Math 221 Course Webpage

Linear Algebra and Applications

Fall 2020, 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
      13:45 – 15:00, LSRC B101 "Love Auditorium" (Section 01)
      13:45 – 15:00, online (Section 02)

Discussion sections (mandatory): depends on your selection at registration
      Mondays 12:00 – 12:50 (Section 01D), Prof. Hain
      Mondays 13:45 – 14:35 (Section 02D), Prof. Hain
      Mondays 15:30 – 16:20 (Section 03D), Prof. Hain
        Days and times TBD    (Section 04D), Prof. Myer

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
Office hours: Tuesdays and Thursdays, 15:00 – 16:30, by Zoom

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

• 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.
  • Keep your distance from others: six feet. Even when you are entering or exiting the classroom; don't gather by the door.
  • 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!
• Lectures and discussion sections will be live-streamed via Zoom.
• Students are expected to attend lecture live, either in person or online as corresponds with their officially registered section.
  • Attendance in lecture is a baseline for class participation grades, which can enhance or detract from homework grades, although earning real credit along these lines requires contribution to in-class discourse.
  • Occasional absence for expected sorts of circumstances are of course not penalized.
  • Students registered for in-person lectures can attend live online if they are quarantined or otherwise incapacitated.
• Your video should remain on by default during discussion section and (if you are online) during lecture.
  • The classroom experience, be it discussion or lecture, 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.
  • There are reasons to turn your video off, particularly if you have issues with your internet connection, your working space, or other external factors. But in general everyone should do their best to participate visually.
• During exams, your video is required to be on unless you have a specific justification for turning it off. For reasons of privacy you won't be asked to detail the justification, but without video, alternate arrangements may need to be made for proctoring.
• Lectures will be recorded and uploaded to the class Sakai website.
  • These recordings are required for rare circumstances in which students must temporarily participate in lecture asynchronously.
  • Posting will ordinarily occur within 24 hours. It takes Zoom time to process video, it takes time to upload large files, and the instructors have daily responsibilities that might prevent them from uploading immediately.
• Nobody is permitted to share any video of anybody else from any portion of the class, including the discussion sections, with parties outside of the class.

Assignments

• Weekly homework will be collected and graded via Gradescope
• There will be two in-class midterm exams:
  • Tuesday 29 September
  • Tuesday 10 November
• There will be a final exam:
  • 14:00 – 17:00 Sunday 22 November
• 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 at 17:00, two hours after the following Tuesday's class.
• Late homework will not be accepted.
• 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.
• Collaboration on homework is encouraged while you discuss the search for solutions, but when it comes time to write them down, the work you turn in 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 books or notes and without giving or receiving help from others.
• Students are expected to adhere to the Duke Community Standard. You must reaffirm your committment to these standards on all work.
• 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 student will receive a score of zero for that assignment, and the instructor reserves the right to further reduce the final grade for the course by one or more letter grades—possibly to a failing grade—at the discretion of the instructor.
• Computer policy: You may use a computational aid for the homework but I recommend avoiding it as much as possible, particularly since electronic devices of all sorts are not allowed on quizzes, in-class exams, and the final exam. Portable electronic devices that are visible or audible during exams will be confiscated until the exam period ends.
• 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 sentences.
• The logic of a proof must be completely clear for full credit.

Homework 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.

Grading scheme

• 15% Discussion section
• 15% Homework
• 20% Midterm #1
• 20% Midterm #2
• 30% Final exam

Links

• list of all courses given in the Math Department in Fall 2020.
• final exam schedule for all Duke courses.
• Official University calendar for academic year 2020–2021.
• 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 policies concerning academic dishonesty and related matters.
• What to do in an emergency
• Duke|ALERT
• Duke Community Standard
• Duke Compact

• Ezra Miller's Math homepage
  
• Ezra Miller's personal home page
  
• 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
Thu Nov 12 04:47:05 EST 2020