Math 630 - Matrix Analysis

Learning Goals

• understand and remember the key ideas, concepts, definitions, and theorems of the subject. Examples include matrix factorizations (e.g., LU or SVD), finite-precision arithmetic, vector and matrix norms, and convergence theorems. More broadly, you should also understand the purpose of numerical linear algebra and some of its major applications and methods.
  --> This information will be discussed in the lecture as well as in the textbook. You will apply and use them on homework and tests.
• have experience using a professional software package, writing code in it, and understanding how some of its functions work. We will focus on the package Matlab in this course, which is the most popular package in mathematics and many application areas. Writing code in this context includes the requirements to deliver code in a form required, such as writing code to stated specifications, using a requested method, complying with a required function header, etc. The knowledge and skills in this item are valuable job skills, which justifies the emphasis here. To the same end, I suggest that you use this opportunity to gain significant experience with the Linux operating system.
  --> This is one of the purposes of the homework and most learning will take place here.
• have some experience how a research paper looks like and foundational experience in writing a professional-grade report in Mathematics. Reading a paper will give you exposure how a professional report should look and sound like. Learning from written material is a crucial skill to develop over time, thus the requirement of reading the textbook ahead of class and the fact that you are responsible also for material not discussed in class in detail. More specifically, you need to learn how to obtain information from research papers, thus there will be a first exposure to research papers. You will then use your observations about structure and style of these papers to write a technical report yourself and gain experience with the process of receiving feedback, editing and revising, and re-submitting. On a technical level, writing the report should expose you to the relevant software in this field, therefore, the use of the typesetting system LaTeX is required for full-time Mathematics students.
  --> I will supply some papers carefully selected for their readability and relevance to the course. The writing, giving and receiving feedback, and editing of the report will take place during the second half of the semester.
• have experience working with peers in a group. Group work requiring communication for effective collaboration with peers and supervisors is a vital professional skill, and the development of professional skills including this networking is a declared learning goal of this course. Additionally, getting to know other students as part of learning groups will prove invaluable on the homework, for the tests in this class, and in preparing for comprehensive exams, and more generally for success in a graduate program. In this spirit, it also a stated goal to help identify the skills needed to be first a successful graduate student and then a responsible scholar in Mathematics.
  --> The groups will be assigned by the instructor and used for group quizzes in class, but also for other group work. We will discuss the skills and expectations explicitly in class, but you should also try to learn by observing your peers and the instructor.