Math 221 - Introduction to Linear Algebra

Spring 2023 - Syllabus - Matthias K. Gobbert

This page can be reached via my homepage at http://www.umbc.edu/~gobbert.

Basic Information

Instructor: Matthias K. Gobbert, gobbert@umbc.edu, office hours Tuesdays and Thursdays 09:00-09:50 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
- Please see this webpage for UMBC Syllabus Language for Equity and Inclusion.
- Please see this Google doc for UMBC Policies and Resources during COVID-19.
Classes: online, Tuesdays and Thursdays, 01:00-02:15, in Class Collaborate; see the detailed schedule for more information on the coverage, due dates, and timing of the synchronous class meetings.
Notice 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 in a flipped classroom format. This means that the contents is delivered asynchronously by the excellent textbook and online by taped videos of my lectures that you study before our synchronous 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 to five students. These groups will be set up in Blackboard to facilitate the submission of group work. 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 Class Collaborate, which is included with Blackboard, see below and note on recordings. We will also have presentations by students on their 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, get to know each other better, have a demonstrated record of using the tools of online learning, and more.
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.
Required prerequisites: a grade of C or better in Math 151 or Math 155; or instructor approval
This book is excellent and required for study before class. David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and Its Applications, 6th edition, Pearson, 2021. The class will use the Pearson's MyLab software, which comes with both the eText and the interactive textbook. You will access MyLab via the course's Blackboard Ultra shell.

Grading rule:

Participation	Homeworks	Quizzes	Test 1	Test 2	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 recorded lectures 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. This grading category will be implemented by Blackboard's automated Attendance tool. To reiterate: As our contents delivery is through my recorded lectures, you are required to study them completely. since they are what a live lecture would be in a lecture format. You are required to study them before class, along with any other reading or preparatory activities, so that we have a common starting point and since you cannot learn actively and with others in the class meetings, if you are not prepared. If you have any concerns about this, see the note above.
The online quizzes are administered in the MyLab system. The detailed schedule indicates the planned due dates of these online quizzes.
The homework assignments will be posted in are administered in the MyLab system. The detailed schedule indicates the planned due date of each homework. 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, we will work on the homework about the associated taped lectures on that topic in class. You should then complete the homework afterwards, 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, due to the organizational difficulties associated with the communication with the grader. Homework 0 is required of all students and is accepted late.
The tests and final exam are administered in the MyLab system. 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 (including homework, lesson plans, PDF transcripts, handouts), for links (to tapings of lectures), for submission of homeworks, quizzes, and exams, and for the synchronous class meetings using Class Collaborate. All meetings will be taped and will be available in Blackboard; see full note on recordings below. 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 and Gradebook the ones we will use. The link to Class Collaborate is on the left of the screen, and its recordings will appear a while after class by following the three dots "..." to View all recordings. 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. 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

Linear Algebra deals with problems that are posed in terms of matrices, which are rectangular arrays of numbers. Typical problems include systems of linear equations and eigenvalue/eigenvector problems. The course also introduces the concepts and properties of vector spaces to demonstrate the rationale and power of mathematical abstraction. Linear Algebra is used in just about any scientific field, for instance, economics, engineering, statistics, and, of course, mathematics itself.

This course will develop both a proficiency with the terminology and calculation techniques of Linear Algebra and with the underlying concepts and their use to solve problems. This approach reflects the fact that it is both the calculation techniques and the fundamental concepts, including the language of Linear Algebra itself, that are ubiquitous in the application areas.

Learning Goals

By the end of this course, you should:

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

To provide some context of the more formal learning goals above, I am sharing some deeper thoughts how we fit into the grander scheme of things. The rationale of a state university is to provide a well-educated workforce to the companies in the State of Maryland as well as to the state and local governments themselves. On a fundamental level therefore, you need to able to learn new material as well as have demonstrated evidence of this ability. These are the fundamental purposes of university courses. This requires us to engage in the learning itself and its demonstration; I am trying to say that it is not the solution to a problem that we are after, and in broader thinking it is not even the solution process, but it is your active struggle to learn that we must encourage. This leads me to the following philosophical grade rubric: To earn a passing grade, you need to solve the problem correctly. To earn a good grade, you need to solve the problem correctly and present the solution process completely and professionally. To earn a very good grade, you need to do these and additionally prove that your solution is correct. This rubric comes from the fact that neither you as customer would be willing to accept a faulty solution or unprofessional or incomplete presentation, nor would the companies in the State be served by faulty solutions. These are some of the guiding principles behind my teaching.

Note on Recordings and Their Publication

This class is being audio-visually recorded so students who cannot attend a particular session and wish to review material can access the full content. This recording will include students' images, profile images, and spoken words, if their camera is engaged and their microphone is live. Students who do not consent to have their profile or video image recorded should keep their camera off and not use a profile image. Likewise, students who do not consent to have their voice recorded should keep their mute button activated and participate exclusively through alternative formats such as email or the chat feature (where available).

UMBC Statement of Values for Academic Integrity

Academic integrity is an important value at UMBC. By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. Consult the the UMBC webpage on Academic Integrity at academicconduct.umbc.edu for the UMBC Undergraduate Student Academic Conduct Policy for undergraduate students and the UMBC Graduate School's Policy and Procedures for Student Academic Misconduct for graduate students.