Instructor: Yitzchak Elchanan Solomon (I go by “Elchanan”, “El” is fine too). I’m a postdoc working in geometry, topology, and their applications.
Office Hours: TBD
Textbook: Linear Algebra and Its Applications (5th Edition), by Lay, Lay, and McDonald
Prerequisites: Math 101
Synchronous Meeting Times: MoWe 9:20PM – 10:20PM (DKU Time)
Course Runs: Oct 26, 2020 – Dec 10, 2020
Grading System: TBD
What is this course about?
When you first encountered vectors in multivariable calculus or physics, you learned that they were objects with magnitude and direction. From a physical perspective, that definition is very important. However, from the mathematical perspective, a vector is something that can be added (to another vector) and scaled: these two operations are the algebra of linear algebra. The adjective “linear” refers to a special kind of transformation (or function), one that does not distort either addition or scaling. Thus, linear algebra is the study of vectors and their transformations. What makes this subject so important is that linear transformations are simple enough to analyze and compute, but expressive enough to show up in virtually every area of pure and applied mathematics.
To give a practical example: functions can be added and scaled, and hence can be considered vectors. Differentiaton is a linear transformation, because (f+g)’ = f’ + g’, and (cf)’ = cf’. Thus, the theory of linear differential equations is part of linear algebra. We can therefore apply theorems and computational tricks from linear algebra to solve seemingly difficult differential equations. Another interesting example is 3d graphics: rotating camera angles and projecting a scene onto a particular point of view are both linear transformations, so computers performing these tasks must use linear algebra to make calculations.
What will I learn in this course?
- Using Gaussian elimination to solve systems of linear equations.
- Matrix algebra, the Invertible Matrix Theorem, the Rank-Nullity Theorem.
- Vector spaces and the concepts of linear independence, span, basis, dimension, and subspace.
- The theory of linear transformations and its relation to matrix algebra.
- Compute eigenvalues and eigenspaces, diagonalize matrices.
- Inner products and their applications in geometry and statistics.
- The theory and use of matrix factorizations.
- Writing short proofs in mathematics.
Course lectures will be entirely asynchronous. Each lecture will consist of a YouTube playlist of short videos. Twice a week, there will be a synchronous, recorded session focusing on theory and problem solving. There will be three open-book and open-note exams. The midterms will also be asynchronous, and you will have a 3 hour time period of your choosing to complete them (within a 24 hour range). The TA and myself with have at least 2 hours of office hours a week. Homework will be assigned weekly on Gradescope. There will be a Piazza page for you to discuss the material among yourselves, with oversight and help from myself and the TA.
Week 1: Systems of Linear Equations
Week 2: Matrix Algebra
Week 3: Determinants
Week 4: Vector Spaces
Week 5: Eigenvalues and Eigenvectors
Week 6: Orthogonality and Least Squares
Week 7: Symmetric Matrices and Quadratic Forms
What are some good study practices?
I recommend you read through the book in addition to watching the lecture videos. Whether you choose to read the book before or after the lecture is matter of personal taste: both can be very helpful. In addition to working on homework problems, it is good to do extra practice problems (by yourself or with your peers) on topics you find more challenging. It is also helpful to write notes for yourself as you watch the lectures and read the book, both technical notes on how to solve problems, as well as “big-picture” notes on the different ideas in the course and how they are related.
- Communication with myself and the TAs will happen by email. Content-related questions should be directed towards the Piazza page, administrative questions to myself and the TAs.
- If you need to request accommodation for exams, either to miss/reschedule an exam (due to an emergency) or to have more time, I need you to send me a note from a Dean, and get in touch with me about alternative plans, at least one week before an exam.
- If you are experiencing technical difficulties in submitting homework or exams, you need to reach out to me before the deadline is over, rather than after. I will add a “late submission” deadline for homeworks on Gradescope, to give a buffer zone for technical problems (no points will be taken off). Once the “late submission” deadline is passed, I can no longer help with technical problems, so if you didn’t get in contact with me before the “late submission” deadline, I will not be able to make any accommodations.
- The lowest homework grade will be dropped.
Civility is an essential ingredient for academic discourse. All communications for this course should be conducted constructively, civilly, and respectfully. Differences in beliefs, opinions, and approaches are to be expected. Please bring any communications you believe to be in violation of this class policy to the attention of your instructor. Active interaction with peers and your instructor is essential to success in this course, paying particular attention to the following:
- Be respectful of others and their opinions, valuing diversity in backgrounds, abilities, and experiences.
- Challenging the ideas held by others is an integral aspect of critical thinking and the academic process. Please word your responses carefully, and recognize that others are expected to challenge your ideas. A positive atmosphere of healthy debate is encouraged.
- Read your online discussion posts carefully before submitting them.
As a student, you should abide by the academic honesty standard of the Duke Kunshan University. Its Community Standard states: “Duke Kunshan University is a community comprised of individuals from diverse cultures and backgrounds. We are dedicated to scholarship, leadership, and service and to the principles of honesty, fairness, respect, and accountability. Members of this community commit to reflecting upon and upholding these principles in all academic and non-academic endeavors, and to protecting and promoting a culture of integrity and trust.” For all graded work, students should pledge that they have neither given nor received any unacknowledged aid.
Academic Policy & Procedures:
You are responsible for knowing and adhering to academic policy and procedures as published in University Bulletin and Student Handbook. Please note, an incident of behavioral infraction or academic dishonesty (cheating on a test, plagiarizing, etc.) will result in immediate action from me, in consultation with university administration (e.g., Dean of Undergraduate Studies, Student Conduct, Academic Advising). Please visit the Undergraduate Studies website for additional guidance related to academic policy and procedures. Academic integrity is everyone’s responsibility.
Academic Disruptive Behavior and Community Standard:
Please avoid all forms of disruptive behavior, including but not limited to: verbal or physical threats, repeated obscenities, unreasonable interference with class discussion, making/receiving personal phone calls, text messages or pages during class, excessive tardiness, leaving and entering class frequently without notice of illness or other extenuating circumstances, and persisting in disruptive personal conversations with other class members.
What resources can help me during this course?
Please consult with me about appropriate course preparation and readiness strategies, as needed. Consult your academic advisors on course performance (i.e., poor grades) and academic decisions (e.g., course changes, incompletes, withdrawals) to ensure you stay on track with degree and graduation requirements. In addition to advisors, staff in the Academic Resource Center can provide recommendations on academic success strategies (e.g., tutoring, coaching, student learning preferences). All ARC services will continue to be provided online. Note, there is an ARC Sakai site for students and tutors. Please visit the Office of Undergraduate Advising website for additional information related to academic advising and student support services.
For additional help with academic writing—and more generally with language learning—you are welcome to make an appointment with the Writing and Language Studio (WLS). To accommodate students who are learning remotely as well as those who are on campus, writing and language coaching appointments are available in person and online. You can register for an account, make an appointment, and learn more about WLS services, policies, and events on the WLS website. You can also find writing and language learning resources on the Writing & Language Studio Sakai site.
If you are experiencing technical difficulties, please contact IT:
- China-based faculty/staff/students 400-816-7100, (+86) 0512- 3665-7100
- US-based faculty/staff/students (+1) 919-660-1810
- International-based faculty/staff/students can use either telephone option (recommend using tools like Skype calling)
- Live Chat: https://oit.duke.edu/help
- Email: firstname.lastname@example.org