# MATH 2210Q Applied Linear Algebra

This is the Spring 2023 class webpage for Section 013 of MATH 2210Q Applied Linear Algebra at UConn.

## Welcome to MATH 2210Q: Applied Linear Algebra!

**Course description:** Systems of equations, matrices, determinants, linear transformations on vector spaces, characteristic values and vectors, from a computational point of view. The course is an introduction to the techniques of linear algebra with elementary applications.

**Prerequisites:** MATH 1132Q (Calulus II), MATH 1152Q (Honors Calculus II), or MATH 2142Q (Advanced Calculus II).

**Textbook:** David C. Lay’s “Linear Algebra and Its Application”, 6th edition. You should purchase the textbook from the UConn bookstore with the MyMathLab bundle.

**Class:** Tuesdays and Thursdays at 3:30-4:45PM in FSB 102.

**Office hours:** Tuesdays and Thursdays at 2:15-3:15PM on webex. You can access my webex link through HuskyCT.

### Class structure

The structure of this class might be different than what you are used to. Instead of lecturing in class and having you do homework at home, you will watch some video lectures at home and then we will mainly focus on solving problems in class. In the beginning of class, I will lecture a little bit to recap the video lectures if necessary, and then I will hand out worksheets for you to work on in groups or independently (whatever you prefer). During class, we will take breaks to discuss problems and check answers.

Towards the bottom of this page, I have posted the complete class schedule for the semester. I have written out which sections and topics I plan to cover each class and what the corresponding video lectures are for those sections. Each week we will cover about three sections of the textbook. Each section may have 1-2 corresponding video lectures that you will need to watch in advance before class in order to be able to complete the worksheets.

**Video lectures:** The video lectures are available at this YouTube channel. If you have trouble accessing the YouTube channel, then you can also view the video lectures here on UConn’s Kaltura server. Feel free to watch some of the videos at x1.5 or x2 speed. I encourage you to take notes while watching the videos, and to pause, rewind, and rewatch parts if you are stuck. Write down any questions you might have so that you can ask them in class! In the course schedule below, I have also linked to the pdf of each video so you can follow along with those notes as well.

**HuskyCT:** All announcements related to the course will be posted on HuskyCT. Assignments and grades will be posted on HuskyCT as well.

**Grading:** The course grade will be composed of worksheets, homework, quizzes, two midterms, and a final exam. The breakdown will be as follows:

Course Component | Weight | |
---|---|---|

Worksheets | 10% | |

Homework | 10% | |

Quizzes | 15% | |

Midterms (2) | 20% | |

Final exam | 25% |

(All grades and assignments will be posted on HuskyCT.)

**Worksheets:** Worksheets will be posted and due on HuskyCT. There will be a worksheet for each section we cover that consists of basic problems, which you will be working on collaboratively with others during classtime. Worksheets are due on HuskyCT on Monday at 11:59PM of the following week and are graded for completion. Solutions will be posted on HuskyCT the following day at 12AM. You should be able to finish the worksheets in the allotted class time, but if not then you will also have the weekend to work on them. All worksheets should be scanned together into one PDF and uploaded to HuskyCT by Monday night. Each worksheet will be graded out of 3 points: 3 - fully complete, 2 - mostly complete, 1 - barely complete, 0 - incomplete.

**Homework:** There will be weekly homework on MyMathLab through HuskyCT. Each homework will be on the sections covered that week. Homework is due Monday at 11:59PM of the following week. The homeworks will be light and are just meant to make sure you are understanding the exercises you are doing in class and to help you prepare for the quiz.

**Quizzes:** There will be weekly quizzes in the beginning of every class on Tuesday. Each quiz will be on the previous weeks material, so each quiz will be on the material that was covered on the worksheets and homework due the previous night. Each quiz will consist of two problems and will take place in the first 10 minutes of class. Quizzes will be graded out of 10 points.

**Midterms:** There will be two midterms. Midterm 1 is on Thur. 2/16 and Midterm 2 is on Thur. 4/6. Practice midterms and review material will be posted on HuskyCT. We will also have review sessions in class on the Tuesday before the exam.

**Final exam:** The final exam will be cummulative and during finals week. The final exam is on Thursday, 5/4/23 from 1:00-3:00PM in FSB 102. No make-ups will be given unless for a reason approved by the Dean of Students.

### Class schedule

Date | Section | Topic | Videos | Video PDFs | ||||
---|---|---|---|---|---|---|---|---|

1/17 | 1.1 | Intro to Linear Alg & Systems of Eqns. | E1, E2 | E1pdf, E2pdf | ||||

1.2 | Row Reduction & Echelon Forms | E3, E4 | E3pdf, E4pdf | |||||

1/19 | 1.3 | Vector Equations | E5, Ov | E5pdf, Ovpdf | ||||

1/24 | 1.4 | Matrix Equations | E7, E8 | E7pdf, E8pdf | ||||

1.5 | Solution Sets of Linear Systems | E9, E10 | E9pdf, E10pdf | |||||

1/26 | 1.7 | Linear Independence | E11, E12 | E11pdf, E12pdf | ||||

1/31 | 1.8 | Linear Transformations | M2 | M2pdf | ||||

1.9 | Matrix of Linear Transformations | M3, M4 | M3pdf, M4pdf | |||||

2/2 | 2.1 | Matrix Operations and Inverses | M5, M6 | M5pdf, M6pdf | ||||

2/7 | 2.2 | Inverse of a Matrix | M7, M8 | M7pdf, M8pdf | ||||

2.3 | Characterizations of Invertible Matrices | M9 | M9pdf | |||||

2/9 | 3.1 | Intro to Determinants | D1 | D1pdf | ||||

3.2 | Properties of Determinants | D2, D3 | D2pdf, D3pdf | |||||

2/14 | 1.1-2.3 | Catch-up and Review Day | ||||||

2/16 | 1.1-2.3 | Midterm 1 | ||||||

2/21 | 3.3 | Cramer’s Rule and Volumes | D4, D5 | D4pdf, D5pdf | ||||

4.1 | Vector Spaces & Subspaces | B1, B2 | B1pdf, B2pdf | |||||

2/23 | 4.2 | Null Spaces, Columns Spaces and Lin. Transf. | B3, B4 | B3pdf, B4pdf | ||||

2/28 | 4.3 | Bases and Linearly Independent Sets | B5, B6 | B5pdf, B6pdf | ||||

4.4 | Coordinate Systems | B7, B8 | B7pdf, B8pdf | |||||

3/2 | 4.5 | Dimension of a Vector Space | B9, B10 | B9pdf, B10pdf | ||||

3/7 | 4.6 | Rank | B11 | B11pdf | ||||

4.7 | Change of Basis | B12 | B12pdf | |||||

3/9 | 5.1 | Eigenvectors & Eigenvalues | F1, F2 | F1pdf, F2pdf | ||||

3/12 - 3/18 | Spring Recess | |||||||

3/21 | 5.2 | Characteristic Equation | F3, F4 | F3pdf, F4pdf | ||||

5.3 | Diagonalization | F5 | F5pdf | |||||

3/23 | 5.4 | Eigenvectors & Linear Transformations | F6 | F6pdf | ||||

3/28 | 6.1 | Inner Product & Orthogonality | G1 | G1pdf | ||||

6.2 | Orthogonal Sets | G2, G3, G4 | G2pdf, G3pdf, G4pdf | |||||

3/30 | 6.3 | Orthogonal Projections | G5 | G5pdf | ||||

4/4 | 1.1-5.4 | Catch-up and Review Day | ||||||

4/6 | 1.1-5.4 | Midterm 2 | ||||||

4/11 | 6.4 | Gram–Schmidt | G6, F7 | G6pdf, F7pdf | ||||

6.5 | Least-Squares Problems | G7 | G7pdf | |||||

4/13 | 7.1 | Diagonalization of Symmetric Matrices | F8 | F8pdf | ||||

4/18 | 7.2 | Quadratic Forms | F9, F10 | F9pdf, F10pdf | ||||

7.3 | Constrained Optimization | F11 | F11pdf | |||||

4/20 | 7.4 | Singular Value Decomposition (SVD) | F12 | F12pdf | ||||

4/25 | Google PageRank and/or Review Day | |||||||

4/27 | 1.1-7.4 | Catchup and Review Day |

(Spring Recess is March 12-18, 2023.)

**Student conduct code:** Students are expected to conduct themselves in accordance with UConn’s Student Conduct Code.

**Academic Integrity Statement:** This course expects all students to act in accordance with the Guidelines for Academic Integrity at the University of Connecticut. Because questions of intellectual property are important to the field of this course, we will discuss academic honesty as a topic and not just a policy. If you have questions about academic integrity or intellectual property, you should consult with your instructor. Additionally, consult UConn’s guidelines for academic integrity.

**Students with Disabilities:** The University of Connecticut is committed to protecting the rights of individuals with disabilities and assuring that the learning environment is accessible. If you anticipate or experience physical or academic barriers based on disability or pregnancy, please let me know immediately so that we can discuss options. Students who require accommodations should contact the Center for Students with Disabilities, Wilbur Cross Building Room 204, (860)486-2020, or http://csd.uconn.edu/.

**Final Exam Policy:** In accordance with UConn policy, students are required to be available for their final exam and/or complete any assessment during the time stated. If you have a conflict with this time you must obtain official permission to schedule a make-up exam with the Dean of Students. If permission is granted, the Dean of Students will notify the instructor. Please note that vacations, previously purchased tickets or reservations, graduations, social events, misreading the assessment schedule, and oversleeping are not viable reasons for rescheduling a final.