Math 2600-01: Linear Algebra TR 9:30–10:45pm in SC 1431 Spring 2022 Instructor: Spencer Dowdall Office: SC 1508 Office phone: 615-322-1555 email: spencer.dowdall@vanderbilt.edu Office Hours: Mon 3:00–4:00 (on Zoom) Tue 4:00–5:00 (in-person) Thu 10:45–12:00 (in-person) and by appointment Course Information Description: Linear algebra is an important bridge to more advanced topics in mathematics; it also has widespread applications to the physical and social sciences, engineering, economics, data science and many other fields. Topics to be covered include: vectors spaces, bases, linear transformations, matrices, row operations, determinants, systems of linear equations, eigenvalues and eigenvectors, inner product spaces, and orthonormal bases. Math 2600 also serves an important role in Vanderbilt’s curriculum in that it provides many students their first introduction to abstract and theoretical mathematics. The course will involve rigorous proofs of theorems, and students will be required to understand and reproduce proofs. Assignments and tests will emphasize both proof writing and computational problem solving. For these reasons, Math 2600 is considered to be a very challenging course. Students should be prepared to invest considerable amounts of time and energy in understanding the material and doing the homework. Goals: Learning objectives for this course include: 1) Gaining mastery in the main topics of linear algebra, 2) Learning how to understand and write mathematical proofs, 3) Developing mathematical communication skills, both written and oral, so that you can explain mathematical ideas to other people. Text: Linear Algebra, 5th edition by Stephen Friedberg, Arnold Insel, and Lawrence Spence. We will cover most of chapters 1 through 5 and potentially chapter 6 or 7. Reading the textbook is essential for understanding the material. For a different perspective on the material, I recommend the free textbook Linear Algebra by Jim Hefferon, available at http://joshua.smcvt.edu/linearalgebra/. Course webpage: Accessible via Brightspace here: https://brightspace.vanderbilt.edu/ View the webpage for all course information including this document, current announcements, instructor information, homework assignments, the schedule of topics, selected solutions, and grades. Grading: Final grades will be computed according to the following breakdown: Homework–21%, Quizzes–8%, Participation–8%, Midterms–18% each, Final Exam–27%. Letter grades will not be assigned based on strict percentage cutoffs, but will take into account the overall student performance this semester. Students who earn at least a 90/80/70/60 are guaranteed to receive a final grade of at least an A-/B-/C-/D-, but the final cutoffs may be more generous than this. Midterm Exams: There will be two in-class exams on: Tuesday February 22 and Tuesday April 5. Final Exam: There will be a comprehensive final exam at 9:00am on Wednesday May 4, as designated by the university registrar (see http://registrar.vanderbilt.edu/calendar/exams/). ∗ This document was last updated January 16, 2022 and may already be obsolete. The current version is always available on the course website. Office Hours: I strongly encourage everyone to visit office hours or make appointments to see me. I would love to meet you and learn more about your background and interests. Do not wait until it is too late – small deficiencies in the beginning tend to rapidly escalate! Instructor Availability: Outside of class, I will be available in office hours and by email. For office hours, you do not need an appointment—simply drop in to any scheduled in-person or Zoom office hour. You may also request an appointment outside of scheduled office hours by email, but please use the scheduled office hours first if possible. I try to answer all emails within 2 business days; I may not be available on weekends or evenings. Quizzes: There will be occasional in-class quizzes designed to check basic understanding of the material. These will occur during the first 5–10 minutes of class, so it is important that you arrive on time. Your lowest quiz score will be dropped. Make-up policy: There will be no make-up exams or assignments. It is your responsibility to arrange your schedule accordingly and complete all work on time. Graded items that are missed due to illness or other extraordinary circumstances must be adequately documented and, except in genuine emergencies, must be approved by the instructor in advance. In cases where some graded item is excused, other graded items will be given more weight when determining final grades. Group work: We will periodically use class time to break into small groups in which students will collaborate on worksheets. This will allow you to practice doing mathematics and develop skill in constructing proofs and explaining your reasoning to others. During the group work sessions, a few students may be selected to present their group’s solutions to the class. Collaborating on the worksheets and presenting to the class will count towards the Participation portion of final grades. Homework: Homework assignments will be announced in class and posted to the course webpage. Assignments will generally be due at 6pm on Thursdays. Solutions should be neat and legible and will be submitted online via Gradescope. To submit on Gradescope, you can either create your solutions electronically (e.g., by typing or writing on a tablet), or else scan hand-written paper solutions with a physical scanner or scanning app like Camscanner or Genius Scan. Access Gradescope via the link in our course Brightspace page (so that your submissions are synced correctly). You are encouraged to work together in groups and discuss homework problems with other students, but your solutions must be written up independently and in your own words. Copying answers from another student or source, or allowing your answers to be copied, is a violation of the Honor Code. I consider homework an essential part of this class. It is often said that the best way to learn mathematics is to do mathematics. To succeed in this class you should take the homework seriously and think carefully—and independently—about each problem. You should also study any distributed solutions and be sure that you understand them. Doing additional exercises is recommended. Late homework policy: To accommodate eventualities that may prevent you from completing an assignment on time, each student is allotted two 3–day homework extensions. To utilize a homework extension, you must email the instructor before the submission deadline to officially request the extension. Outside of these extensions, late homework submissions will be penalized as follows: • • • • within 18 hours of the submission deadline: 10% off within 30 hours of the submission deadline: 20% off within 78 hours of the submission deadline: 40% off later than 78 hours after the submission deadline: at this point solutions will be posted to the course website and submissions will no longer be accepted. Mezzanine Students: Graduate students registered for the 5600-level of this course will be required to do an additional project that explores and develops an advanced topic in linear algebra. Details of the project will be arranged individually with each 5600-level student. Attendance: Attendance is very important for this class, as it will help you better understand the material. I strongly encourage you to actively participate by asking questions and engaging in class discussion. I also encourage you to read the text in advance as this will allow lectures to be more interactive and focused on the topics you find most challenging. Students are expected to attend all scheduled classes and are responsible for all announcements, assignments, and material covered in class. Consult the daily schedule on the course webpage for the list of sections to be covered. See Vanderbilt’s ‘Class Attendance’ policy in the Undergraduate Catalog. Technology Policy: Please do not use cell phones or computers in class (except to take notes or access the text etc). It is distracting. You may not use calculators or any other electronic devices for tests. While I do not recommend you rely on computers, you may use calculators or advanced computer programs (I recommend Sage) to guide your way or check answers in homework problems. However, your solutions should be self-contained and must demonstrate an understanding of what’s going on. And remember that on exams you will have to work without computational aids. Registration deadlines: The last day for students to add a math course in YES is Monday, January 24th. After this date students will not be permitted to add a math course or change sections of a math course. Between January 25th and January 30th, students may change the level of a course (e.g. switching from Math 1301 to Math 1300 or vice versa) by contacting the DUS (John Rafter). Concerns/Feedback: If at any time you wish to discuss class procedures, grades, or any class difficulty or situation, please contact me during regular office hours or via email. Any concern that cannot be resolved directly with me should be referred to Dr. John Rafter, Director of Undergraduate Studies. If you have feedback, concerns, or suggestions about this course that you would like to share anonymously, please submit them to the “Anonymous Feedback” survey in Brightspace. Safety Protocols: A reminder that this class will comply with all University health and safety protocols regarding the Covid-19 pandemic. In particular, all students are expected to wear masks at all times in the classroom. Note that these protocols are subject to change. Accommodations: If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Student Access Services (www.vanderbilt.edu/student-access/). They will determine with you what accommodations are appropriate and communicate them to the instructor. This service is confidential. Honor Code: Vanderbilt’s Honor Code governs all work in this class. All work submitted for credit must be the student’s own and should reflect the student’s own understanding of the material.
