Teaching Fall Semester 2006

This Fall I'm teaching two graduate courses, MAT 5653 ODE I and MAT 5223 Complex Variables I. Course syllabi together with assignments follow. More information is available on the WEBCT homepage for each course.

Course Syllabus
MAT 5653.001 Differential Equations I
MW 5:30-6:45 pm BB 3.04.08

PROFESSOR: Walter B. Richardson, Jr.
OFFICE: MS 3.03.22
OFFICE PHONE: 210.458.4760
WEBPAGE: www.math.utsa.edu/~wrichard
EMAIL: walter.richardson@utsa.edu
OFFICE HOURS: MW 4:00-5:20pm and by appointment.

Textbook: Ordinary Differential Equations, V.I. Arnold ISBN 0-262-51018-9.

PEDAGOGY: The course will be taught using a lecture-problem solving format. It will be essential that you have convenient access to a PC, and from the beginning are able to use Internet Explorer or other browser, Adobe Acrobat Reader, as well as WEBCT. In addition, those who are taking the course remotely must get access to a scanner for getting your homework to me in a timely fashion as a .pdf file. The most important component of the course will be the Homework which I plan to assign every week or ten days, at least initially. While problems, exercises, homework, etc. should form the basis of any good mathematics course, it will be particularly important in a distance learning environment, as my primary means of feedback from students. Office Hours will be the other means for me to get that feedback.

GRADING: The grading will consist of 75% homework, and 25% Take-Home Final Exam.

COURSE OBJECTIVES/SCOPE Prerequisites: MAT 3613 and MAT 4213, or consent of instructor. Solution of initial-value problems, linear systems with constant coefficients, exponentials of operators, canonical forms and generic properties of operators, and contractions.

DATES TO REMEMBER:

• August 23, Wednesday -- First Day of Classes

• September 8, Friday 5:00pm. CENSUS DATE. Last day to drop or withdraw without a grade; drop an
  individual course and receive a 100% refund.

• October 24, Tuesday -- Last Day to drop individual course and receive a “W”

• December 6-12 Final Examinations

Homework Assignments:

Assignment 1 - Review of Undergraduate Ordinary Differential Equations, see WebCT for .pdf file.

Course Syllabus
MAT 5223.001 Theory of Complex Variables I
MW 7:00-8:15 pm BB 3.04.08

PROFESSOR: Walter B. Richardson, Jr.
OFFICE: MS 3.03.22
OFFICE PHONE: 210.458.4760
WEBPAGE: www.math.utsa.edu/~wrichard
EMAIL: walter.richardson@utsa.edu
OFFICE HOURS: MW 4:00-5:20pm and by appointment.

Textbook: Complex Variables, 2^nd Edition, Ablowitz and Fokas, ISBN 0-521-53429-1.

PEDAGOGY: The course will be taught using a lecture-problem solving format. It will be essential that you have convenient access to a PC, and from the beginning are able to use Internet Explorer or other browser, Adobe Acrobat Reader, as well as WEBCT. In addition those who are taking the course remotely must get access to a scanner for getting your homework to me in a timely fashion as a .pdf file. The most important component of the course will be the Homework which I plan to assign every week or ten days, at least initially. While problems, exercises, homework, etc. should form the basis of any good mathematics course, it will be particularly important in a distance learning environment, as my primary means of feedback from students. Office Hours will be the other means for me to get that feedback.

GRADING: The grading will consist of 75% homework, and 25% Take-Home Final Exam.

COURSE OBJECTIVES/SCOPE Prerequisites: MAT 3213 or MAT 4213. Complex integration, Cauchy’s theorem, calculus of residues, and power series. Objectives: To develop the theory of functions of a complex variable that is necessary for students pursuing advanced graduate studies in mathematics, physical sciences, engineering and many other areas. Scope: The course will cover complex numbers, holomorphic functions, complex integration, calculus of residues, and Taylor and Laurent series.

DATES TO REMEMBER:

• August 23, Wednesday -- First Day of Classes

• September 8, Friday 5:00pm. CENSUS DATE. Last day to drop or withdraw without a grade; drop an
  individual course and receive a 100% refund.

• October 24, Tuesday -- Last Day to drop individual course and receive a “W”

• December 6-12 Final Examinations

Assignments:

Assignment 1 – Problems from sections 1.1 and 1.2 from Fokas, see WebCT for details.

Teaching Spring Semester 2006

Note the format of this page has changed to make it more convenient. The weekly assignments in both classes will be posted at the top of the page in reverse chronological order. The material previous on the page is still here – just scroll down to view a list of the lecture notes, homework assignments, syllabi, etc.

Week #5 – February 12-18

Imaging: You should read the following sections from Epstein: Sections 3.4,3.5,3.6. There will be a pre-recorded video available under WebCT sometime Monday. You should have watched this before class on Tuesday evening. In addition Assignment #2 is now posted and due on Tuesday, February 21.

Problem Solving: Read Weeks, Chapter 4 on Orientability. Understand the construction of the Mobius Strip, the Klein Bottle and the Projective plane. The second homework has already been assigned and is now posted. It will be due on Tuesday, February 21. Solutions for the first homework are posted.

Week #5 – February 19-25

Imaging: We have finished with Chapter 3 from Epstein's book. Go over the notes and see if you understand the formula for the inverse of the Radon transform on radial functions. We talked briefly about representing images on the computer and how one might perform linear and nonlinear filtering of an image to remove noise. The second homework deadline was extended to Tuesday, February 28.

Problem Solving: Read Weeks, Chapter 5 on Connected Sums

Week #5 – February 12-18

Imaging: You should read the following sections from Epstein: Sections 3.4,3.5,3.6. There will be a pre-recorded video available under WebCT sometime Monday. You should have watched this before class on Tuesday evening. In addition Assignment #2 is now posted and due on Tuesday, February 21.

Problem Solving: Read Weeks, Chapter 4 on Orientability. Understand the construction of the Mobius Strip, the Klein Bottle and the Projective plane. The second homework has already been assigned and is now posted. It will be due on Tuesday, February 21. Solutions for the first homework are posted.

PROFESSOR: Walter B. Richardson, Jr.
WEBPAGE: www.math.utsa.edu/~wrichard EMAIL: walter.richardson@utsa.edu
OFFICE HOURS: Friday afternoons via the web, and by appointment over the phone

Pedagogy: This semester I am at the IMA, so the courses will be taught over the internet. While we will not have the bandwidth of closed circuit television, aka the usual distance learning classrooms at UTSA, I believe that we can make this a valuable two-way, realtime learning experience. One offering not only challenges, but opportunities not otherwise available. It will be essential that you have convenient access to a PC, and from the beginning are able to use Internet Explorer or other browser, Adobe Acrobat Reader, as well as WEBCT. In addition you will need get access to a scanner for getting your homework to me in a timely fashion as a .pdf file.

The way I forsee the lectures working is as follows, although modifications will be made as necessary. To the maximum extent possible I want the 1:15 minute period to be as interactive as possible, the way it would be if I were there on campus. This will be recorded as a .ram (Real Player) file that will then be available through WEBCT for those who cannot attend that particular lecture. I would strive not for a polished "canned" lecture without questions, but rather to encourage questions and discussion of mathematical ideas. Of course, this presupposes that the technology is working as hoped. A alternative would be for me to record a a 45 minute lecture offline, which we would view together, followed by a 30 minute question and answer period. We'll see what works best given our constrainsts. I may also end up getting a tablet PC, if my need to write on the board is overwhelming.

The most important component of the course will be the Homework which I plan to assign on a weekly basis, at least initially. While problems, exercises, homework, etc. should form the basis of any good math course, it will be particularly important this semester, as my primary means of feedback from the students. A few of you have taken courses from me in the past and know that I usually get feedback immediately by asking questions of students during the lecture and encouraging them to ask if they don't understand part of the lecure. While I hope to maximize that aspect with two-way audio during the lectures, clearly it will be harder for me to assess whether a particular topic is harder for students to grasp. Homework and Office Hours will be the means for me to get that feedback.

Office Hours will be the hardest part to implement. In Fall of 2004 I taught the graduate Complex class using MacNerney's notes and a modified Moore method, with I believe good success. A crucial component of the course was my office hours - which often amounted to ten hours per week, on that course alone. It was important that students were able to come to my office and run a proposed argument by me on the board. Clearly, things will be different this semester, but I hope that with the use of Yahoo Messenger,MS Messenger and the whiteboard application, and the Discussion/Chat features of WebCT, we will be able to share the visual information that is so important in mathematics. If nothing else, you can scan your question as a .pdf file, email it to me, and we can both have the same document in front of us, as we talk over the phone. There may be rough edges at first, but I belive we can make it work.

Grading: The grading will consist of 70% homework, 15% Take Home Mid Term exam, and %15 Final Research Project (This is tentative and the weighting could chang slightly.).

Dates to Remember:

• January 17, Tuesday -- First Day of Classes

MAT 5023 Problem Solving Seminar 7:00-8:15pm BB 3.04.08

Textbook: The Shape of Space, Second Edition, Jeffrey R. Weeks, ISBN 0-8247-0709-5.

Homework Assignments:
Assignment 0 Review Lecture 0; answer the questions listed at the end of the first page - you can begin looking at the questions on groups (these won't figure directly into the course material until perhaps the end of the semester, but will give me an idea of your background as you begin the course. The first page is most important.) Familiarize yourself with WebCT, write down your math background - a list of the math courses you have had - and how you might use what you learn about curves/surfaces in this class, scan it, and send it as a .pdf file to me under WebCT.

Assignment 1 A gentle introduction to surfaces and their representations.
Assignment 1 Solutions

Assignment 2 Determine which letters of the alphabet are topologically equivalent. It will be easiest if you use the Roman alphabet with all caps - say Helvitica font - to avoid letters like "i", but the principles will be the same. For each equivalence class you should include a paragraph or discussion of why the members of that class are equivalent.

Lectures as PDF files. (Some are LaTeXed typeset notes, some handwritten and scanned; on occasion when I spend the hour plus on review and questions, there will not be a set of formal notes for that day - you must get them by reviewing the realplayer file under WebCT.)
Lecture 1  Tuesday, January 17
Lecture 2  Thursday, January 19
Lecture 3  Tuesday, January 24
Lecture 4  Thursday, January 26
Lecture 5  Tuesday, January 31
Lecture 6  Thursday, February 2
Lecture 7  Tuesday, February 7
Lecture 8  Thursday, February 9
Lecture 9  Tuesday, February 14
Lecture 10  Thursday, February 16
Lecture 11  Thursday, February 21
Lecture 12  Thursday, February 23
Lecture 13  Thursday, February 28
Lecture 14  Thursday, March 2
Lecture 15  Thursday, March 7
Lecture 16  Thursday, March 9
Spring Break!

MAT 6973 Special Topics: Mathematics of Imaging 5:30-6:45pm BB 3.04.08

Textbook: Introduction to the Mathematics of Medical Imaging, Charles L. Epstein, ISBN 0-13-067548-2.

Homework Assignments:
Assignment 0 Review Lecture 0 and make sure you are familiar with the ideas of vector space, inner product, norm, improper integrals, and projections. Familiarize yourself with WebCT, write down your math background - a list of the math courses you have had - and what areas of imaging are most interesting to you, scan it, and send it as a .pdf file to me under WebCT.

Assignment 1 First Assignment is a review of ODE. You may need to get a copy of a standard textbook such as Boyce and DiPrima and review the chapters on Initial Value Problems and Boundary Value Problems.
Assignment 1 Solutions

Assignment 2

Lectures as PDF files. (Some are LaTeXed typeset notes, some handwritten and scanned; on occasion when I spend the hour plus on review and questions, there will not be a set of formal notes for that day - you must get them by reviewing the realplayer file under WebCT.)
Lecture 1  Tuesday, January 17
Lecture 2  Thursday, January 19
Lecture 3  Tuesday, January 24
Lecture 4  Thursday, January 26
Lecture 5  Tuesday, January 31
Lecture 6  Thursday, February 2
Lecture 7  Tuesday, February 7
Lecture 8  Thursday, February 9
Lecture 9  Tuesday, February 14
Lecture 10  Thursday, February 16
Lecture 11  Thursday, February 21
Lecture 12  Thursday, February 23
Lecture 13  Thursday, February 28
Lecture 14  Thursday, March 2
Lecture 15  Thursday, March 7
Lecture 16  Thursday, March 9
Spring Break!

Transfer Point for Real Player video files:
(These are available through WebCT)
Lecture 9 Video February 14, Mat6973