Syllabus¶
Instructor Information¶
Course Information¶
Text book: “Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares” by Boyd and Vandenberghe. You can find the book as a free PDF here.
Lecture Outlines: You will find the outlines that I use for preparing my lectures here. I encourage you to use these outlines as templates for your own notes.
Software. We will be using the Anaconda distribution of Python 3.8. This is free software. Even if you have Python already installed on your computer you should install this distribution since it includes Jupyter notebook and several Python modules we will need.
Laptop. Since we will be using Jupyter notebook every week, you should have a laptop or tablet with you during class.
Useful links for Jupyter.
Markdown cheatsheet. Markdown is a scheme used to format text in Jupyter notebook.
LaTeX math symbols - this is useful reference for typesetting mathematics with Jupyter notebook.
Python 3 documentation. This is the official documentation of Python 3. See the Tutorial section for introduction to Python and Library Reference for a systematic description of standard Python tools.
matplotlib documentation. Matplotlib is a Python module for creating graphs and plots. We will use it a lot. Matplotlib documentation is unfortunately incomplete and often quite confusing, but it includes many code examples that can be helpful.
numpy documentation. Numpy is the main scientific computing module of Python. We will use it extensively.
Learning Goals:
Construct a system of linear equations from an application.
Represent a system of linear equations in matrix form.
Solve a system of equations with and without the aid of technology.
Determine if a given set of vectors is a subspace of \(\mathbb{R}^n\).
Find a basis for a given subspace of \(\mathbb{R}^n\) and determine its dimension.
Convert a vector from one coordinate basis to another.
Find a matrix representation of a linear transformation between \(\mathbb{R}^n\) and \(\mathbb{R}^m\).
Add, multiply, and transpose matrices.
Determine if a matrix is invertible and compute its inverse if it is.
Identify if a set of vectors is orthogonal.
Identify if a matrix is orthogonal.
Construct an orthonormal basis for a given subspace.
Compute the orthonormal projection of a vector onto a subspace.
Calculate the area of a parallelogram using determinant.
Understand the connection between determinant and the geometry of linear transformations.
Calculate the eigenvalues and eigenvectors of a matrix.
Apply eigenvalues/vectors to solve systems of LODEs.
Solve the least squares problem.
Compute the singular value decomposition.
Understand how to use computer software to aid in all of the above.
Recitation Information¶
Grade Information¶
Grades are available in an online spreadsheet here, and are listed by a grade code that I will email you during week 2.
Grades will be calculated as follows:
Exams |
Homework |
Activities |
Participation |
Final Exam |
65% |
15% |
15% |
5% |
20% |
This table adds up to 120%! For an explanation, check under Final Exam.
Grades will be calculated using the standard grade scale:
F |
D |
D+ |
C- |
C |
C+ |
B- |
B |
B+ |
A- |
A |
0 |
60 |
64 |
67 |
70 |
74 |
77 |
80 |
84 |
87 |
90 |
Please note that the values in this table are the lower threshold for each letter grade.
Homework: We will be using UBx for homework. There will be one assignment every 2 weeks, due on Fridays. For specific due dates consult the tentative calendar near the end of this syllabus.
UBx uses Python to automatically generate and grade questions. In addition, there are some problems that will require you to work in Jupyter notebook, so you will need to download and install the latest version of Anaconda. Don’t worry, any programming you will need to do will be minimal and thoroughly explained in the problem.
In-class activities: In addition to the biweekly homework, we will have in-class activities every week. These activities will be done during class, turned in as a PDF on Brightspace, and graded (part of the grade will be completion). The lowest two grades will be dropped.
Recitation participation: It couldn’t be easier to get 5% of the final grade, just show up and engage. Participation in recitation will be evaluated by the TA on a weekly basis. You will be allowed 2 absences without a grade penalty.
Proficiency exams: Exams in this class will be handled differently than what you may be used to. Instead of having one or two midterms covering multiple sections of material, we will have short, 25 minute exams covering only the material from the previous 2 weeks. Exams will take place the first half of class on the designated exam days (see tenative schedule). Do not leave after finishing the exams because we will cover new material for the second half of class.
Each exam will have 4 questions worth 4 points each for a total of 16 points. If your score is 14 or more, you pass the exam and will receive a 100%. If your score is 12 or 13 it will be considered a marginal pass and you will receive a 70%. If your score is 11 or less, you do not pass the exam and will receive 0%.
If you are unhappy with your score on the exam, you will have the opportunity to retake it. If you opt to retake an exam, only your retake grade will be counted. You must have made an honest attempt the first time to be permitted to retake an exam. Exam retakes will take place during the first 25 minutes of class on the designated days. If you are not retaking the exam, you do not need to show up to the first 25 minutes of class on those days. We will still cover new material after exams and retakes.
Exam 7 retake will be handled differently. Since exam 7 is on the last day of class, the retake will be incorporated into the final exam period.
Your aggregate score for the proficiency exams portion of the final grade will be the average of the individual exam grades (100 for passing, 70 for a marginal pass, 0 otherwise). There will be a total of seven proficiency exams.
Final exam: If your average grade on the first 6 exams is at least 75%, you may opt out of the final exam. You may still show up to the final exam period to take the exam 7 retake, but will not be required to take the final exam. If your average grade on the first 6 exams is less than 75%, you will be required to take the final exam, and if you don’t, you will receive a 0 on the final exam.
For those of you that end up taking the final exam, I will reduce the weight of the proficiency exams from 65% of the final grade to 45% of the final grade, with the final exam making up the remaining 20%.
The final exam will have one question from each of the 7 proficiency exams, and you will have 1.5 hours to complete it. The exam 7 retake will take place after the final exam has been collected, and you will be given 25 minutes to complete it.
The final exam will be Wednesday, May 15 11:45 AM - 1:15 PM. The exam 7 retake will be Wednesday, May 15 1:20 - 1:45 PM.
Tentative Schedule¶
Week |
Topics and exam schedule |
|---|---|
Week 1 |
Mon 1/22: No class
Wed 1/24: Systems of equations; Activity 1
Fri 1/26: Solving systems, Using Jupyter
|
Week 2 |
Mon 1/29: Applications; Activity 2
Wed 1/31: Number of solutions
Fri 2/2: Solution sets; HW 1 due Sunday at midnight
|
Week 3 |
Mon 2/5: Exam 1; Vector spaces
Wed 2/7: Subspaces and span, Activity 3
Fri 2/9: Linear independence
|
Week 4 |
Mon 2/12: Exam 1 retake; Basis
Wed 2/14: Coordinates, Activity 4
Fri 2/16: Change of basis; HW 2 due Sunday at midnight
|
Week 5 |
Mon 2/19: Exam 2; linear transformations
Wed 2/21: Matrix representation, Activity 5
Fri 2/23: Kernel and 1-1
|
Week 6 |
Mon 2/26: Exam 2 retake; Range and onto
Wed 2/28: Invertibility, Activity 6
Fri 3/1: Activity 6; HW 3 due Sunday at midnight
|
Week 7 |
Mon 3/4: Exam 3; Matrix algebra
Wed 3/6: Matrix muliplication
Fri 3/8: Activity 7
|
Week 8 |
Mon 3/11: Exam 3 retake; Applications
Wed 3/13: Activity 8
Fri 3/15: Inverse; HW 4 due Sunday at midnight
|
Week 9 |
Mon 3/25: Exam 4; Determinants
Wed 3/27: Area of parallelogram, Activity 9
Fri 3/29: Geometry of lin trans, Activity 10
|
Week 10 |
Mon 4/1: Exam 4 retake; Eigenvalues and eigenvectors
Wed 4/3: Applications, Activity 10.5
Fri 4/5: Diagonalization; HW 5 due Sunday at midnight
|
Week 11 |
Mon 4/8: Exam 5; Describing vectors
Wed 4/10: Vector geometry, Activity 11
Fri 4/12: Length and inner product
|
Week 12 |
Mon 4/15: Exam 5 retake; Projections and reflections
Wed 4/17: Orthogonality, Activity 12
Fri 4/19: Gram-Schmidt; HW 6 due Sunday at midnight
|
Week 13 |
Mon 4/22: Exam 6; Inconsistent systems
Wed 4/24: Activity 13
Fri 4/26: Least Squares
|
Week 14 |
Mon 4/29: Exam 6 retake; Pseudo-inverse
Wed 5/1: Unit circle under transformation, Activity 14
Fri 5/3: SVD, Activity 15; HW 7 due Sunday at midnight
|
Week 15 |
Mon 5/6: Exam 7
Wed 5/8:
Fri 5/10:
|
Week 16 |
Wed 5/15: Final exam at 11:45 AM |
Proficiency Exams by Topics:¶
Exam 1 |
Systems of linear equations, solutions, matrix equations, applications |
Exam 2 |
Vector spaces, subspaces, basis, dimension, coordinates |
Exam 3 |
Linear transformations, matrix representation, 1-1 and onto |
Exam 4 |
Matrix algebra and its applications |
Exam 5 |
Determinant, eigenvalues and eigenvectors, systems of LODEs |
Exam 6 |
Vector geometry, norms, inner products, orthogonality |
Exam 7 |
Least squares, singular value decomposition |
Final |
One questions from each of the above exams with two more on least squares and SVD |
Useful Information¶
COVID-19 Information Due to the continuing COVID-19 pandemic, high-quality masks are recommended during class and office hours. High-quality masks include N95 or KN95 or similarly rated masks. If you are feeling sick, stay home and contact me via email. For more information at the pandemic health and safety policies, please see the Health and Safety Guidelines.
Important Dates:
Jan 24: first day of classes
Jan 31: last day to add/drop
Mar 18-23: Spring break
Apr 16: last day to resign
May 7: last day of classes
Academic Integrity. Academic integrity is critical to the learning process. It is your responsibility as a student to complete your work in an honest fashion, upholding the expectations your individual instructors have for you in this regard. The ultimate goal is to ensure that you learn the content in your courses in accordance with UB’s academic integrity principles, regardless of whether instruction is in-person or remote. Thank you for upholding your own personal integrity and ensuring UB’s tradition of academic excellence. The academic integrity policy is available at:
While you are encouraged to collaborate with your peers to problem solve while working on the projects, each student is responsible for producing an original project report on their own. Any outside resource that is used during the project (this includes code taken from class notes or other sources) or while writing the report must be properly cited in the report.
Collaboration of any kind on the quizzes is forbidden, as is the use of any materials not approved of by the instructor.
Accessibility Resources. If you have any disability which requires reasonable accommodations to enable you to participate in this course, please contact the Oce of Accessibility Resources in 60 Capen Hall, 716-645-2608 and also the instructor of this course during the first week of class. The office will provide you with information and review appropriate arrangements for reasonable accommodations, which can be found on the web at:
Critical Campus Resources
Sexual Violence. UB is committed to providing a safe learning environment free of all forms of discrimination and sexual harassment, including sexual assault, domestic and dating violence and stalking. If you have experienced gender-based violence (intimate partner violence, attempted or completed sexual assault, harassment, coercion, stalking, etc.), UB has resources to help. This includes academic accommodations, health and counseling services, housing accommodations, helping with legal protective orders, and assistance with reporting the incident to police or other UB officials if you so choose. Please contact UB’s Title IX Coordinator at 716-645-2266 for more information. For confidential assistance, you may also contact a Crisis Services Campus Advocate at 716-796-4399.
Mental Health. As a student you may experience a range of issues that can cause barriers to learning or reduce your ability to participate in daily activities. These might include strained relationships, anxiety, high levels of stress, alcohol/drug problems, feeling down, health concerns, or unwanted sexual experiences. Counseling, Health Services, and Health Promotion are here to help with these or other issues you may experience. You can learn more about these programs and services by contacting:
Counseling Services:
120 Richmond Quad (North Campus), 716-645-2720
202 Michael Hall (South Campus), 716-829-5800
Health Services:
Michael Hall (South Campus), 716-829-3316
Health Promotion:
114 Student Union (North Campus), 716-645-2837