University of Connecticut College of Liberal Arts and Sciences
Department of Mathematics
Math 2210 Spring 2021 (Roby)

Tom Roby's Math 2210Q Home Page Spring 2021
Applied Linear Algebra

Questions or Comments?

  • For questions about the course material or structure: Please ask in the appropriate discussion forum in Zulip. (If you ask me such questions by email, I will redirect you there.) You can also talk to your classmates or me during class and right afterwards.
  • For questions about using HuskyCT: Once you are logged in to HuskyCT, click Student Help in the top bar.
  • For questions about enrollment, your individual circumstances, or suggestions for improving future versions of the course: Please email me: Tom Roby (delete initials from end).
  • My Homepage:
  • Office: MONT 239; Phone: 860-486-8385 (I will not be physically present on campus this semester because of COVID-19.)
  • Office hours: Mondays 5–6PM and Fridays 2–3PM, and by appointment, over Zoom, at the link: Feel free also to catch me right before or after class (on the class Zoom link). I am happy to schedule appointments by email, which I check frequently.

Class Information

COORDINATES: Classes meet Tuesdays and Thursdays from 11:00–12:15 (Section 003) and 12:30–1:45 (Section 009) over Zoom. A link will be sent by email and available in HuskyCT to registered students.

PREREQUISITES: MATH 1132 (Calulus II), 1152 (Honors Calculus II), OR 2142 (Advanced Calculus II).

TEXT: You will need to obtain a copy of the textbook, which is David C. Lay: Linear Algebra and Its Applications. Any edition you can find from the 3rd on should be fine for this class, except that the problem numbers may vary slightly. I recommend any version that you can get cheaply. The homework solutions are written for the 4th Ed.; a few of the numerical problems have different numbers, and a few of the theoretical problems have different problem numbers.

WEB RESOURCES: The homepage for this course will be available and updated at

HuskyCT: We will make limited use of HuskyCT, because of its many deficiencies. A copy of the course schedule (below) will be posted there that includes links to solutions for selected HW exercises (which are for your personal use only, not to be shared). You will turn in worksheets and homework assignments in Husky CT. For classroom discussions, we will use Zulip (now that Piazza requires payment).

GRADING: Your grade will be based on two midterm exams, an individual final oral exam, worksheets, homework and participation.

The breakdown of points is:

Midterms Oral Final Worksheets Homework Participation
25% each 20% 10% 10% 10%

EXAMS: The exam dates are already scheduled (see below), so please mark your calendars now. Your final will be individually scheduled for a 20-minute slot during finals week, making it easy to avoid conflicts. All exams (like math itself at this level) are cumulative. No makeups will be given; instead if you have an approved reason for missing an exam, your other exams will count for the appropriately higher percentage. I reserve the right to give a followup oral exam to verify your understanding if there are any questions about academic integrity

STUDENT WORKFLOW: In the course schedule, each section in the text has a single line indicating the topic, which may correspond to multiple video lectures. For each section you should:

  1. WATCH the VIDEO LECTURE(S), take notes (pdfs of slides are available for reference or annotation), and ask questions on Zulip by 02:00AM the morning before class. I will answers these questions at the start of class. If your final average is on a grade boundary, I will look at the frequency and quality of your posts as a significant factor in determing your final grade.
  2. DO the XIMERA ACTIVIES as a self check;
  3. Show up to class prepared to ask questions and work in small groups on the worksheets.
  4. DO the WORKSHEET problems during classtime and SUBMIT them by 11:59PM MONDAY of the following week.
  5. USE the ZULIP DISCUSSION BOARD, CLASSROOM INTERACTIONS, and OFFICE HOURS anytime you get seriously stuck;
  6. CHECK your WORKSHEET against the solutions (posted the morning after the due date);
  7. READ the TEXTBOOK to fill in gaps, see an alternate presentation, straighten out confusing points;
  8. DO as many HW problems as you can (prioritizing the mandatory ones, and SUBMIT them by 11:59PM FRIDAY of the following week.
  9. CHECK your HW against the solutions (posted the morning after the due date);

Most weeks we will cover three sections of the textbook.

This course will be fast-paced and cover quite a bit of material. I strongly encourage you to work ahead whenever possible, since you never know when circumstances beyond your control may conspire to set you behind. The video lectures for the entire semester are already available.

VIDEO LECTURES: There are short video lectures, one or more for each section. I recommend (a) trying to watch them at higher speed (1.4x -- 2x) if they make sense, (b) rewinding to rewatch any parts you find confusing, and (c) watching them again later in the course to review (e.g., before exams).

The video lectures are available at this YouTube Channel, and the links in the schedule below take you directly to individual videos. If you have trouble accessing them there, you can also find the complete set of videos lectures on UConn's Kaltura server (if you have UConn credentials).

XIMERA: Ximera provides an interactive platform for self-testing your understanding of the material. There is one Ximera activity for each section/topic. These will count towards your participation grade since they are meant to be formative rather than summative.

ZULIP: The Zulip discussion board allows you to ask questions and interact with one another (and the instructor) between class meetings. It is an open-source platform similar in feel to Slack. We use Zulip because of its excellent ability to include math notation using LaTeX/MathJax. The quality and quantity of your posts in Zulip count towards your participation grade. If you don't have questions, please try to help out your fellow students who might be confused, or post asummary of the video lecture.

PARTICIPATION: Ximera, Zulip, asking good questions in class and working productively in your groups all count towards your participation grade. This includes keeping your webcam on so that you are visible during class, except for brief periods where you have an important reason for turning it off. (If you have a special situation around this, please check with me privately.)

WORKSHEETS: Every section has a worksheet of basic problems, which you will be working on collaboratively with others during classtime. Worksheets are due by 11:59PM MONDAY of the following week in HuskyCT. These will be graded for completion rather than accuracy.

HOMEWORK: Recommended homework is assigned for each section, and is due in HuskyCT by 11:59PM FRIDAY of the week following the week that section is covered. The problems are grouped as Mandatory (Mand.) and Recommended (Rec.). In order to be well-prepared for exams you should be able to do all the homework problems. As with the worksheets, solutions to these (for the 4th edition) will be released shortly afterwards, and they will be graded more for completion than accuracy. If you are using a different edition of the text, a few of the numerical exercises may differ, but you can ask on the discussion board what the correct answer is if you're really stuck after looking at the solution.

You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. Equally importantly, it is a poor learning strategy.

LATE/UNREADABLE ASSIGNMENTS: Late homework and worksheets (up to 48 hours beyond the 2-hour grace period) will receive half credit, after that none. Homework and worksheets that are not easily readable (e.g., because of bad photo quality) will not be graded and will not receive credit. Various smartphone scanning apps can help produce very readable PDF images of your work.

SOFTWARE: In most areas of mathematics it is frequently helpful to use computer software not only for computations, but also to explore examples, search for patterns, or test conjectures. For linear algebra there are several extensive and sophisticated commercial software packages, including MATLAB, Maple, and Mathematica. Matlab is particularly good at linear algebra for applications. All of these can be expensive, depending on your site license, but are currently available to UConn students.

An excellent alternative to the above is the free open-source computer algebra system Sage. There are many commands for linear algebra, and a textbook (linked below) has been written that makes significant use of Sage examples. Sage also provides a full-fledged programming environment via the Python programming language, but you don't need to be a programmer to use it. I highly recommend trying it out online, and installing a copy on your computer.

ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used unless otherwise specifically indicated on the exam.

CONTENT: Linear Algebra is a beautiful and important subject, rich in applications within mathematics and to many other disciplines. For many of you this is the first course to begin bridging the gap between concrete computations and abstract reasoning. Understanding the notions of vector spaces, linear (in)dependence, dimension, and linear transformations will help you make sense of matrix manipulations at a deeper level, clarifying the underlying structure.

APPLICATIONS: This class may be your only chance to understand the theory of linear algebra, i.e., why things work the way they do. In the future, this deeper understanding will be your key to harnessing the power of this subject to solve problems and shed light on your projects. We need all the time we have to get to the most important tools, e.g., the Singular Value Decomposition (SVD), leaving unfortunately little time to focus on applications. The text has a sections on applications sprinkled throughout, and I encourage you to read them as you have time, during or after the term, particularly ones relevant to your current career path.

ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Take advantage of the online discussions and office hours and the wealth of information on the web.

Section Due Date Topics Videos Ximera HW (due following Fri.)
§1.1 1/19 T Intro to Linear Alg & Systems of Eqns. E1, E1pdf, E2, E2pdf, XA1.1 Mand: 3, 12, 21, 24, 25, 31.
Rec: 1, 2, 10, 13, 15, 16, 32.
§1.2 1/19 T Row Reduction & Echelon Forms E3, E3pdf, E4, E4pdf, XA1.2 Mand: 2, 13, 19, 21, 24.
Rec: 10, 14, 29, 31.
§1.3 1/21 R Vector Equations E5, E5pdf, Ov, Ovpdf, XA1.3 Mand: 6, 7, 15, 21, 23, 25.
Rec: 3, 9, 12, 14, 22.
§1.4 1/26 T Matrix Equations E7, E7pdf, E8, E8pdf, XA1.4 Mand: 1, 13, 17, 19, 22, 23, 25.
Rec: 4, 7, 9, 11, 31.
§1.5 1/26 T Solution Sets of Linear Systems E9, E9pdf, E10, E10pdf, XA1.5 Mand: 11, 15, 19, 23, 30, 32.
Rec: 2, 6, 18, 22, 27.
§1.7 1/28 R Linear Independence E11, E11pdf, E12, E12pdf, XA1.7 Mand: 1, 7, 15, 16, 20, 21.
Rec: 2, 5, 9, 32, 34, 35.
§1.8 2/2 T Linear Transformations M2, M2pdf, XA1.8 Mand: 2, 8, 9, 21, 31.
Rec: 4, 13, 15, 17.
§1.9 2/2 T Matrix of Linear Transformations M3, M3pdf, M4, M4pdf, XA1.9 Mand: 1, 8, 13, 19, 23, 26, 34.
Rec: 2, 7, 9, 15, 20, 32, 36.
§2.1 2/4 R Matrix Operations and Inverses M5, M5pdf, M6, M6pdf, XA2.1 Mand: 5, 7, 10, 15.
Rec: 2, 18, 20, 22, 27, 28.
§2.2 2/9 T Inverse of a Matrix M7, M7pdf, M8, M8pdf, XA2.2 Mand: 9, 11, 15, 16, 29.
Rec: 3, 6, 7, 13, 23, 24, 32, 37.
§2.3 2/9 T Characterizations of Invertible Matrices M9, M9pdf, XA2.3 Mand: 11, 13, 15, 28.
Rec: 1, 3, 5, 8, 17, 26, 35.
§3.1 2/11R Intro to Determinants D1, D1pdf, XA3.1 Mand: 13, 20, 21, 37, 39.
Rec: 4, 8, 11, 31, 32.
§3.2 2/11 R Properties of Determinants D2, D2pdf, D3, D3pdf, XA3.2 Mand: 8, 10, 16, 19, 27, 34.
Rec: 2, 3, 18, 20, 26, 32, 36, 40.
§1.1–2.5 2/16 T Catchup & Review Day     Do Practice Midterm by today!
§3.3 2/23 T Cramer's Rule and Volumes D4, D4pdf, D5, D5pdf, XA3.3 Mand: 6, 22, 23, 26.
Rec: 4, 5, 29, 30.
§4.1 2/23 T Vector Spaces & Subspaces B1, B1pdf, B2, B2pdf, XA4.1 Mand: 3, 8, 13, 23, 31.
Rec: 1, 12, 15, 17, 22, 32.
§4.2 2/25 R Null Spaces, Columns Spaces and Linear Transf. B3, B3pdf, B4, B4pdf, XA4.2 Mand: 11, 17, 25, 33, 34.
Rec: 3, 6, 14, 19, 21, 24, 32, 36.
§4.3 3/2 T Bases and Linearly Independent Sets B5, B5pdf, B6, B6pdf, XA4.3 Mand: 14, 21, 23, 29, 30.
Rec: 3, 4, 8, 10, 15, 24, 31.
§4.4 3/2 T Coordinate Systems B7, B7pdf, B8, B8pdf, XA4.4 Mand: 13, 15, 17, 21, 32.
Rec: 2, 3, 5, 7, 10, 11, 23.
§4.5 3/4 R Dimension of a Vector Space B9, B9pdf, B10, B10pdf, XA4.5 Mand: 8, 21, 23, 26, 29.
Rec: 1, 4, 11, 14, 28.
§4.6 3/9 T Rank B11, B11pdf, XA4.6 Mand: 7, 17, 24, 27, 28.
Rec: 2, 5, 10, 13, 19.
§4.7 3/9 T Change of Basis B12, B12pdf, XA4.7 Mand: 3, 11, 13, 15.
Rec: 1, 5, 7, 9.
§5.1 3/11 R Eigenvectors & Eigenvalues F1, F1pdf, F2, F2pdf, XA5.1 Mand: 2, 6, 13, 21, 23, 31.
Rec: 7, 11, 15, 19, 24, 25, 27.
§5.2 3/16 T Characteristic Equation F3, F3pdf, F4, F4pdf, XA5.2 Mand: 9, 19, 21.
Rec: 2, 5, 12, 15, 20.
§5.3 3/16 T Diagonalization F5, F5pdf, XA5.3 Mand: 11, 21, 24, 26.
Rec: 1, 4, 5, 9, 15, 17.
§5.4 3/18 R Eigenvectors & Linear Transformations F6, F6pdf, XA5.4 Mand: 6, 7, 10, 15, 25.
Rec: 1, 3, 16, 23.
§1.1–5.4 3/23 T Catchup & Review Day     Do Practice Midterm 2 by today
§6.1 3/30 T Inner Product & Orthogonality G1, G1pdf, XA6.1 Mand: 3, 5, 19, 25, 27, 29.
Rec: 10, 16, 18, 23.
§6.2 3/30 T Orthogonal Sets G2, G2pdf, G3, G3pdf, G4, G4pdf, XA6.2 Mand: 8, 14, 23, 27, 28, 29.
Rec: 3, 6, 9, 11, 20, 21, 26.
§6.3 4/1 R Orthogonal Projections G5, G5pdf, XA6.3 Mand: 1, 7, 17, 21, 24.
Rec: 6, 9, 11, 13, 23.
§6.4 4/6 T Gram–Schmidt G6, G6pdf, F7, F7pdf, XA6.4 Mand: 17, 19.
Rec: 1, 3, 7, 9, 11.
§6.5 4/6 T Least-Squares Problems G7, G7pdf, XA6.5 Mand: 3, 17, 19, 21.
Rec: 5, 7, 9, 11.
§7.1 4/8 R Diagonalization of Symmetric Matrices F8, F8pdf, XA7.1 Mand: 1, 3, 5, 8, 13, 25.
Rec: 10, 17, 19, 29.
§7.2 4/20 T Quadratic Forms F9, F9pdf, F10, F10pdf, XA7.2 Mand: 8, 11, 21, 27.
Rec: 1, 5, 13, 19.
§7.3 4/20 T Constrained Optimization F11, F11pdf, XA7.3 Mand: 1, 3, 7, 11.
Rec: 5.
§7.4 4/22R Singular Value Decomposition (SVD) F12,F12pdf, No XA7.4 Mand: 3, 9, 17, 19.
Rec: 1, 11, 18.
§ 4/27 R Google PageRank and/or Review Day      
WEEK OF 3–7 MAY INDIVIDUAL FINAL EXAMS (covers entire course)

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