# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

1 Page

### home3

Course: MATH 6338, Fall 2008
School: Georgia Tech
Rating:

Word Count: 363

#### Document Preview

6338 HOMEWORK MATH #3 Due date: June 30, 2008 Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for grading. Write LEGIBLY on the FRONT side of the page only, and STAPLE your pages together. 1. Let M be a closed subspace of a normed linear space X. (a) Prove...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Georgia >> Georgia Tech >> MATH 6338

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
6338 HOMEWORK MATH #3 Due date: June 30, 2008 Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for grading. Write LEGIBLY on the FRONT side of the page only, and STAPLE your pages together. 1. Let M be a closed subspace of a normed linear space X. (a) Prove that if X is separable, then X/M is separable. (b) Prove that if X/M and M are both separable, then X is separable. Hint: Let {fn +M }nN be a countable dense subset of X/M , and let {gn }nN be a countable dense subset of M . Then S = {fm + gn }m,nN is a countable subset of X. (c) Give an example of X, M such that X/M is separable, but X is not separable. 2. Let X be a Banach space, and let {xn }nN be a sequence of vectors in X. Show that the following two statements are equivalent. Hint: (a) HahnBanach. {xn }nN is minimal, i.e., no xm lies in the closed span of the other vectors in the sequence: m N, xm span{xn }n=m . / (b) There exists a sequence {n }nN in X that is biorthogonal to {xn }nN , i.e., xn , m = mn = 1, m = n, 0, m = n. 3. Let {xn }nN be a sequence in a Banach space X. Consider the following two statements. Prove that statement (a) implies statement (b). (In fact, the converse is also true, but you dont need to prove it.) Hint: HahnBanach. (a) n=1 | xn , | converges uniformly with respect to th...

Textbooks related to the document above:
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Georgia Tech - MATH - 1522
MATH 1522 CQUIZ #5NAME: December 2, 2005Answer the following questions clearly and completely. 1 5 1. Let u1 = 1 and u2 = 1 . Let V = span{u1 , u2 }. 1 2 (8 points) a. Use the Gram-Schmidt procedure to nd an orthogonal basis for V .(Pr
Georgia Tech - MATH - 1522
MATH 1522 CQUIZ #3NAME: October 21, 2005Answer the following questions clearly and completely. 2 0 1. Let A = 3 1 1 2 1 1 2 0 1 3 3 0 . 2 0(6 points) a. Compute det(A) by using cofactors to reduce the 4 4 determinant to a sum of 3 3 dete
Georgia Tech - MATH - 4107
MATH 4107HOMEWORK #4DUE: April 9, 2007Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for
Georgia Tech - MATH - 6338
MATH 6328HOMEWORK #4DUE: April 13, 2006Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for
Georgia Tech - MATH - 4317
MATH 4317HOMEWORK #1DUE: August 29, 2003Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. NOTES. Your grade on this and every h
Georgia Tech - MATH - 2406
MATH 2406EXAM INAME: September 27, 2004Answer the following questions clearly and completely. PROVIDE PROOF, WORK, OR EXPLANATION FOR EACH PART OF PROBLEMS 24. There are 35 points total. NOTE: Throughout this exam, you can assume that scalars a
Georgia Tech - MATH - 6338
MATH 6338HOMEWORK #4Due date: July 11, 2008Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected
Georgia Tech - MATH - 2406
MATH 2406EXAM 2NAME: November 8, 2004Answer the following questions clearly and completely. PROVIDE PROOF, WORK, OR EXPLANATION FOR EACH PART. There are 35 points total. NOTE: Throughout this exam, you can assume that scalars are real. (8 point
Georgia Tech - MATH - 2406
MATH 2406HOMEWORK #1DUE: September 1, 2004Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected
Georgia Tech - MATH - 2406
MATH 2406FINAL EXAMNAME: December 6, 2004Answer the following questions clearly and completely. PROVIDE PROOF, WORK, OR EXPLANATION FOR EACH PART. There are 55 points total, plus 5 points extra credit. NOTE: Throughout this exam, you can assume
Georgia Tech - MATH - 4317
MATH 4317HOMEWORK #5DUE: November 12, 2003Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected
Georgia Tech - MATH - 1522
MATH 1522 CQUIZ #2NAME: October 21, 2005Answer the following questions clearly and completely. (9 points) 1. Let A = 1 2 0 0 3 1 , B= , x= . 1 2 1 1 1 2 Either compute the following products or write Undened if not dened. a. AB =b. xT A =c.
Georgia Tech - MATH - 6338
MATH 6328HOMEWORK #2DUE: February 12, 2007Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected
Georgia Tech - MATH - 7337
MATH 7337FINAL EXAMDUE: Noon, December 13, 2006Work the following problems and hand in your solutions. YOU MUST WORK INDEPENDENTLY. You may use any book or your notes, but you may not use anyone elses notes. You may not discuss this exam with a
Georgia Tech - MATH - 6338
Georgia Tech - MATH - 1502
MATH 1502EXAM #2NAME: March 10, 2005Answer the following questions clearly and completely. Unless otherwise specied, you must provide work justifying your solution. Use the back of the page for scratchwork if needed, but clearly indicate if any
Georgia Tech - ALGS - 06
Cryptography and RSA1 RSACryptography is concerned with the following scenario: Two people we shall call them Alice and Bob wish to communicate in the presence of an eavesdropper Eve. Suppose that Alice wants to send to Bob secret message x. Crypto
Georgia Tech - MATH - 2403
1. Find general solutions of the following equations: (a) (y 2 + 1)y + et = 0 (b) y + 2. Solve the following Initial Value Problems: (a) y + (b) 1 sin t y= ; 2(t + 1) t+1 y(0) = 1 et 2 y= t+1 (t + 1)2 2 + cos t (y 2 2 2y + 2)earctan t = 0; y t
Georgia Tech - MATH - 3012
The following facts may be useful on your quiz on Friday (and will also be given to you on the quiz itself). Geometric Series: The following two relationships hold for every a and every r.a + ar + ar2 + ar3 + + arn =a - arn+1 1-r a 1-ra + ar
Georgia Tech - IPSTETD - 276
Georgia Tech - IPSTETD - 55
Georgia Tech - IPSTETD - 95
Georgia Tech - IPSTETD - 76
Georgia Tech - ETD - 03302005
Georgia Tech - ETD - 04062004
Georgia Tech - ETD - 06242004
VARIABLE FREQUENCY MICROWAVE REFLOW OF LEAD-FREE SOLDER PASTEA Thesis Presented to The Academic Faculty by Pamela Patrice ReidIn Partial Fulfillment Of the Requirements for the Degree Master of Science in the School of Chemical &amp; Biomolecular Eng
Georgia Tech - ETD - 07122004
THE ROLE OF CAVEOLAE IN THE LOSS OF ERK2 ACTIVATION IN STRETCHED SKELETAL MYOTUBESA Dissertation Presented to The Academic Faculty By Anne Claire BellottIn Partial Fullfillment Of the Requirements for the Degree Master of Science in the School of
Georgia Tech - ETD - 04072004
Georgia Tech - ETD - 06072004
Georgia Tech - MATH - 4317
MATH 4317HOMEWORK #3DUE: June 26, 2007Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for
Georgia Tech - MODULE - 10
COOPERATIVE EXTENSION SERVICE West Virginia University Center for Extension and Continuing EducationPFS - 004SanitationGood sanitation can be the difference between a profitable poultry operation and an unprofitable operation. Cleanliness is the
Georgia Tech - MODULE - 10
Hazard Communication Subpart Z 29 CFR 1910.1200 Adopted from OSHA Office of Training and Education HAZARD COMMUNICATION/hazcom/1-95 About 32 million workers are potentially exposed to one or more chemical hazards. There are an estimated 575,000 exist
Georgia Tech - MODULE - 12
Permit-Required Confined Spaces, 29 CFR 1910.146 Glossary of Terms Acceptable entry conditions: the conditions that must exist in a permit space to allow entry and to ensure that employees involved with a permit-required confined space entry can safe
Georgia Tech - MODULE - 7
Georgia Tech - MODULE - 1
LESSON PLAN Introduction to OSHA 1-Hour Module Overview This module will give a general overview of OSHA and how they operate. Starting with the need for OSHA creation initially, the session will go through some of the major elements of how OSHA oper
Georgia Tech - MODULE - 9
Lesson Plan: Student Guide 1-Hour Personal Protective Equipment Overview Overview This lesson will review the basic elements of the personal protective equipment and noise standards and the workplace safety and health requirements as they apply to 3r
Georgia Tech - ME - 6754
me/6754/fulton/copyright228Fri Mar 27 09:31:45 19981WARNING CONCERNING COPYRIGHT RESTRICTIONS The Copyright Law of 1976 (United States Code, Title 17) governs the making of photocopies or other reproductions of copyrighted material. Under certa
Georgia Tech - ME - 6754
EDM 6- 24EDM 6- 25EDM 6- 26EDM 6- 27EDM 6- 28EDM 6- 29EDM 6- 30EDM 6- 31EDM 6- 32
Georgia Tech - ME - 6754
DRAFT03/24/98BIBLIOGRAPHYAdiba, M. and Nguyen, G. T., &quot;Knowledge Engineering for CAD/VLSI on a Generalized Data Management System,&quot; Knowledge Engineering in ComputerAided Design by Gero, J. S. (Ed.), North Holland, 1985, pp. 259-283. Adler, P. S
Georgia Tech - ME - 6754
DRAFT03/23/98CHAPTER 3 ENGINEERING PRODUCT AND PROCESS DESCRIPTIONThe &quot;Islands of Automation&quot; in the product development process are increasingin volume at an alarming rate. There is a tendency to address these islands as a basic problem and t
Georgia Tech - ME - 6754
DRAFT03/23/98CHAPTER 4 INTRODUCTION TO DATABASES4.1 INTRODUCTIONA database is an organized repository of data. Nowadays the databases act as communication channels for applications that share data between themselves. A Database Management Syste
Georgia Tech - ME - 6754
DRAFT 03/24/98CHAPTER 10 GOODNESS MEASURES FOR INTEGRATION10.1 INTRODUCTIONMeasuring goodness is an important step for any effort. Specially helpful are measures that can quantify the results. The measures not only tell how good a particular eff
Georgia Tech - ME - 6754
Homework Set 9Georgia Tech CS/ME 6754, COA 8676E Spring 200111-1Using the ER model for the taking the course/university database create the following information models (schemas): STEP Express STEP Express-G For the STEP models, concentrate o
Georgia Tech - ME - 6754
APPENDIX AHandouts Notes on Literature Survey Paper and Term Project Homework SetsAPPENDIX A-1ME 6754Problem Set I Due:Organize the input and output for the stress analysis of a space truss composed of pipe crosssection members of different l
Georgia Tech - ME - 6754
DRAFT03/23/98CHAPTER 6 INTEGRATION APPROACHES VIA DBMS6.1 INTRODUCTIONExisting engineering environments generally comprise incompatible tools and data servers linked together in a &quot;Rube Goldberg&quot; fashion to provide the semblance of integration.
Georgia Tech - CS - 4210
Homework 2 (due Mon. 6/20)1. (Related lecture on Wed. 6/15) Consider the following serializer code:serializer { queue a, b, c; crowd cr; int i = 0; /* initially zero */ void foo() { enqueue(a) until i != 0; join_crowd(cr) { . /* critical section */
Georgia Tech - CS - 1050
Answers: All nerds are good at math. Buffy is good at math. Buffy is a nerd.P(x) = x is a nerd Q(x) = x is good at math For all x, P(x) Q(x) Q(x) P(x) Invalid by converse error!It is difficult to study whenever I am tired. I found it easy to stu
Georgia Tech - CS - 8803
Week 1/24-1/28Search and Replication in Unstructured Peer-to-Peer NetworksGnutellas search method through TTL-based flooding introduces many duplicate messages, especially in high connectivity networks. As a result, it is frequently not easy to
Georgia Tech - CS - 2002
Some more Q #4 sample problems (1) Consider the following B+-tree:1523311 1445678014481113131518(a) (1 point) Which nodes (disk pages) would be accessed to nd all items in the range 5 to 12, inclusive? (b)
Georgia Tech - CS - 4400
Some more Q #4 sample problems (1) Consider the following B+-tree:1523311 1445678014481113131518(a) (1 point) Which nodes (disk pages) would be accessed to nd all items in the range 5 to 12, inclusive? (b)
Georgia Tech - CS - 3361
CS3361: Final Preparation. Notice that the following questions are a sample of the kind of questions that could be on the final. However, they certainly do not cover everything that could be on the final. They are merely intended to give you some ide
Georgia Tech - CS - 1050
CS1050 HW 5 Section 1.8 1) Determine whether each of the following functions from the set {a,b,c,d} to itself is oneto-one. a. f(a)=b, f(b)=a, f(c)=c, f(d)=d b. f(a)=b, f(b)=b, f(c)=d, f(d)=c c. f(a)=d, f(b)=b, f(c)=c, f(d)=d 2) Determine whether eac
Georgia Tech - CS - 4210
Homework 4 (due 4/21/2004)Assumption: all variables originally hold the value 0. Answer the ones we didn't do in class. 1. Consider the following sequence of operations in a distributed shared memory system:P1: W(x)1 P2: P3: P4: W(x)3 W(x)2 R(x)3 R
Georgia Tech - CS - 4210
Homework 2 (due Wed. 6/9)1. Consider the following serializer code:serializer { queue a, b, c; crowd cr; int i = 0; /* initially zero */ void foo() { enqueue(a) until i != 0; join_crowd(cr) { . /* critical section */ } } void bar() { enqueue(b) unt
Georgia Tech - CS - 4440
TAKE_HOME QUIZ 2 - CS 4440 Emerging Database Technologies and Applications (Given : November 25 in class) Due December 8, 2003 (submit a hardcopy to Dani Denton 385-4785 in room 252 in College of Computing, by 4 p.m. Hard Deadline.) Total Points: 75.
Georgia Tech - CS - 4420
CS 245: Database System PrinciplesNotes 5: Hashing and MoreHector GarciaMolinaExtended with Ullman's notesCS 245 Notes 5 1Hashingkey h(key)&lt;key&gt; Buckets (typically 1 disk block). . .CS 245 Notes 52Two alternatives. . . records .
Georgia Tech - CS - 12
Paper # 204 : Application-Aware Adaptation for Mobile ComputingProblems to be addressed/ObjectivesThe paper proposes to address the following issues in data access for mobile environments. i. &quot;Scalability&quot;, because of the increase in size of t
Georgia Tech - CS - 8803
Paper # 204 : Application-Aware Adaptation for Mobile ComputingProblems to be addressed/ObjectivesThe paper proposes to address the following issues in data access for mobile environments. i. &quot;Scalability&quot;, because of the increase in size of t
Georgia Tech - CS - 2004
Paper # 91 - Enhancing the Web's Infrastructure - From Caching to Replication1) Problems to be addressed/ ObjectivesThis paper proposes a design strategy that seeks to address two of the most challenging and important issues facing the users of t
Georgia Tech - CS - 8803
Paper # 91 - Enhancing the Web's Infrastructure - From Caching to Replication1) Problems to be addressed/ ObjectivesThis paper proposes a design strategy that seeks to address two of the most challenging and important issues facing the users of t
Georgia Tech - CS - 2004
Paper #14 - The Connectivity Server: Fast Access to Linkage Information on the Web1) Problems to be addressed/ ObjectivesThis paper explains the mechanism of the construction of the neighborhood graph of a set of URLs, while minimising the time re