchi, p.26, #7). The family of mappings introduced here plays