CAAM 560
Homework Assignments
Fall 2013
Fall 2013 Reading Assignments
Read in the order listed in the assignment. Critique each of the sections of our book, i.e., write some relatively brief comments about each appendix or chapter. You may use the ollowing four questions as a guide as to what to write:
1) Is the unit of value to the readers of the book, why or why not?
2) What did you like, if anything, about the unit?
3) What did you dislike, if anything, about the unit?
4) What changes, if any, would you like to see in the unit?
In the past these were the guidelines for students. However now I am just asking you to give me your impressions. In particular
do we need to add anything or rewrite anything.
Also please give me typos or ackward statement that you find. My expectation is that you should give me
half a page or so for each unit.
As you read for the first time read for general understanding not to be able to reproduce the proofs. You will want to re-read later on, but that is standard in mathematics. Some of the proofs in either the chapters or the appendices are challenging. I have included them so you can gain an appreciation for the result and for mathematical proof techniques. I would like you to have a reading assignment a week, but we always fall short of that. Ideally, I would like you to read each chapter before we discuss it in class. The appendices make the book self-contained. If you have never seen the material in the appendices before then you will have to spend more time on the material. But it can, and has been, navigated by others with minimal background. I feel that you will learn more in this class than in most classes you have taken. I have failed if you do not leave feeling mathematics is elegant, beautiful, and useful. Much of the material is essentially new and is not readily available in other texts.
Reading Assignment 1. Read Appendices A,B,C,E, and Chapter 1. For each unit that you read write a short (half page) giving your impressions of that unit. Due Wednesday, September 4, 2013 (Date changed to Friday September 6, 2013) In class
Reading Assignment 2. Chapter 3 and brief comments on the Evans-Tapia Note. Due Wednesday September 18, 2013, In class.
Reading Assignment 3. Chapter 4. Due Wednesday October 2, 2013.
Reading Assignment 4. Chapters 2,5,6, and 7. Due Wednesday, October 9, 2013.
Reading Assignment 5. TBA.
Fall 2013 Problem Set Assignments and Exam Information
The problem sets are important. I want you to work together to discuss the solutions. However, you must write up the solutions to the problem set on your own. Moreover, I want them well-written and complete. You should be able to return to the write-up after some time and completely understand the write-up. In the beginning, we will schedule help sessions. Then there will be a time when I feel that you have shown that you should be on your own. I am willing to help you as much as you need.
Problem Set Assignment 1. Chapter 1. Problems 1,2,4,5, and 8. Due Monday September 16, 2013. Rework of Problem Set 1 is due Wednesday October 9, 2013.
Problem Set Assignment 2. Chapter 4. Problems 3,4,9, and 10. Due Wednesday October 2, 2013.
Problem Set Assignment 3. Problems:Chapter 1(#9,14,&16), Chapter 6 (#6), and Chapter 7 (#3). Due Wednesday October 16, 2013.
Exam Chapters 1-8: Monday October 21, 2013.
Problem Set Assignment 4. Problems TBA. Due TBAFall 2013 Lecture Notes
Lecture 1, Class Information and Guidelines 8/26/13
Lectures 2 and 3, Chapter 3: The Isoperimetric Problem Revisited, 8/28-30/13
Lecture 4, Chapters 1 & 4, 9/4/13
Lectures 5-7, Chapter 4 (contin.), 9/6-16/13
Lectures 8-10, Chapter 5, 9/18-23/13
Lectures 11-12, Chapter 6, 9/25-27/13
Lectures 13-14, Chapter 7 (updated 9/30/2013), 9/30-10/2
Lectures 15-16, Chapter 8, 10/8-12/13
Fall 2012 Reading Assignments
Reading Assignment 1.
Read Appendix E, and Chapters 1 and 3. Due Monday, August 29, 2012
Reading Assignment 2. Chapters 4 and 5. Due Friday September 5, 2012
Reading Assignment 3. Appendix A,B,C and Chapter 2. Due Monday September 19,2012
Reading Assignment 4. Read Chapters 6 and 7. Due Wednesday October, 2012
Reading Assignment 5. Due Monday, November 5, 2012 (This assignment will be graded like one of the problem sets)
Read in this order Appendix D, Chapter 8, and Chapter 9. Give usual reading assignment comments . However, include the following specific comments
-Read carefully Section 8.8 An Abstract Analogy. Comment on this Section.
Do you think that it adds something to the book or does not really add anything?
-Read the two proofs of Theorem 9.4.1. Recall that the first proof is borrowed from Wilansky.
The second proof is mine. Contrast the two proofs. Is my proof the perfect proof of this theorem, why or why not?
-Carefully read and then comment on Davood’s proof of Theorem 9.5.1, the extended Farkas Theorem. Do you think that his proof is particularly clever? Recall that this theorem had been searched for by me for several years. It allows us to complete our multiplier theory.
Reading Assignment 6. Due Monday, November 12, 2012 (This assignment will be graded like one of the problem sets)
Read Chapters 10, 11, 12, and 13. Chapters 10-13 can be found on the CAAM 560 Assignment page right below Fall 2011 Homework Assignments under the titles Chapter 10 Lecture , … , Chapter 13 Lecture.
Reading Assignment 7. Due Monday, November 30, 2012 (The last day of class)
(This assignment will be graded like one of the problem sets)
- Read and comment on the three papers
1. William Karush’s master ‘s thesis.
2. A Characterization of Inner Product Spaces (by RAT).
3. The Isoperimetric Problem Revisited (by RAT).(I will use your comments in revision)
Fall 2012 Problem Set Assignments
Problem Set Assignment 1: Chapter 1: Problems 3, 4, 6, 7, and 11. Due Wednesday, September 5, 2012
Problem Set Assignment 2: Chapter 3: Problems 3,4,5,6, and 7. Due Wednesday, September 12, 2012
Problem Set Assignment 3: Chapter 1: Problems 18, 26, 31, and 32.
Problem Set Assignment 4: Chapter 4: Problems 13, and 16. Work Problem 13 in two ways. The first is from the definition of convexity and the second is using differential characterizations.
Chapter 5: Problem 1
Chapter 6: Problem 4
Dragster Problem: A dragster runs a quarter mile track in a straight line attempting to accelerate hard and end up with as large a top speed at the end of the ¼ mile as possible. This top speed is measured from placing two clocks at the end of the strip (track). One clock is always placed at the end of the ¼ mile track and the other 66 feet inside the track (before the end) or 66 feet outside (after the finish line). Of course a simple difference formula is used to approximate the speed. It is generally felt that a dragster accelerates for the full ¼ mile or to the second clock when the second clock is past the end of the quarter mile. So you may assume this. Prove that if the second clock is placed inside the quarter mile, then the actual speed at the end of the quarter mile is greater than the estimated speed while if the second clock is placed outside the quarter mile the actual speed is less than the estimated speed. In the old days the second clock was outside, today it is required to be inside, why do you think that this is so?
Lecture Notes
Lecture 0, 8/22/11
Lecture 1, 8/24/11
Lecture 2, 8/26/11
Lecture 3, 9/9/11
Lecture 4, 9/19/11
Lecture 5, 10/3/11
Lecture 6, The Remarkable Isoperimetic Problem and the Euler-Lagrange Equation Revisited, 10/12/11
The Euler-Lagrange Equation as a multiplier rule, 11/9/11
Chapter 9 Lecture
Chapter 10 Lecture
Chapter 11 Lecture
Chapter 12 Lecture
Chapter 13 Lecture
11/28/11 Lecture