Math 18: Linear Algebra

Lectures B00 (Kemp) & C00 (Chan)

About this Course

Welcome to Math 18! This is a one quarter course on linear algebra. Linear algebra is, in many ways, the backbone of mathematics, engineering, and science. It plays a central role in computation at all levels, including the most basic: the device you're using to read this webpage, at its core, is doing nothing but linear algebra all day long. Linear algebra is fundamental to statistics, foundational to physical sciences, and is the ground floor of calculus. (Calculus is about approximating structures with simpler linear structures; linear algebra is the theory of those simpler linear structures.) This course will also introduce you, gently, to the world of mathematical thinking and rigor. It may well be the most important course you ever take!

Course Information

Instructional Staff

Todd Kemp Lead Instructor APM 5202
Pak-Yeung Chan Instructor APM 6432
Paul Orland Lead TA APM 6436
Ryan Schneider Lead TA APM 2202
Chenyang An TA APM 6414
Xiaomeng Hu TA APM 6446
Finley McGlade TA APM 6414
Xihan (Henry) Qian TA
Frederick Rajasekaran TA
Nicholas Sieger TA
Keren Shao TA APM 6446
Xie Wu TA APM 5801
Runqiu Xu TA APM 6446
Christopher Xue TA APM 5412
Nicholas Zhao TA APM 6414

We will also have support from the Academic Achievement Hub's Supplemental Instruction. SI Leaders will be embedded in our discussion sections to facilitate active learning, and there will also be separate SI Sessions run through the Teaching + Learning Commons.

Please note: Piazza should be your first stop for any course-related communication with the instructional staff. We ask that when you have a question about the class that might be relevant to other students, you post your question on Piazza instead of emailing us. That way, everyone can benefit from the response. Please only email your instructor/TA in the case of an urgent private matter (relevant to your enrollment in the course).

Class Meetings

In the following scheduled meeting times, physical locations are listed where relevant. However: all instruction will be remote for (at least) the first two weeks of the Winter quarter, conducted through Zoom. Zoom meeting coordinates can be found in Canvas.

Lecture B00 (Kemp) MWF1:00pm - 1:50pmJEANNIE AUD
Lecture C00 (Chan) MWF3:00pm - 3:50pmPETER 110
Discussion B01 (Zhao) Tu2:00pm - 2:50pmRemote
Discussion B02 (Zhao) Tu3:00pm - 3:50pmRemote
Discussion B03 (Xue) Tu4:00pm - 4:50pmRemote
Discussion B04 (Wu) Tu3:00pm - 3:50pmRemote
Discussion B05 (Wu) Tu4:00pm - 4:50pmRemote
Discussion B06 (Xue) Tu5:00pm - 5:50pmRemote
Discussion B07 (Wu) Tu5:00pm - 5:50pmRemote
Discussion B08 (Wu) Tu6:00pm - 6:50pmRemote
Discussion B09 (Xu) Tu2:00pm - 2:50pmRemote
Discussion B10 (Orland) Tu1:00pm - 1:50pmRemote
Discussion B11 (Schneider) Tu4:00pm - 4:50pmRemote
Discussion B12 (Zhao) Tu5:00pm - 5:50pmRemote
Discussion B13 (Zhao) Tu6:00pm - 6:50pmRemote
Discussion B14 (Xu) Tu4:00pm - 4:50pmRemote
Discussion B15 (Xu) Tu5:00pm - 5:50pmRemote
Discussion B16 (Xu) Tu6:00pm - 6:50pmRemote
Discussion B17 (Qian) Tu10:00am - 10:50amRemote
Discussion B18 (Qian) Tu11:00am - 11:50amRemote
Discussion B19 (An) Tu12:00pm - 12:50pmRemote
Discussion B20 (An) Tu1:00pm - 1:50pmRemote
Discussion B21 (Rajasekaran) Tu9:00am - 9:50amRemote
Discussion B22 (Rajasekaran) Tu10:00am - 10:50amRemote
Discussion B23 (McGlade) Tu5:00pm - 5:50pmRemote
Discussion B24 (McGlade) Tu6:00pm - 6:50pmRemote
Discussion B25 (Sieger) Tu11:00am - 11:50amRemote
Discussion B26 (Sieger) Tu12:00pm - 12:50pmRemote
Discussion C01 (Shao) Tu12:00pm - 12:50pmRemote
Discussion C02 (Shao) Tu1:00pm - 1:50pmRemote
Discussion C03 (Shao) Tu5:00pm - 5:50pmRemote
Discussion C04 (Shao) Tu6:00pm - 6:50pmRemote
Discussion C05 (Hu) Tu6:00pm - 6:50pmRemote
Discussion C06 (Hu) Tu7:00pm - 7:50pmRemote
Quiz 1 Thu, Jan 20 30 minutes in 24 hour windowRemote
Midterm Exam Thu, Feb 38:00pm - 9:50pmRemote
Quiz 2 Thu, Feb 24 30 minutes in 24 hour windowRemote
Final Exam Sat, Mar 123:00pm - 5:59pmTBA

Calendar of Meeting Times

Calendar of Course Content

The following calendar is subject to revision during the term. The section references are only a guide; our pace may vary from it somewhat.

Week Monday Tuesday Wednesday Thursday Friday Saturday
Jan 3
1.1 Systems of linear equations
Jan 4
Jan 5
1.2 Row reduction & echelon forms
Jan 6 Jan 7
1.3 Vector equations
Jan 13
Jan 10
1.4 Matrix equation
Ax = b
Jan 11
Jan 12
1.5 Solution sets
Jan 13 Jan 14
1.7 Linear independence
Deadline to Add a Course
Jan 15
Jan 17
Martin Luther
King Day
Jan 18
Jan 19
Catch Up & Review
Jan 20 Jan 21
1.8 Linear transformations
Jan 22
Jan 24
1.9 The matrix of a linear transformation
Jan 25
Jan 26
2.1 Matrix operations
Jan 27 Jan 28
2.2, 2.3 Inverse of a matrix
Deadline to Drop w/o 'W'
Jan 29
Jan 31
4.1 Vector spaces and subspaces
Feb 1
Feb 2
4.2 Null spaces & column spaces
Feb 3
Feb 4
4.3 Linear independent sets; bases
Feb 5
Feb 7
4.5 Dimension
Feb 8
Feb 9
4.4 Coordinate systems
4.5 Rank
Feb 10 Feb 11
3.1 Determinants
3.2 Determinant properties
Deadline to Drop w/ 'W'
Feb 12
Feb 14
3.3 Determinants and volume
Feb 15
Feb 16
5.1 Eigenvectors and eigenvalues
Feb 17 Feb 17
5.2 Characteristic polynomial
Feb 18
Feb 21
Martin Luther
Presidents' Day
Feb 22
Feb 23
Catch Up & Review
Feb 24 Feb 25
5.3 Diagonalization
Feb 26
Feb 28
6.1, 6.7 Inner product,
length, & orthogonality
Mar 1
Mar 2
6.2 Orthogonal sets
Mar 3 Mar 4
6.3 Orthogonal projections
Mar 5
10 Mar 7
6.4 Gram-Schmidt orthogonalization
Mar 8
Mar 9
7.1 Spectral Theorem
Mar 10 Mar 11
Mar 12

Reading:  Reading the sections of the textbook corresponding to each lecture is critical. Homework, quizzes, and exams will rely on material in the textbook; you are responsible for material in the assigned reading whether or not it is discussed in the lecture.



Course: Math 18

Title: Linear Algebra

Credit Hours: 4 (Students may not receive credit for both Math 18 and 31AH.)

Prerequisite: Math Placement Exam qualifying score, or AP Calculus AB score of 3 (or equivalent AB subscore on BC exam), or SAT II Math Level 2 score of 650 or higher, or Math 4C, or Math 10A, or Math 20A, or consent of instructor.

Catalog Description: Matrix algebra, Gaussian elimination, determinants, Linear and affine subspaces, bases of Euclidean spaces. Eigenvalues and eigenvectors, quadratic forms, orthogonal matrices, diagonalization of symmetric matrices. Applications. Computing symbolic and graphical solutions using MATLAB. See the UC San Diego Course Catalog.

Textbook: Linear Algebra and its Applications (6th Edition), by David C. Lay, Steven R. Lay, and Judi J. McDonald; published by Pearson (Addison Wesley).

Subject Material: We will cover parts of chapters 1-7 of the text.

Lecture: Attending the lecture synchronously, or viewing the lecture podcast or Kaltura recording asynchronously, is a fundamental part of the course; you are responsible for material presented in the lecture whether or not it is discussed in the textbook.  You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

Discussion Sections: Discussion sections will be highly interactive. You will work in small groups on concept check and challenging exercises, to cement your understanding of core ideas from the course, and build a community of learning in this large class. Attendance of discussion sections is required, which means you must attend the section you are officially enrolled in. To gain full participation credit for the course, you must attend at least 8 out of the 10 discussion sections during the quarter.

Homework: Homework is a very important part of the course and in order to fully master the topics it is essential that you work carefully on every assignment and try your best to complete every problem. Weekly homework is assigned through MyLab, accessible in Canvas. Unless otherwise stated, you have unlimited attempts on each homework problem. All problems completed before the due date will receive full credit. You may continue to work on problems you did not complete before the deadline, for 50% credit until the end of the quarter. Your total homework score will be based on all the total possible homework points available; no homework assignment scores will be dropped at the end of the quarter.

MATLAB: In applications of linear algebra, the theoretical concepts that you will learn in lecture are used together with computers to solve large scale problems.  Thus, in addition to your written homework, you will be required to do homework using the computer language MATLAB.  The Math 18 MATLAB Assignments page contains all information relevant to the MATLAB component of Math 18.

Quizzes: There are two quizzes, in Weeks 3 and 8; see above for the dates. Each quiz will have a 30 minute time limit. You will take it remotely, any time in a 24-hour window, through Gradescope.

Exams: The midterm exam and final exam are scheduled for the Thursday of Week 5 and the first Saturday of exam week; see above for details. The exams are planned to take place in-person; this may change depending on UC San Diego policy and the public health situation at the time. More information will follow closer to these exams about precise logistics and policies.

Exam Versions: There may be different versions of exams given, whether in-person or remote, synchronous or asynchronous. All versions of any exam will cover the same topics and will be calibrated to the same level of difficulty.

Collaboration Guidlines: You are allowed, and encouraged, to collaborate with other students in the MyLab homework and MATLAB assignments. It is up to your own best judgment to make sure you are learning the material through those collaborations. No collaboration is allowed on quizzes or exams. Moreover, "homework assistance" online sites such as Chegg are NEVER allowed for use in this class on homework, quizzes, or exams. Any use of Chegg or similar services will be considered serious Academic Integrity violations.

Academic Integrity: In this course, and in your life as a UC San Diego student, we expect you to Excel with Integrity, and to adhere to the UC San Diego Integrity of Scholarship Policy.

Why? Math 18 is a core, foundational course for a wide variety of other mathematics, engineering, and physical science courses. This class is designed to aid your mastery of this important material, for its own sake and for the sake of your learning in all the further courses that rely heavily upon it. Every course component in Math 18 is formulated to cement your understanding, verify what you've mastered, and let us and you know where you need to prioritize your time and energy reviewing. All of our course policies around academic integrity are meant to make sure you are getting the best, most accurate information about your learning in this course. Any students who choose to violate our integrity policies are not just being unfair to their peers; they are ultimately cheating themselves out of a solid foundation in linear algebra.

That means we’re all in this together and we actually want the same thing. You, your peers, and the instructional team all want a class that has academic integrity. We want to be able to trust one another, and we want grades to be fair and honest reflections of learning. How can you ensure this type of environment is created in Math 18? Here are some specific examples:

We are aware that the temptation to inappropriately collaborate, or use disallowed resources, is especially high right now during this period of remote/hybrid instruction. We urge you to remember that your integrity is worth more than any advantage you might hope to gain. We will (unfortunately) have to use all tools at our disposal to detect any academic integrity violations, for which there is a zero-tolerance policy. Penalties for these offenses always include assignment of a failing grade in the course, along with administrative sanctions, including up to suspension and dismissal from UC San Diego. Both failing grades and the administrative penalties could impact your ability to get into a capped major or be admitted into graduate or professional schools. Maintain your integrity, and don't risk major consequences to your career at UC San Diego and beyond.

Grading Policies: Your total grade in this course will be determined by the following components.

Your letter grade will be determined by your cumulative average at the end of the term and will be based on the following scale:

A+ A A- B+ B B- C+ C C-
97 93 90 87 83 80 77 73 70
The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, we may adjust the above scale to be more generous.

Missed quiz/exam policy: There will be no make-up exams or quizzes. If you must miss a quiz or midterm exam, the portion of credit assigned to that quiz or exam will be transferred to a portion of your final exam. For example: a selection of questions on the final exam will cover similar material to the midterm exam; if you must miss the midterm, the 15% credit it is worth will be determined by your scores on that selection of final exam questions. In fact, this will be automatic: if your grade from that portion of the final exam is higher than your midterm score, it will be counted instead of the midterm. The same holds true for quiz 1 and quiz 2. Nevertheless: you should make every effort to write the quizzes and the midterm; this policy is meant only to accommodate true emergencies.

There will be no make-up final exam. If you miss the final exam, you will be assigned a score of 0 on that component of the class. If you have a conflict with the scheduled final exam time, you should not enroll in Math 18 this quarter. If an unexpected emergency or crisis prevents you from attending the final exam at the end of the quarter, and if you are in passing standing in the class at that time, you may be eligible for an Incomplete grade that will allow you to take the final exam at a later date. The circumstances under which Incompletes can be granted are tightly controlled by the university.

Here are two links regarding UC San Diego policies on exams:

Regrade Policy: Your quizzes, exams, and MATLAB homework will be graded using Gradescope. If you find errors in grading, you will have an opportunity to request a regrade. A regrade window will be open approximately one week following the due date, during which you can leave careful, thoughtful comments about where you feel a grading error was made. No regrade requests will be considered after the specified window. Please note: any regrade request may result in regrading of the entire assignment, and your overall score could go up or down.

Administrative Deadline: Your scores for all graded work will be posted in Gradescope and in Canvas. It is your responsibility to check your scores and contact your TA before the end of Week 10 to resolve recording errors. Questions regarding missing or incorrectly recorded scores will not be considered after the last day of instruction.

Considerate Conduct: Here are a few of our expectations for etiquette in and out of class.

Equity, Diversity, and Inclusion: We are committed to fostering a learning environment for this course that supports a diversity of thoughts, perspectives, and experiences, and respects your identities, including race, ethnicity, heritage, gender, sex, class, sexuality, religion, ability, age, educational background, etc. Our goal is to create a diverse, inclusive, and empowering learning environment where all students feel comfortable and can thrive.

Our instructional staff will make a concerted effort to be welcoming and inclusive to the wide diversity of students in this course. If there is a way we can make you feel more included please let one of the course staff know, either in person, via email/discussion board, or even in a note under the door. Our learning about diverse perspectives and identities is an ongoing process, and we welcome your perspectives and input.

We also expect that you, as a student in this course, will honor and respect your classmates, abiding by the UC San Diego Principles of Community. Please understand that others’ backgrounds, perspectives and experiences may be different than your own, and help us to build an environment where everyone is respected and feels comfortable.

If you experience any sort of harassment or discrimination, please contact the instructor as soon as possible. If you prefer to speak with someone outside of the course, please contact the Office of Prevention of Harassment and Discrimination.

Students with Disabilities: We aim to create an environment in which all students can succeed in this course. If you have a disability, please contact the Office for Students with Disability (OSD), which is located in University Center 202 behind Center Hall, to discuss appropriate accommodations right away. We will work to provide you with the accommodations you need, but you must first provide a current Authorization for Accommodation (AFA) letter issued by the OSD. You are required to present their AFA letters to faculty (please make arrangements to contact your instructor privately) and to the OSD Liaison in the Math Department (Holly Proudfoot, in advance so that accommodations may be arranged. You will find more information here.

Basic Needs and Food Insecurities: If you are experiencing any basic needs insecurities (food, housing, financial resources), there are resources available on campus to help, including The Hub and the Triton Food Pantry. Please visit here to for more information.