CAAM 560
Homework Assignments
Fall 2018
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 giving your impressions about each appendix or chapter. I am interested mainly in comments that might help me in rewriting of the unit. For appendices B, C, and E your reading can be rather light in some sense you should know much of this material. Do not spend too much time on the last parts of Appendix E, it is heavy reading. I do want you to do a good job of reading Chapter 1.
Reading Assignment 1: Due Monday, August 27, 2018. Read Chapters 1,2,and Appendices A,B, and C.
Reading Assignment 2: Due Wednesday, September 12, 2018. Read Appendix E and Chapter 4.
Reading Assignment 3: Due Monday, September 24, 2018. Read Chapter 5,6,7, and 8.
Reading Assignment 4: Due Wednesday, October 10, 2018. Read Chapter 9, Appendix D, and Baker's paper.
Reading Assignment 5: Due Wednesday, October 17, 2018. Read and comment on the ship building paper, the characterization of inner product spaces paper, and the Tapia Letter.
Reading Assignment 6: Due Friday, November 9, 2018. Read Chapters 10 and 11.
Reading Assignment 7: Due Friday, November 16, 2018. Read Chapters 12,and 13.
Reading Assignment 8: Due Wednesday, November 21, 2018. Read the papers of Cottle, Karush, and Kuhn-Tucker.
Reading Assignment 9: Due TBD. Read the paper of Byrd, Cocola, and Tapia.
Reading Assignment 10: Extra Credit. This means that you will get an "A" without doing this work. I put it there just in case someone wants something extra to do. (A) MOW. Sofia Kovaleskya. It is clear that she and Weierstrass had a strong relationship. I ask you to comment on the question: Was this relationship romantic, and if so was it in both directions. (B) Read the BFGS paper that is contained in the class file of papers. In the last part of the paper the mean-value theorem and Taylor's theorem coupled with the form of the derivatives lead to interesting theory. To me it is beautiful that these pieces fall together so well. Do you agree?
Problem Set Assignments and Exams
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: Due September 14, 2018.
Chapter 1. Problems 1,2,4,5, and 8. Also read and comment on the paper by Evans and Tapia (Evans-Tapia Note (PDF-File) or ( Evans-Tapia Note (Weblink). ).
Extra Problem. Let P[0,1] be the vector space of polynomials in one real varible and of arbitrary degree defined on the interval [0,1]. Use the material in the Evans‐Tapia paper to argue that no matter how you norm this vector space it will never be complete.
Problem Set Assignment 2: Monday, Due October 1, 2018.
Chapter 4. Problems 3,4,9, and 10.
Problem Set Assignment 3: Wednesday, Due October 24, 2018.
Chapter 1(#9,14,16), Chapter 6(#6), and Chapter 7(#3).
Exam 1: Handout on October 24, 2018 and collect on November 2, 2018.
Problem Set Assignment 4: Due November 30, 2018.
The assignment consists of all the problems, and read and provide your input about the article attached. Homework in PDF File.
Exam 2: Handout on November 30, 2018 and collect on December 14, 2018.
Mathematician of the Week
Be prepared to talk about the selected mathematician and to turn in a brief paragraph or two on your impressions on Friday/Monday.Week 1: Hausdorff, (Farewell Letter-pdf-file), (html link) . Due 8/24/2018.
Week 2: Pierre de Fermat. Due: 8/31/2018.
Week 3: Galileo. Due 9/7/2018.
Week 4: Euler. Due 9/14/2018.
Week 5: Cantor. Due 9/28/2018.
Week 6: Newton. Due 10/5/2018. (Newton felt rejected by his mother; why? Comment on what impact if any you believe that his mother’s rejection made on him.)
Week 7: Lagrange. Due 10/12/2018.Please comment on the impact on his mathematical productivity caused by his first wife’s death and by the marriage to his second wife.
Week 8: G.H. Hardy. Due 10/19/2018. I do not want you to tell me about the life of Hardy. Instead since Hardy is so well known for his quotes concerning mathematics (A Mathematician’s Apology). Read his quotes, pick out one that you like and one that you don’t like and tell me why you feel that way about the selected quotes.
Week 9:R.L. Moore . Due 10/26/2018. Tell me about the man. Comment on his good and his bad. Is he a hero or a villain or both? Does racism in mathematics exist today? Comment on my letter to the UT students. It is in your reading list. Also read the excerpt from Chapter 3 on Racism in my book, The Precious Few. It is included in your reading material.
Week 11: David Blackwell. Due 11/7/2018. Read the three entries that I have included in our reading material, Reflections on the Blackwell – Tapia Conference, Blackwell NMS letter, and the excerpt from Chapter 3 of my book.
Week 14: Due 11/30/2018.(The last day of instruction). I want you to share with me your view on the statement that extreme mathematical talent is at times accompanied by some form of mental instability on the part of the individual. I do realize that this notion is a touchy topic and insulting to many, but I want your views on the subject. You have all read and written about the life of Cantor. I personally believe that the strong rejection of respected mathematicians enhanced his depression. It is hard to deal with rejection, let alone professional rejection. As additional background look at profiles of John Nash, Kurt Godel, and Ted Kaczynski (The Unabomber).The Unabomber claimed all along that he did not have mental problems. His lawyers and prison psycologists all felt that he did what do you think:?Last year a student in class argued something along the lines that in the case of an extremely mathematically gifted individual some forms of mental conditions allow the person to focus more directly on the math problem at hand and not wander off in various directions, and he claimed that he had literature to back up his point. I often argue that doing mathematics can be the most isolating activity among all the STEM activities. Math is different, you do not have to deal with people, and many mathematicians do show this in social situations. So some say that mathematicians often have social disorders. Please read a bit about Grigori Perelman. So write about what you want to about mathematicians and our uniqueness.
Papers
A Characterization of Inner Product Spaces
Reflections Blackwell-Tapia Conference
Byrd-Cocola-Tapia Paper(updated 11/15/18)
Lecture Notes
Class Information and Guidelines 8/20/2018
Isoperimetric Talk 8/27/2017
Chapters 1 and 4, 8/2018
Chapter 4, 8-9/2018 (updated 9/7/2018)
Chapter 5, 9/2018(updated 9/17/2018)
Chapter 6, 9/2018
Chapter 7, 10/2018 (updated 9/28/18, be aware that T_s was replaced by T_l)
Second Order Optimality Conditions 10/2018
CAAM Note 10/15/2018
Chapter 8, 10/2018 (updated 10/3/2018, T_s replaced by T_l)
Chapter 9, 10/2018(updated 10/5)
Chapter 10,10/2018 (updated 11.10.2018)
Chapter 11, 11/2018 (updated 11/10/18)
Chapter 12,11/2018
Chapter 13,11/2018
Chapter 14,12/2018
Fall 2016
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 giving your impressions about each appendix or chapter. I am interested mainly in comments that might help me in rewriting of the unit. For appendices B, C, and E your reading can be rather light in some sense you should know much of this material. Do not spend too much time on the last parts of Appendix E, it is heavy reading. I do want you to do a good job of reading Chapter 1.
Reading Assignment 1: Due August 31, 2016. Read Chapters 1,2,and 3.
Reading Assignment 2: Due September 7, 2016. Read Appendices A,B and C.
Reading Assignment 3: Due September 19, 2016. Read Appendix E and following sections:
Reading Assignment 4: Due October 3, 2016. Read Chapters 5,6,7, and 8.
Reading Assignment 5: Due October 12, 2016. Read Appendix D and Chapter 9.
Reading Assignment 6: Due November 7, 2016. Carefully read Chapter 10 and critique: (1) Davood's proof of the Farkas theorem in the generality of a vector space; (2) The two proofs of our basic theorem of the alternative; (3)Our proof works for the restricted Motzkin Theorem where there are no c_i's, Why does it not work when c_i's are present? Do you think we can make it work for the full Motzkin Theorem?
Reading Assignment 7: Due November 14, 2016. Read Chapters 11, 12, and 13.
Reading Assignment 8: Due November 21, 2016. Read and comment on the papers: A Characterization of Inner Product Spaces and the RQI Paper.
Reading Assignment 9: Due December 2, 2016. Read the papers of Cottle, Karush, and Kuhn-Tucker.
Problem Set Assignments and Exams
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: Due September 12, 2016.
Chapter 1. Problems 1,2,4,5, and 8. Also read and comment on the paper by Evans and Tapia (Evans-Tapia Note (PDF-File) or ( Evans-Tapia Note (Weblink). ).
Extra Problem. Let P[0,1] be the vector space of polynomials in one real varible and of arbitrary degree defined on the interval [0,1]. Use the material in the Evans‐Tapia paper to argue that no matter how you norm this vector space it will never be complete.
Problem Set Assignment 2: Due September 26, 2016.
Chapter 4. Problems 3,4,9, and 10.
Problem Set Assignment 3: Due October 17, 2016.
Chapter 1(#9,14,16), Chapter 6 (#6), and Chapter 7 (#3).
Problem Set Assignment 4: Due November 28, 2016.
The assignment consists of all the problems, and read and provide your input about the article attached. Homework in PDF File.
Exam 1: Handout on October 26, 2016 and collect on November 2, 2016.
Exam 2: During Finals period.