This course is about Linear Algebra. It is a condensed version of the undergraduate course that is taught each semester here at Johns Hopkins. In the span of 8 weeks, you'll learn what is typically taught in a 14-week introductory course!
As a subject, Linear Algebra is remarkable because its theory has been worked out and its basic problems can be explicitly solved. Because of this, the subject serves as reliable tool for a wide variety of disciplines: pure mathematics, data science, physics, computer science, economics, engineering, etc. Practitioners of those subjects can often solve problems germane to their disciplines by rephrasing them as linear algebra problems. The role of this course is to teach you how to solve those problems.
Managing Your Schedule. This course is designed to accommodate you — a diverse group of students, with varied schedules, who are located all over the globe. There will be no mandatory events which require your attendance at a particular time for this course. Instead, you will design your own schedule. Each Sunday, I will release all of the content for the upcoming week simultaneously. You are free to choose how to complete that week's work in way a that best fits your schedule. The typical week's content will consist of:
It is highly recommended that you fix a weekly schedule (like you would have in a typical, in-person class) and follow it for the duration of the course. Redesigning your schedule each week in an ad hoc manner can wear you down in ways you may not be consciously aware of. Because of the accelerated pace of this class, the average workload for this course will be around 12 hours per week.
Fighting Isolation.
This class has no classroom. So we will have to work to build a community online. I encourage you to do the following:
In class, we all benefit when someone asks a question or makes a comment. Think of posting to the forum as the online version of raising your hand and speaking out loud in class. I encourage you to post your questions or just discuss the course content in general. The TAs and I will check the discussion forum regularly and contribute. Note that this forum allows you to post and answer anonymously, and you should do that if that makes you feel more comfortable.
In a physical classroom, there is a lot of non-verbal communication. In an online environment, you will need to be more explicit. We will (usually) not know about an issue unless you tell us. Please do not hesitate to send us an e-mail (or post a concern to the discussion board).
I will leave this one up to you. It's nice to have a place to talk that's just students. In the past, students in this class have spearheaded a group chat.
Linear Algebra with Applications, Fifth Edition, Otto Bretscher. ISBN: 978-0321796943
Your grade for this course will be computed as the weighted average of 8 weekly homework assignments (20%, lowest HW grade dropped), 7 weekly quizzes (20%, lowest quiz grade dropped), a midterm exam (20%), and a final exam (40%).
Exams. There will be two exams in this course: a midterm exam and a comprehensive final exam. These exams are comparable to the exams which are typically given in the semester-long course. In particular, the midterm is designed to be completed in 50 minutes, and the final is designed to take 2 hours. Because there are complications inherent to online testing, the time limits on the exams have been extended to 90 minutes and 4.5 hours, respectively.
Both exams will be conducted through Blackboard. The exams will each be available for several days; please, take them at a time that best fits your schedule.
| Exam | Availability Window | Time Limit | Midterm Exam | Thursday, July 2 at 6 A.M. ET – Monday, July 6 at 6 A.M. ET | 90 Minutes | Final Exam | Thursday, July 30 at 6 A.M. ET – Saturday, August 1 at 6 P.M. ET | 4.5 hours |
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Quizzes. Each week, there will be a quiz on the content from that week's learning module. You may complete the quiz at any time during the week before 11:59 P.M. ET on Sunday. The quiz is designed to take 15 minutes, and you will be given a 40 minutes to complete it. You may take the quiz up to two times, and your highest score will count as your quiz grade for that week.
Proctoring. Exams and Quizzes will be proctored via the Respondus browser and Respondus monitor. Instructions on how to install and use the browser can be found here. The use of textbooks, notes, and other outside resources is not allowed on quizzes and exams. You may use blank, lined or unlined paper for computations during these assessments. Following the completion of each exam or quiz, please scan your scratch-work and upload it to Blackboard as a PDF. We will use this work to award partial credit.
The primary instruction in this course will be delivered via video lectures. Each video lecture will consist of a series of short videos which together cover the content normally delivered in a 50 minute class. One advantage of this course is that you do not need to absorb the content of a 50 minute lecture all at once. Space out your viewing of these short videos in a way that best fits your schedule and learning style.
There will be three to four video lectures posted each week.
This outline of this course is as follows:
| Learning Module | Chapter Covered | Week 1 | Solving Systems of Linear Equations | Chapter 1 | Week 2 | Linear Transformations | Chapter 2 | Weeks 3 – 4.5 |
The Vocabulary of Linear Algebra and the Rank-Nullity Theorem |
Chapter 3 | Week 4 | Midterm Exam | Weeks 4.5 – 5 & 5 |
Orthogonality and Least-Squares | Chapter 5 | Week 6 | Determinants | Chapter 6 | Week 7 | Eigenvalues and Eigenvectors | Chapter 7 | Week 8 | The Singular Value Decomposition | Chapter 8 |
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This course will have weekly homework assignments which will be released each Sunday. Homework will consist of both an individual and group component. Both components will be due by 11:59 P.M. ET on the following Sunday.
The problems assigned will be similar to those given in the normal semester course. To help you organize your week, I will break down the homework set by video lecture. The problems that are more conceptual in nature will comprise the group homework. It is highly encouraged that you space out your homework throughout the week.
Show your work. It's important to show both your work and your reasoning in your homework solutions. To see how to write complete answers, please read the solution guide.
Homework Groups. Beginning the second week of class, you will be placed in a group with three of your fellow classmates. With this group you will complete the group component of the homework. It will be up to you to choose when and how to meet.We will offer certain office hours that are specifically designated as time to work with your group. Groups who would prefer to work under the guidance of an instructor should come to these office hours. You'll be given a breakout room and help (if you need it).
Collaborate! You are encouraged to talk to your classmates about the material covered in class and collaborate on all parts of the homework. However any of the individual component of your homework must be primarily your own work. To avoid the pitfalls of plagiarism, please write up this portion of your assignment alone and independently. If you've worked on a problem with another student, please acknowledge that collaboration in your write up.
Use of online solution banks is prohibited and will be considered a violation of the ethics code.
TBA.
Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at least one week prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.
There may be a student in this class who requires the services of a note taker. This is an opportunity to share notes through the Student Disability Services Office. If you are interested in performing this service, please register as a notetaker with Student Disability Services.
"Undergraduate students enrolled in the Krieger School of Arts and Sciences or the Whiting School of Engineering at the Johns Hopkins University assume a duty to conduct themselves in a manner appropriate to the University's mission as an institution of higher learning. Students are obliged to refrain from acts which they know, or under circumstances have reason to know, violate the academic integrity of the University. [The JHU Code of Ethics]"
Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.