MATH133 Syllabus - Winter 2020 PDF

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Welcome to Math 133! M C G ILL U NIVERSITY, D EPARTMENT OF M ATHEMATICS AND S TATISTICS C OURSE O UTLINE , W INTER 2020

Math 133: Linear Algebra and Geometry (3 credits) Lecture time and location: Tuesdays and Thursdays, 4:05pm - 5:25pm, SADB M-1 Course instructor: Tyrone Ghaswala Email: [email protected] (please use your McGill email address and begin the subject line with MATH 133. I will respond to all emails within 48 hours) Office: Burnside Hall Room 1243 (12th floor, take a left out of the elevators or stairs). Office hours: Tu 2:00pm - 3:30pm and Th 1:00pm - 2:30pm, or by appointment. These hours are subject to change and any changes will be posted on the course website on myCourses. Course website: We will be using myCourses. Anything and everything course related will be posted there. Course overview: Linear algebra is one of the most powerful and beautiful parts of mathematics. It is widely applied in many fields such as computer science, economics, engineering, epidemiology, ecology, physics, psychology, statistics and anything that involves dealing with a lot of data (to name just a few)! Starting from the seeminly innocent topic of solving linear systems of equations, we will be lead to 2- and 3-dimensional geometry, building intution for tackling higher-dimensional problems. Along the way we will be introduced to determinants, eigenvalues, eigenvectors, and diagonalisation. As the course progresses, so will the level of abstraction, allowing us to apply the same tools to seemingly unrelated problems, which is where the true power of linear algebra lies! Prerequisite: A course in functions. Restrictions: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent. Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics. Not open to students who are taking or have taken MATH 134. Required Course Materials: It is not necessary to pruchase anything for this course. The textbook for this course is freely available online at https://lyryx.com/linear-algebra-applications/ : W. K. Nicholson, Linear Algebra with Applications, Open Edition. Lyryx Learning Inc. Base Textbook, Version 2019, Revision A. Please download it and save a copy on your computer so you can annotate it. Or you may want to find a printing service to have it printed for cheap, as you wish. Please ignore the online assignments mentioned on the textbook’s webpage, we will use our own (through WebWork). Optional Course Materials: The following are a few resources you may find useful. Beware that the notation may be different from ours, the material covered will almost certainly be different, and the difficulty of the exercises may vary wildly from what is expected in our course. The McGill library has more elementary linear algebra textbooks than you can poke a stick at, including the last one listed below. • Shaum’s Outline of Linear Algebra is a low-cost textbook, which is generally used in Math 223/270, a possible follow-up to Math 133. • Linear Algebra Done Wrong - Sergei Treil. Another open source textbook, and you can download a pdf at https://www.math.brown.edu/˜treil/papers/LADW/LADW.html. • Elementary Linear Algebra - Anton and Rorres. One of the many standard linear algebra textbooks, some editions are available at the McGill library. Evaluation: You will be evaluated in 3 ways: through the online WebWork assignments, midterms, and a final. No calculators will be allowed for the midterms and final.

Final Grade = (Webwork assignments)· 10% + (Midterm 1) · 20 % + (Midterm 2) · 20% + (Final exam) · 50 %. There will be 5 WebWork assignments, each worth 2%, plus a set 0 which does not count towards your final grade. Below are the dates for all of the assessments. Webwork assignments • • • • • •

Set 0 - Open at 12:00pm on 6th Jan. No due date. Set 1 - Open at 12:00pm on 20th Jan. Due at 11:59pm on 24th Jan. Set 2 - Open at 12:00pm on 3rd Feb. Due at 11:59pm on 7th Feb. Set 3 - Open at 12:00pm on 17th Feb. Due at 11:59pm on 21st Feb. Set 4 - Open at 12:00pm on 9th Mar. Due at 11:59pm on 13th Mar. Set 5 - Open at 12:00pm on 23rd Mar. Due at 11:59pm on 27th Mar.

Midterms • Midterm 1, in class on 13th Feb. • Midterm 2, in class on 17th Mar. Final: To be advised. In accord with McGill University’s Charter of Students’ Rights, students in this course have the right to submit in English or in French any written work that is to be graded. Tutorials: Our graduate Teaching Assistants (TAs) will hold weekly tutorials, starting on the second week of class, which you signed up for through Minerva when you registered for the class. You are expected to attend. This is a great chance to work through problems with your classmates while the TAs are around. Mathematics is not a spectator sport, and struggling with problems is the best way to learn. Here are the contact details of your TAs: • Sections 4, 5: C´eline Kerriou, [email protected], BURN 1023, office hour Fri 10:30 - 11:30am. • Sections 2, 3: Reginald Lybbert, [email protected], BURN 1036, office hour Fri 2:00 - 3:00pm. Extra help: Here are some resources for extra help in the course: • Office hours: Come and ask me anything, or at least drop by to say hi and introduce yourself! • FRezCa (First Year Residence Cafeteria): A drop-in help centre for first year students to ask any questions and work together in a convivial place: the Royal Victoria College Cafeteria. It is offered for math, physics, biology and chemistry students. It is free of charge! For our course, FRezCa starts in the second week of classes, and is staffed Mondays, Wednesdays and Thursdays from 2:30pm to 4:30pm. More information is at their website: https://www.mcgill.ca/ose/frezca. • The Helpdesk: Located in BURN 911, this is a departmental resource. It is a space open for you to work, alone or in study groups. It is staffed by knowledgeable students who can help answer your questions about the material (feel free to also ask them about other math courses to take, or their experience as a math major). The room is usually open and staffed from 10am to 5pm on weekdays. • Each other: Make as much of an effort as you can to meet other people in your class as early as possible. Not only will this give you people to work with and ask for help, it will also make your time here more enjoyable! Helping other people understand material is one of the most effective ways to learn. Academic integrity: Cheating and copying is absolutely, 100%, completely, super-duper unacceptable and just plain wrong. You are all mature enough not to cheat, and you are only robbing yoursef of your education if you do so. McGill University values academic integrity. Therefore all students must understand the meatning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see http://www.mcgill.ca/students/srr/honest/ for more information). Student well-being, mental health and barriers to learning: We all experience moments of struggle, doubt, questioning, pain... You don’t have to go through this alone, please visit the Wellness Hub and find resources

to support you: https://mcgill.ca/wellness-hub/. If you experience barriers to your learning in this course, please let me know about your situation. Also, the Office for Students with Disabilities might be of help: https://mcgill.ca/osd/. Some other important things: • Mathematics is not a spectator sport (you will hear me say this lots of times during the semester), and the best way to learn is to do problems and exercises. There are lots of these in the book, online, and I will provide you with additional practice problems throughout the semester. • I expect you to care about your education first, and your grades second. You can expect me to do the same. Begging for extra grades is simply a waste of your time and my time. However, if you are working hard and genuinely attempting to learn and understand the material, I will be more than willing to help you out however I can! • There will be no need for calculators or smarter devices during class, or during the assessments. In the interest having control over our devices (and not the other way around), unless you are using your device for note-taking purposes, it should be well out of sight and off or silent during class. • Instructor-generated course materials (e.g., handouts, notes, slides, exam questions, etc.) are protected by law and may not be copied or distributed in any form or in any medium without explicit permission of the instructor. No audio or video recording of lectures or presentations is allowed in any format, openly or surreptitiously, in whole or in part without permission from your instructor. Note that infringements of copyright can be subject to follow up by the University under the Code of Student Conduct and Disciplinary Procedures. • In the event of extraordinary circumstances beyond the University’s control, the content and/or evaluation scheme in this course is subject to change, provided that there be timely communications to the students regarding the change. Tentative schedule: This schedule is not written in stone, and may change as the semester goes on. Week Jan. 6 Jan. 13 Jan. 20 Jan. 27 Feb. 3 Feb. 10 Feb. 17 Feb. 24 Mar. 2 Mar. 9 Mar. 16 Mar. 23 Mar. 30 Apr. 6

Notes First class Jan. 7 Webwork 1 due Jan. 24 Webwork 2 due Feb. 7 Midterm 1 Feb. 13 Webwork 3 due Feb. 21

Topics Linear systems, Gaussian elimination RREF, Rank, vector geometry Lines, dot product, projection Planes, cross product, matrix algebra Inverses and determinants Vector spaces, subspaces Bases, dimension Coordinates, linear maps

Book sections 1.1-1.2 1.3, 1.6, 4.1 4.1, 4.2 4.2, 4.3, 2.1 2.3, 2.4, 2.5, 3.1, 3.2 6.1, 6.2 6.3, 6.4 9.1, 4.4, 7.1

linear maps, range and nullspace Rank-nullity theorem, matrices as linear maps More on linear maps, isomorphisms Diagonalisation, eigenvalues, eigenvectors Dynamical systems, least squares regression

7.1, 7.2 2.6, 7.2, 9.1 2.6, 7.3 3.3, 5.5, 9.3 3.4, 5.6

Break Webwork 4 due Mar. 13 Midterm 2 Mar. 17 Webwork 5 due Mar. 27 Last class Apr. 9...