Math 430 - Matrix Analysis

Basic Information

• Instructor: Matthias K. Gobbert, gobbert@umbc.edu, office hours Tuesdays and Thursdays 11:30-12:30 in MP 416 in-person, by appointment online, or by e-mail.
  Dr. Gobbert has accumulated extensive experience in teaching with state-of-the-art technology. Since participating in the first cohort in the Alternative Delivery Program (ADP) in 2006, he uses hand-writing on tablet laptops for all lectures. These lectures are taped and hosted online for streaming, with the added benefits of allowing for pausing, rewinding, and reviewing. Using the taped lectures for contents delivery, Dr. Gobbert uses a team-based active-learning teaching model, in which students work on problems in learning groups during class. Since 2019, his classes use online comprehension quizzes on the lectures and fully online submission of all assignments, complete with online grading. Since starting online teaching full-time in 2020, the synchronous class meetings are used additionally for student presentations to maximize active student engagement. In 2010, Dr. Gobbert received the University System of Maryland Board of Regents' Faculty Award for Excellence in Mentoring.
• This syllabus consists of this frontpage and the sub-pages
  • detailed schedule,
  • general rules and procedures including grading guidelines, and
  • The official ECR website is part of this syllabus.
• Classes: Tuesdays and Thursdays, 01:00-02:15, in SOND 409; see the detailed schedule for more information on the coverage, due dates, and timing of the synchronous class meetings.
  Note on time commitment: Notice that in a regular semester, you are supposed to spend about 10 to 12 hours per week on this course. If you cannot devote this time, consider if you want to be in this course.
  This course will be taught as a reading class. This means that you need to study the textbook ahead of class and be ready to discuss its contents in our class meetings. The synchronous class meetings will use a team-based active-learning teaching model, in which students work on problems in learning groups formed by the instructor with the help of the instructor.
  Learning groups: I will form learning groups of about four students. These groups are strongly encouraged to also communicate outside of class.
  Synchronous class meetings: Our synchronous class meetings are an opportunity for active teamwork with your learning group, while the instructor is available immediately for questions. These meetings will take place in-person in the classroom. We will also have presentations by students on homework solutions in the synchronous class meetings. This and the other strategies above are designed to foster student engagement as well as give you chances to participate more actively and to get to know each other better.
  If you have any concerns about any of these items, such as concerns about adequate internet connection, about team work, or special needs related to learning styles, please reach out to me as soon as possible, so I can clarify questions and/or we can work out alternate appropriate approaches and metrics. My goal is definitely that anyone can participate successfully in this course, even if you might need to do it completely asynchronously, but we need to communicate about this.
• Prerequisites: a grade of C or better in Math 221 Linear Algebra, Math 251 Multivariable Calculus, MATH 300 Introduction to Mathematical Reasoning, Math 301 Mathematical Analysis I, or consent of instructor.
• These books are available as hardcover as well as eTexts. You need to have at least the required textbook available in class.
  • Required textbook: Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, 2nd edition, SIAM, 2023. Webpages of the textbook (SIAM Book Code OT188, ISBN 978-1-61197-743-1, eISBN 978-1-61197-744-8) https://epubs.siam.org/doi/10.1137/1.9781611977448 and the Study and Solutions Guide (SIAM Book Code OT189, ISBN 978-1-61197-745-5, eISBN 978-1-61197-746-2) https://epubs.siam.org/doi/10.1137/1.9781611977462.
    The publisher SIAM gives you a 20% discount for buying this book, since it is adopted as required textbook. But there is an even better option: Our department has a SIAM Student Chapter. If you join SIAM, which is free of charge to you, through our student chapter, you become a (student) member of SIAM. Buying any SIAM book as a member gives a 30% discount. I would recommend to proceed in this way. You will then also get invited to activities of our student chapter, which is great for meeting other students and faculty.
    The link to join SIAM is www.siam.org/membership. You will have to create an account. To join for free, you have to select UMBC as institution; there is a detailed FAQ item on how to do this: on this Membership page, next to Join and Renew, click on Member FAQ. Then scroll down to and expand the subheader "How do I get a free student membership online?" We are in the list as UNIVERSITY OF MARYLAND BALTIMORE COUNTY. After joining, you can order the textbook from the above textbook page with the member discount.
  • Textbook from Math 221 Linear Algebra as reference: David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and Its Applications, 6th edition, Pearson, 2021. Any recent edition should suffice.
• Grading rule:
  

  Participation	Quizzes and Homeworks	Test 1	Test 2	Test 3	Final Exam
  10%	10%	20%	20%	20%	20%

  • Active participation is the key to success in any class, mathematics or otherwise. This category gives you credit for all associated activities including studying the textbook completely, preparing for the synchronous class meetings as assigned, the active participation in team work, the participation in synchronous class meetings, and adequate professional behavior in all aspects of the course, such as communicating with the instructor, team mates, respectful behavior in communications, and timely submission of work, for instance.
  • The homework assignments will be posted in the Blackboard site of our course, see below. The detailed schedule indicates the planned due date of each homework, but the Blackboard assignments list the official due dates and times. Working the homework is vital to understanding the course material, and you are expected to work all problems. In the flipped classroom format of this course, you should work on the homework about the associated textbook sections before class. We will then compare and complete the homework in class, and it is then due before the start of the next topic. Late submission of homeworks, except Homework 0, cannot be accepted under any circumstances. Homework 0 is required of all students and is accepted late. The team work in this class is educational in nature, meaning that each and every student has to solve each and every problem; the work is not split up and credit is only given to team members who actively participate (and in particular only if you are present). The detailed schedule indicates the planned due dates of some quizzes, but the Blackboard assignments list the official due dates and times. There will also be in-class quizzes using learning groups formed by the instructor. For instance, they may be designed to initiate class discussion or to give me feedback on your learning. They may be technical or non-technical in nature. A Quiz 0 will be given on some material that is critical to your success in this class.
  • The tests and final exam are conventional pencil-and-paper exams. To help you focus on what is relevant, they are closed-book and closed-notes. See the detailed schedule for the dates of the exams.
  Additional details or changes will be announced as necessary. See also general rules and procedures for more information. Announcements may be made in class, by e-mail, or in Blackboard. You are responsible for checking your UMBC e-mail address sufficiently frequently.
• We will use the course management system Blackboard Ultra for posting of all material and for submissions. Notice that Blackboard Ultra is the new version of Blackboard that is more mobile friendly. The main navigation buttons are arranged along the top of the screen, with Content, Announcements, and Gradebook the ones we will use. I will also use Blackboard to send Announcements to the class, which goes to your UMBC account by default. Therefore, you must either check your UMBC e-mail regularly or have the mail forwarded to an account that you check frequently. You should have your notifications in Blackboard turned on! Do not use Blackboard to message me, since I may not find it in a timely fashion; rather use conventional e-mail to my UMBC address listed above.

Course Description

The intent is to teach this course as a deepening of the coverage of Math 221 Linear Algebra. To this end, I will make complete review material of that course available and we will beging by summarizing that material. We will build on that by studying the required textbook of this course and practicing solving problems together. Note that there is a complete Study and Solutions Guide available, which can provide useful starting ideas and a final check, but additional details will be needed for successful homework submission.

Learning Goals

• understand and remember the key ideas, concepts, definitions, and theorems of the subject. Examples in this course include linear dependence and independence, the concept of a vector space, eigenvalues and eigenvectors, and the rank theorem. More broadly, you should also understand the purpose of linear algebra.
  --> This information will be discussed in the lecture. You will apply and use them on homeworks, quizzes, and exams.
• be able to apply mathematical theorems and computational algorithms correctly to answer questions, and interpret their results correctly, including potentially non-unique solutions or breakdowns of algorithms. Examples include choosing among several methods to solve a problem and how to react to intermediate solutions found that may indicate a breakdown of the method.
  --> The class discussions, homework, and exams address these skills.
• appreciate the power of mathematical abstraction and understand how mathematical theory is developed. Classical example of mathematical abstraction in this class are the existence and uniqueness theorem for systems of linear equations and the axiomatic definition of a vector space which is done in abstract generality after observing that the axioms hold true concretely for vectors in the special case of Rⁿ.
  --> These integration goals will be supported by the lectures.
• have experience working actively with peers in a group, both on the scale of the class and in a smaller team. 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 for homework and exams.
  --> Group discussions and quizzes will contribute to this goal.
• have gained experience with a wide variety of teaching and learning techniques, with the goal of encouraging life-long learning.
  Examples of teaching techniques include: the use of recorded lectures (that are to be studied before class meetings), the pedagogical technique of a flipped classroom (where we work actively), the user of team-based learning (where you work with peers), and more.
  Examples of learning techniques include: learning by reading (e.g., assigned reading before class meetings), learning by hearing (e.g., voice-over in recorded lectures or verbal discussions in class meetings), learning by writing (e.g., answering interpretative questions that require long-hand English answers), learning by talking (e.g., verbal presentations to class), and more.
  The reflection on your use of study techniques is a declared learning goal of this course, since it is vital to recognize one's own strengths and weaknesses for best success in live-long learning.
  -->All aspects of the course will serve as examples.

Philosophical Underpinning

Other Information

• The recommended literature on my homepage
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• How to get started with Matlab at UMBC (maintained by CIRC)
• An introduction to LaTeX gives some pointers how to get started with LaTeX, has a small sample document as well as a larger Template for Project Reports.

• UMBC High Performance Computing Facility (HPCF) including general information, list of projects, publications page, and resources for users.
• Center for Interdisciplinary Research and Consulting (CIRC)

UMBC Statement of Values for Academic Integrity