Math 221 Course Webpage

Linear Algebra and Applications

Fall 2024, Duke University

General information

Goal: Students will become proficient in both using and understanding the theory and algorithms of linear algebra and will learn how to write rigorous mathematical arguments.

Lectures: Tuesdays and Thursdays
      11:45 – 13:00, Physics Building 259

Text: Linear Algebra: A Geometric Approach, by Ted Shifrin and Malcolm Adams, second edition.
In past semesters, this textbook has been available for 3-hour checkout at the Duke Libraries; search the Libraries' Top Textbooks program.

Contact information for the Instructor

Name: Professor Ezra Miller
Address: Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Email: ezramath.duke.edu   —   this is the primary mode of contacting me!
Zoom: https://duke.zoom.us/my/ezra.miller
Webpage: https://math.duke.edu/people/ezra-miller
Course webpage: you're already looking at it... but it's https://services.math.duke.edu/~ezra/221/221.html
Canvas site: available to registered students via Duke NetID
Office hours: Tuesday, 13:00 – 14:15
                        Thursday, 13:00 – 14:15

Help Room

Emergency procedures

Course description

Goal: Students will become proficient in both using and understanding the theory and algorithms of linear algebra, and they will learn how to write rigorous mathematical arguments.

Course content: Chapters 1 – 7 of the course text, by Shifrin & Adams
Most items constitute one lecture each; some fill two lectures:

• vectors
• n-dimensional geometry
• Gaussian elimination
• linear systems
• matrix algebra
• linear transformations
• elementary matrices; transpose
• linear subspaces
• linear independence
• bases; dimension
• abstract vector spaces
• inner products
• projections; least squares
• orthonormal bases; Gram-Schmidt algorithm
• changes of basis
• abstract linear transformations
• determinants
• formulas for determinants
• eigenvalues and eigenvectors
• spectral theorem
• Jordan form
• systems of ordinary differential equations (ODE)

Lecture and video policies

• (This item is a hold-over from the pandemic. But the overarching message of respect for health and safety is still valid.)
  Everyone attending class in person, including students and the lecturer, must comply with the Duke Compact regarding health and safety of yourself and others.
  • Keep your mask on at all times, if required.
  • Failure to comply will result in immediate dismissal from the classroom. In particular,
  • kindly remind the lecturer if they are not in compliance, and dismiss them if they refuse to comply!
• Recordings of lectures from Fall 2020 are posted on the Math Department video server. Each video has been edited to delete identifying information of students whose faces (and, alas, names) occasionally appeared onscreen; if you detect identifying information that accidentally remains, please inform the instructor.
• Students are expected to attend lecture live, in person, unless circumstances require lecture to be delivered virtually, in which case attendance online is expected. There is currently no plan to enable hybrid lectures.
  • Class participation can enhance or detract from homework grades. Attendance in lecture is a baseline for participation, which more substantially requires contribution to in-class discourse.
  • Occasional absence for expected sorts of circumstances (e.g., illness, athletic participation, religious holidays) is not penalized.
• Lectures might sometimes need to be held online or with a recording.
  • There will usually be days of advance warning if this step needs to be taken, although in case of instructor illness advance warning might not be possible.
  • Links for these online sessions will be available on the course Canvas page.
  • These links are not to be shared. Sharing can result in class disruptions from unwanted third parties and can constitute a breach of class participants' privacy.
  • Your video should remain on by default during any virtual synchronous lecture. The classroom experience is a communal one. It is dependent on multi-way communication. You should be able to see the lecturer and your classmates, and they should be able to see you.
  • That said, there are valid reasons to turn your video off, particularly if you have issues with your internet connection, your working space, or other external factors. Turn off your video if you must, but in general everyone should do their best to participate visually.

Assignments

• Weekly homework will be collected via Canvas
• There will be two in-class midterm exams:
  • Thursday 10 October
  • Thursday 21 November
• There will be a final exam:
  • 9:00 – 12:00 Thursday 12 December
• Quizzes may be given if homework performance lags.

• Due dates for the homework assignments this semester are listed in the table below.
• You should work on the homework for a section of the book immediately after the class in which it is covered.
• Homework for the book sections covered in a week will be due before midnight on Thursday the following week.
• Late homework will not be accepted.
• Submit your homework solutions using Canvas "Assignments":
      Math 221 Canvas –> Assignments
• Missed quizzes or exams: in general there will be no make-ups, but some accommodation may be possible in one of the following four situations: personal emergencies or tragedies, an incapacitating illness, a religious holiday, or varsity athletic participation. Please visit these web-pages now to familiarize yourself with the procedures.
• Oral collaboration on homework is encouraged while you discuss the search for solutions, but when it comes time to write them down,
• The written work you submit must be yours alone: you are not allowed to consult anyone else's written solution, and you are not allowed to share your written solutions. (It is very easy to tell when solutions have been copied or written together.) If you collaborate, you must indicate—on the homework page—who your collaborators were.
• Collaboration of any sort on quizzes, in-class exams, or the final exam is not permitted: you must work completely independently, without collaborating or consultating human, electronic, or written sources (including but not limited to books or notes) and without giving or receiving help from others. Portable electronic devices that are visible or audible during exams will be confiscated until the exam period ends. It bears repeating that the instructor has a long record of detecting and convicting violations of the Duke Community Standard, resulting in a wide range of sanctions, from grade changes to dismissal from the University. Again, don't test me.
• Students are expected to adhere to the Duke Community Standard. Students affirm their commitment to uphold the values of the Duke University community by signing a pledge that states:
  • I will not lie, cheat, or steal in my academic endeavors;
  • I will conduct myself honorably in all my endeavors;
  • I will act if the Standard is compromised.
  The instructor has a long record of detecting and convicting violations, resulting in a wide range of sanctions, from grade changes to removal from the University. Every case brought by the instructor has resulted in sanctions: I have never lost a case. Don't test me.
• If a student is responsible for academic dishonesty on a graded item in this course, then the student will have an opportunity to admit the infraction and, if approved by the Office of Student Conduct, resolve it directly through a faculty-student resolution agreement; the terms of that agreement would then dictate the grading response to the assignment at issue. If the student is found responsible through the Office of Student Conduct and the infraction is not resolved by a faculty-student resolution agreement, then the sanctions can be severe and, depending on the nature of the infraction, might be out of the hands of the instructor, being instead determined by the Office of Student Conduct or another University body.
• Consulting generative AI is prohibited for all aspects of this course, including homework, midterms, and (if applicable) term projects. Instead of asking a computer, ask a classmate or the instructor.
• Non-AI computation: You may use a non-AI computational aid, such as a computer algebra system, for the homework but it is recommended that you avoid it as much as possible, particularly since electronic devices of all sorts are not allowed on quizzes, in-class exams, and the final exam.
• All submitted work (including quizzes and exams, in addition to homework) must be typeset or written neatly and legibly. On exams, instead of erasing please use a single line crossout; this can sometimes help your score, if what you crossed out turns out to have been correct.
• If a question requires more than a single expression or equation, then your response must be phrased in complete English sentences. Writing mathematics requires as much grammatical rigor as writing about literature or history. Would you write a sentence without a subject or a period in a Philosophy essay?
• The logic of a response to a homework or exam question must be completely clear for full credit.

• If you registered for Math 721 instead of Math 221, then in addition to all of the other work listed on this syllabus, you must submit a term paper of roughly 8 - 10 pages. Parameters for this assignment must be discussed with the instructor starting no later than Fall break.
• Math 721 has an altered grading scheme to take the additional graduate coursework into account.
• Math 721 students are encouraged to contact the instructor as early in the semester as possible to discuss the altered grading scheme as well as the term project.

Homework and lecture schedule

This schedule reflects the current plan, but it is subject to change. The exam schedule, however, is fixed.

If a lecture or assignment hasn't been posted, and you think it should have been, then please do email me. Sometimes I encounter problems (such as, for example, the department's servers going down) while posting assignments; other times, I might simply have forgotten to copy the updated files into the appropriate directory, or to set the permissions properly.

Read and study the text carefully before attempting the assignments. Make sure you fully understand the given proofs and examples. Note that there are examples in the text similar to most of the homework problems. The material in gray shaded boxes consists of definitions; learn them precisely. (Often when students say they do not know how to do a problem it is because they don't know the definitions of the terms in the problem.) The material in blue shaded boxes introduces points of logic and techniques of proof that you will find helpful in writing your arguments. If you have trouble understanding something in the text after working on it for a while, then see me in office hours or e-mail me.

Lecture notes

Lecture videos

Grading scheme

• 20% Homework
• 20% Midterm #1
• 25% Midterm #2
• 35% Final exam

Links

• list of all courses given in the Math Department in Fall 2024.
• final exam schedule for all Duke courses.
• Official University calendar for academic year 2024–2025.
• Academic Resource Center (ARC) for Learning Consultations, Peer Tutoring, Learning Communities, ADHD/LD Coaching, Outreach Workshops, GRE/MCAT Prep, Study Connect, and more.
• Fundamental University definitions and policies concerning academic dishonesty and related matters.
• What to do in an emergency
• Duke|ALERT
• Duke Community Standard

• Ezra Miller's Math homepage
  
• Ezra Miller's personal home page — information there is old; it has barely been updated in the past decade
  
• Duke Mathematics

The fine print

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.

ezramath.duke.edu
Sun Sep 22 17:14:35 EDT 2024