Tom Roby's Math 2210Q Home Page Fall 2021
EXAMS: The midterm dates are already scheduled (see below), so please mark your calendars now. The final exam is scheduled by the registrar around mid-semester. 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. If you miss the final for reasons approved by the Dean of Students, then you will have one chance to take a -- make-up final exam in the second or third week of the following term. -- 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:
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 (BUT NO LATER THAN END OF WEEK 2) 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. In particular, CSD wants a great deal of lead time for scheduling exams.
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.
|2210Q LECTURE AND ASSIGNMENT SCHEDULE|
|Section||Due Date||Topics||Videos||Ximera||HW (due following Fri.)|
|§1.1||8/31 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||8/31 T||Row Reduction & Echelon Forms||E3, E3pdf, E4, E4pdf,||XA1.2||Mand: 2, 13, 19, 21, 24. |
Rec: 10, 14, 29, 31.
|§1.3||9/2 R||Vector Equations||E5, E5pdf, Ov, Ovpdf,||XA1.3||Mand: 6, 7, 15, 21, 23, 25. |
Rec: 3, 9, 12, 14, 22.
|§1.4||9/7 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||9/7 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||9/9 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||9/14 T||Linear Transformations||M2, M2pdf,||XA1.8||Mand: 2, 8, 9, 21, 31.|
Rec: 4, 13, 15, 17.
|§1.9||9/14 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||9/16 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||9/21 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||9/21 T||Characterizations of Invertible Matrices||M9, M9pdf,||XA2.3||Mand: 11, 13, 15, 28. |
Rec: 1, 3, 5, 8, 17, 26, 35.
|§3.1||9/23 R||Intro to Determinants||D1, D1pdf,||XA3.1||Mand: 13, 20, 21, 37, 39. |
Rec: 4, 8, 11, 31, 32.
|§3.2||9/23 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.
|§1.1–2.3||9/28 T||Catchup & Review Day||Do Practice Midterm by today!|
|THURSDAY 30 SEPTEMBER: FIRST MIDTERM EXAM (through §2.3)|
|§3.3||10/5 T||Cramer's Rule and Volumes||D4, D4pdf, D5, D5pdf,||XA3.3||Mand: 6, 22, 23, 26. |
Rec: 4, 5, 29, 30.
|§4.1||10/5 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||10/7 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||10/12 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||10/12 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||10/14 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||10/19 T||Rank||B11, B11pdf,||XA4.6||Mand: 7, 17, 24, 27, 28. |
Rec: 2, 5, 10, 13, 19.
|§4.7||10/19 T||Change of Basis||B12, B12pdf,||XA4.7||Mand: 3, 11, 13, 15. |
Rec: 1, 5, 7, 9.
|§5.1||10/21 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||10/26 T||Characteristic Equation||F3, F3pdf, F4, F4pdf,||XA5.2||Mand: 9, 19, 21. |
Rec: 2, 5, 12, 15, 20.
|§5.3||10/26 T||Diagonalization||F5, F5pdf,||XA5.3||Mand: 11, 21, 24, 26. |
Rec: 1, 4, 5, 9, 15, 17.
|§5.4||10/28 R||Eigenvectors & Linear Transformations||F6, F6pdf,||XA5.4||Mand: 6, 7, 10, 15, 25. |
Rec: 1, 3, 16, 23.
|§6.1||11/2 T||Inner Product & Orthogonality||G1, G1pdf,||XA6.1||Mand: 3, 5, 19, 25, 27, 29. |
Rec: 10, 16, 18, 23.
|§6.2||11/2 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||11/4R||Orthogonal Projections||G5, G5pdf,||XA6.3||Mand: 1, 7, 17, 21, 24. |
Rec: 6, 9, 11, 13, 23.
|§1.1–5.4||11/9 T||Catchup & Review Day||Do Practice Midterm 2 by today|
|THURSDAY 11 NOVEMBER SECOND MIDTERM EXAM (through §5.4)|
|§6.4||11/16 T||Gram–Schmidt||G6, G6pdf, F7, F7pdf,||XA6.4||Mand: 17, 19. |
Rec: 1, 3, 7, 9, 11.
|§6.5||11/16 T||Least-Squares Problems||G7, G7pdf,||XA6.5||Mand: 3, 17, 19, 21. |
Rec: 5, 7, 9, 11.
|§7.1||11/18 R||Diagonalization of Symmetric Matrices||F8, F8pdf,||XA7.1||Mand: 1, 3, 5, 8, 13, 25. |
Rec: 10, 17, 19, 29.
|22–28 NOVEMBER IS THANKSGIVING BREAK: NO CLASSES|
|§7.2||11/29 T||Quadratic Forms||F9, F9pdf, F10, F10pdf,||XA7.2||Mand: 8, 11, 21, 27. |
Rec: 1, 5, 13, 19.
|§7.3||11/29 T||Constrained Optimization||F11, F11pdf,||XA7.3||Mand: 1, 3, 7, 11. |
|§7.4||12/2 R||Singular Value Decomposition (SVD)||F12,F12pdf,||No XA7.4||Mand: 3, 9, 17, 19. |
Rec: 1, 11, 18.
|§||12/7 T||Google PageRank and/or Review Day|
|§1–7.4||12/9 R||Catchup and Review Day|
| WEEK OF
13–19 DECEMBER FINAL EXAM (covers entire course), DETAILS TBA|
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