MAT 223 – Linear Algebra I
线性代数网课代修 Orthogonality, orthonormal sets, Gram-Schmidt orthogonalization process, least square approximation. Linear transformations from R n to R m.
Systems of linear equations, matrix algebra, determinants. Vector geometry in R 2 and R 3 . Complex numbers. R n : subspaces, linear independence, bases, dimension, column spaces, null spaces, rank and dimension formula. Orthogonality, orthonormal sets, Gram-Schmidt orthogonalization process, least square approximation. Linear transformations from R n to R m. The determinant, classical adjoint, Cramer’s rule. Eigenvalues, eigenvectors, eigenspaces, diagonalization. Function spaces and applications to a system of linear differential equations. The real and complex number fields.
Prerequisites The prerequisite for the course is Grade 12 Advanced Functions (MHF4U). 线性代数网课代修
Textbook. Weekly readings will come from notes posted on the course website. These notes are your primary resource. The following textbook serves as an additional resource, and is completely optional. Linear Algebra with Applications, Open Edition, by Nicholson. This book is an “Open Educational Resource” available for free download at:
Please note that section numbers and terminology/notation match between the notes and the book.
Course Website. You can access the MAT 223 course website through Quercus. Homework assignments, readings, messages, handouts and other important information will be posted on the website, so you should check it regularly.
Here is a short summary of the different delivery mode options available in in Fall 2023:
- LEC 0101 will have synchronous online lectures. Zoom links for this section can be found here.
- LEC 0102 will have one hour of synchronous online lecture (M 10-11), and two hours of in-person lecture (TH 9-11 in DV 2074). Zoom links for the M 10-11 class can be found here.
- LEC 0103 & LEC 0105 will be fully in-person (all three hours are in-person).
- All tutorials are in-person only.
- Tests will be in-person for all students (no exceptions), and take place during the TH 6-8pm timeslot. Test dates will NOT overlap with MAT232 tests.
Office Hours. Please do not be hesitant to come to office hours. The staff of MAT 223 are happy to answer your questions outside of class, during our scheduled office hours (see above for dates/times).In addition to these hours, before tests and exams we will hold extra office hours. The times of these hours will be posted on the course webpage. If you cannot make any of the scheduled office hours,please let the instructor know, and hopefully an alternate meeting can be arranged.
Tutorials will begin the week of September 11. All students must be enrolled in a tutorial section. The main purpose of the tutorial is to give you an opportunity to ask questions and work through examples together with your TA. To get the most from your tutorial, you should review the lecture material so that you come prepared to work and ask questions. 线性代数网课代修
Copyright Policy. Course materials prepared by the instructor are considered by the University to be an instructor’s intellectual property covered by the Copyright Act, RSC 1985, c C-42. Thesematerials are made available to you for your own study purposes, and cannot be shared outside of the class or “published” in any way. Lectures, whether in person or online, cannot be recorded without the instructor’s permission. Posting course materials or any recordings you may make to other websites without the express permission of the instructor will constitute copyright infringement. Please note,posting HW and/or test questions to online forums outside of our course discussion board constitutes a copyright violation, and may also constitute an academic offence.
Privacy & Course Videos – Notice of video recording and sharing (Download and re-use prohibited).
For those students enrolled in LEC 0101 (the one with all LEC online): This section,including your participation, will be recorded on video and will be available to students in the course for viewing remotely and after each session. Course videos and materials belong to your instructor, the University, and/or other sources depending on the specific facts of each situation, and are protected by copyright. In this course, you are permitted to access session videos and materials for your own academic use, but you should not download, copy, share, or use them for any other purpose without the explicit permission of the instructor. For questions about recording and use of videos in which you appear please contact your instructor.
Tech Requirements for LEC 0101, 0102.
The minimum technological requirements for taking part in online courses can be found in U of T’s “Student Tech Requirements for Online Learning”Please have a look at this to ensure you have the technology that you’ll need to succeed while taking courses online. In addition to the minimium requirements included in the link above, in this course we recommend:
- A camera or scanner. (For digitizing assessments – while you can type your work, many find this a better solution for mathematics.)
- Speakers/Headphones and a Microphone. (If you will be taking part in “live” course compo-nents.)
- A video camera. (If you will take part in “live” course components – this will help facilitate working in small groups during LEC.)
Additionally, you will need to set up your “UTM Zoom Account” (as opposed to any personal Zoom account); visit https://utoronto.zoom.us/ before your first class to get that set up. Access to online classes will be restricted to those with U of T Zoom accounts. 线性代数网课代修
Inclusion & Accessibility
The University of Toronto is committed to equity, human rights and respect for diversity. All members of the learning environment in this course should strive to create an atmosphere of mutual respect where all members of our community can express themselves, engage with each other, and respect one another’s differences. U of T does not condone discrimination or harassment against any persons or communities.
The University provides academic accommodations for students with disabilities in accordance with the terms of the Ontario Human Rights Code. This occurs through a collaborative process that acknowledges a collective obligation to develop an accessible learning environment that both meets the needs of students and preserves the essential academic requirements of the University’s courses and programs.
At UTM, the Accessibility Office can provide more information about accessibility accommodations for students.
Generative AI – The use of generative AI is not allowed in MAT223H5F. Note that:
- The knowing use of generative artificial intelligence tools, including ChatGPT and other AI writing and coding assistants, for the completion of, or to support the completion of, an examination, term test, assignment, or any other form of academic assessment, may be considered an academic offense in this course.
- Representing as one’s own an idea, or expression of an idea, that was AI-generated may be considered an academic offense in this course. 线性代数网课代修
- Students may not copy or paraphrase from any generative artificial intelligence applications,including ChatGPT and other AI writing and coding assistants, for the purpose of completing assignments in this course.
- This course policy is designed to promote your learning and intellectual development and to help you reach course learning outcomes.
Course Structure 线性代数网课代修
The main purpose for the course structure outlined below is to use peer-reviewed pedagogical tools in the classroom, in a manner that is compatible with the goals of the course, to help you deeply understand very complex material and succeed in the course.
A weekly cycle in this course consists of the seven day cycle Monday → Sunday. During that cycle there are several components:
- READING: You will complete a pre-class reading, which will include specific learning objec- tives to meet, and practice exercises to help you meet them.(This is to be completed by Sunday evening before the week’s classes begin.)
- PCRA: After completing the reading you will take a pre-class quiz to check that you are prepared to take part in the in-class activities for the week.(This is to be completed by Sunday evening before the week’s classes begin.)
- In-Class Activities:Class time will be spent helping you learn the more subtle and confusing parts of the course, and actively work on problems.
- Asynchronous Activities: Each week there will be a short activity for you to complete on your own at home. It is paired with a video that takes up the activity after you complete it.
- Tutorials: Each week in tutorial you will work on a worksheet and have a chance to ask questions. As a reminder, all tutorials are in person.
- Post-Class HW: Outside of class you will work on homework assignments to help you practice what you’ve learned and solidify your knowledge.
- Weekly Guide: To help you keep track of what you need to do for each week, we will provide you with a “Weekly Guide” on the course page that outlines the week’s work cycle, and gives you direct links to each of the components you need to complete.
The following diagram should help explain the weekly work cycle in MAT 223.
As part of this course we will be conducting two surveys to help us assess the different course delivery options available this year. This includes learning about student perceptions and attitudes towards,and preferences for and interest in, online/hybrid delivery options for MAT courses. More information about these surveys will be sent out in future course announcements. Completion of both surveys is worth 2% of your final course grade.
Term Tests 线性代数网课代修
- There will be 2 (two) Term Tests. As a reminder, all tests in MAT 223H5F will be in-person. Term Tests will take place during the Thursday 6-8pm time slot regardless of LEC section. By registering for this class, you agree to be available at this time on these 2 dates. (They are part of the course schedule on the official UTM Timetable.) The dates of the tests are as follows:
Test #1 October 19, 2023
Test #2 November 16, 2023
Make Up Test November 30, 2023
- If you miss Test #1 or Test #2, you do not need to submit any documentation. You will automatically be eligible to write the Make Up Test on November 30th.
- If you miss the Make Up Test, you must provide valid documentation such as the UTM Veri-fication of Illness or Injury form.
The documentation must be sent to the assistant coordinator Minh Trinh within 1 week of the missed test.
PLEASE NOTE: you may not use the ACORN Declaration of Absence Tool for the Make Up Test.
(Each course can select one assessment which is excluded from use of this tool. In our course,that assessment is the Make Up Test.)
- The marking scheme will be adjusted as follows for students who have missed a test:
One missed test: You are eligible to write the Make-Up Test on November 30, and this will replace the missed test grade.
Two missed tests: You are eligible to write the Make-Up Test on November 30. The make up test will then be worth 25% of your course grade, and the final exam will be worth 55% of your final grade.
Missed make up: There will be no second make up test, regardless of the reason. If you miss the make up for a (documented) valid reason, then the relevant weight will be transferred to the final exam. This is a situation that we strongly discourage from happening. Please reach out to the course coordinator, or an academic advisor, if you are missing substantial amounts of class,so that we can try to help you get back on track, offer support and guidance about how best to proceed in the course, and/or point you towards relevant supports. If you do not write the make up test, and do not provide documentation for your absence, then you will receive a grade of 0 for the make up.
- Note: It is recommended to write the regular term tests if you are able to. If you miss a term test, you miss out on receiving valuable feedback early in the course. Also, the material on the make-up may be different than the material tested on the missed test. In fact, the material covered on the make up will cover anything from the course up to and including “Week 10”:for comparison, Test 1 covers weeks 1-4 and Test 2 covers weeks 5-8. For those who must miss a test (e.g. due to illness), writing the make-up test gives an opportunity to not have as much weight shifted to the final exam. 线性代数网课代修
The final exam of the course will take place during the examination period in December, and will be 3 hours long. It will cover all the material from the course. The date, time, and location of the exam will be arranged by the Exam’s Office, and posted once it has been set.
There will be 7 (seven) homework assignments in this course: the best 6 (six) will count towards your grade. Please see the course outline, on the last page, for the HW schedule. Homework is due before 11.59pm on the due date.We will use Crowdmark for written homework submission, and WebWork for the online homework.Please see the schedule on the course website for homework due dates. Please see the Crowdmark instructions posted on the course page, and consider submitting the (optional, no credit) “Crowdmark Practice Assignment,” to make sure you know how Crowdmark works before it counts.
Each student can request a 36h extension for HW (not PCRAs) once during the semester. If you submit your HW late (when using your 36h extension), you must notify the assistant coordinator Minh Trinh) that you have submitted late and you’re using your extension, otherwise your HW will get a grade of 0. Your email should include your name, your student id # and the HW for which you are using your extension.
Outside of these extensions, late assignments are not accepted.
Assignments consist of two components: written and online. Each assignment is worth a total of 10 points: 8 for the written component, and 2 for the online.
Written Component. The written component of each assignment will be submitted online on Crowdmark before 11.59pm on the due date. Technical issues (e.g. slow internet, computer crashing)will not be accepted as an excuse for not completing an assignment on time. You will be given your assignment roughly a week before the due date, to allow you time to work on it, ask questions, and write up your assignment, digitize it and submit it to CM. Please don’t wait until the last minute to start your assignment, so that any issues you run into (including uncertainty over the content of the assignment or the statement of the assignment questions, writing up solutions neatly, and digitization/upload of your assignment) may be resolved in time.
It is ok (and you are encouraged) to work together on material related to the course, including discussing the written assignments. HOWEVER, you must write up your own solutions independently.It is an academic offence to copy someone’s solution, or to let someone copy yours. It is an academic offence to copy from a solution manual or a website. Please see the links below concerning UTM’s code of behaviour and academic honesty.
The online component of each assignment will be due by 11.59pm on the due date. Technical issues will not be accepted as an excuse for not completing an assignment. (So don’t wait until the last minute to start.)
The online component of each assignment will be done using the “WebWork” system: it is a free (open
source) online homework platform that links directly from Quercus. In particular, you do not need to
create any account: simply click the ”WebWork” link from the course page to access the system.
PCRA – “Pre-Class Readiness Assessment” 线性代数网课代修
Each week you will complete a short quiz based on the weekly reading before the week’s classes begin.This quiz is meant to help you assess how well you understood the reading and how well prepared you are for the week’s classes. You will have unlimited attempts on each PCRA until the due date.It is important that you answer the quiz questions to the best of your ability, so that you get a sense of what you need help with, and so that your instructor can see what might be confusing students and needs extra review in class. The PCRA is worth 4% of your final grade, with the best 10 of 11 counting towards your grade.
Each week we will make use of some “Polling Questions” that will help you and your instructor check understanding of basic concepts. These are graded for participation only – you and your instructor need your honest attempts at solving these problems to assess what you might need help with. Participation on these questions is worth 4% of your final grade. To earn a full 4% you must participate in a minimum of 80% of the polls. We will use the MathMatize platform for these problems. Instructions for setting up a MathMatize account are posted on the course page.Please note that this requires you to bring a device (e.g. smart phone, tablet, laptop) which canconnect to the internet to class. If you do not have access to such a device, please contact the course coordinator.
Help & Suggestions for Success
If you need help there are many resources available to you. Please come and ask us for help as soon as you need it. Try not to let yourself fall behind. Here are some suggestions for succeeding in this course,including some options that may be helpful if you feel you need additional help/support. However,all of these suggestions apply equally to all students: in fact, making use of the following resources is the hallmark of a successful student!
- All course staff have office hours, which are posted on the course page, and at the top of this document. 线性代数网课代修
- We will make extensive use of the course discussion board. Instructors and TAs have extra hours allocated to checking in on the discussion board, and most questions posted should be answered in less than 24h. (Usually faster than that, but evenings and weekends may result in slower response times.)
- You will have opportunities to ask questions in Tutorials.
- You may find working in a small study group can be very helpful. This may be complicated by busy schedules, but you can use tools like Zoom if that helps find common times among classmates.
- The Academic Skills Centre also has much to offer: https://www.utm.utoronto.ca/asc/.
- Additionally, see the “Support Services & Resources” section of the course page for links to a wide variety of supports and resources available to UTM students.
Code of Behaviour / Plagiarism
Academic integrity is essential to the pursuit of learning and scholarship in a university, and to ensuring that a degree from the University of Toronto Mississauga is a strong signal of each student’s individual academic achievement. As a result, UTM treats cases of cheating and plagiarism very seriously. The University of Toronto’s Code of Behaviour on Academic Matters outlines behaviours that constitute academic dishonesty and the process for addressing academic offences. Potential offences include, but are not limited to:
- In papers and assignments:
- Using someone else’s ideas or words without appropriate acknowledgement.
- Submitting your own work in more than one course, or more than once in the same course,without the permission of the instructor.
- Making up sources or facts.
- Obtaining or providing unauthorized assistance on any assignment.
- On tests and exams:
- Using or possessing unauthorized aids.
- Looking at someone else’s answers during an exam or test.
- Misrepresenting your identity.
- In academic work:
- Falsifying institutional documents or grades.
- Falsifying or altering any documentation required, including (but not limited to) doctor’s notes. 线性代数网课代修
All suspected cases of academic dishonesty will be investigated following procedures outlined in the Code of Behaviour on Academic Matters.
If you have questions or concerns about what constitutes appropriate academic behaviour or appropriate research and citation methods, you are expected to seek out additional information on academic integrity from your instructor or from other institutional resources.
Here are some other relevant links:
(Office of the Dean: Academic Integrity)
(Preventing Academic Offences)
(Advice on avoiding plagiarism)
(Policies for exams)
(Videos about Academic Integrity)
Email Policy 线性代数网课代修
Before you send an email to course staff, please check if the answer to your question is in the syllabus or on the discussion board. If your question is administrative or about course policy, please email the course coordinator (Jaimal Thind: [email protected]) rather than your instructor. All emails to course staff should come from your “utoronto” email account, and contain “MAT 223” in the subject heading. You can expect a response to your email within ∼24h (excluding weekends).
Course Goals and Learning Objectives
In this course we will study Linear Algebra and some of its applications.
- Students will learn about connections between, and different perspectives on algebraic objects and tools such as linear systems, matrices, transformations and subspaces.
- Students will do this by mastering procedural tasks involving these objects and tools, but also by analyzing and solving problems related to the conceptual underpinnings of these objects and tools.
- Rigorous mathematical proof is lightly introduced, and students will be expected to determine if a mathematical statement (related to the course content) is true or false and justify their answer with some rigour.
- Students will also be introduced to writing mathematics with an audience of peers in mind, and will be expected to reflect on their written work with those peers.
- Students will also gain an appreciation of a few of the many applications of linear algebra outside of mathematics; this is partly to help students understand the mathematical framework for those applications, but also to inspire students to continue their study of linear algebra and mathematics. 线性代数网课代修
Upon completion of this course…
- Students should be able to apply various algorithms and procedures to solve a variety of computational problems.
- Additionally, students should (with respect to key terminology and notation from linear algebra) be able to:
- Recognize and express the meaning of said terminology and notation.
- Recall the statements of key theorems and definitions.
- Interpret a novel definition or statement which involves terminology or notation.
- Reformulate a statement involving some of the terminology and/or notation using different terminology and/or notation, including passing from algebraic to geometric interpretations and vice-versa. 线性代数网课代修
With respect to an extensive list of linear algebraic objects, (such as vectors, matrices, linear systems, transformations, subspaces, etc) be able to:
- Create examples which have and/or lack various combinations of properties.
- Visualize or graphically depict those objects (where applicable) including detail about rel-evant features they may have.
- Verify that a statement or claim about such objects is true using a brief mathematical argument, or prove that the statement is false by applying the previous skill to create an appropriate counterexample.
- Be able to apply the computational and analytical skills listed above to solve problems involving familiar and novel applications.
- Have begun to develop their ability to learn new mathematics by reading written mathematics;in particular by reading and actively interacting with a set of “scaffolded” readings specificallydesigned for this course.
- Be able to write short mathematical explanations geared towards an audience of peers, and receive and effectively respond to feedback on this work from their peers.