Math 18: Linear Algebra

Lectures A00 (Anzaldo), B00 and C00 (Agrawal), D00 (Pardo Guerra)

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

Name Role Office Office hours (see Canvas for Zoom links) Email
Leesa Anzaldo
Lead Instructor APM 7432 In-person: TuTh 11am-12:30pm
Remote: Mondays 5pm-6pm
Shishir Agrawal
Instructor APM 1210
Sebastian Pardo Guerra
Instructor APM
Maxwell Johnson Lead TA HSS 5027
Nicholas Karris Lead TA HSS 5027
Jordan Benson
TA HSS 5044
Arseniy Kryazhev
TA HSS 5029
Haoyu Li
TA HSS 4024
Alexander Mathers
TA HSS 4072
Gregory Patchell
TA HSS 4008
Shubham Saha
TA HSS 4005
Yifan Xiao
TA APM 5748
Zehong Zhao
TA HSS 4073
Snigdha Allada
Eric Gu
Jiaxin Guan
Margaret Luo
Eric Nguyen
Itai Maimon

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.

Class Meetings

Lecture A00 Meetings Date Time Location
Lecture A00 (Instructor: Anzaldo)
9:30am - 10:50am JEANN AUD
Discussion A01 (TAs: Li, Zhao; Tutor: Gu) Th 8:00pm - 8:50pm PODEM 1A19
Discussion A02 (TAs: Patchell, Saha; Tutors: Allada, Guan) Th 6:00pm - 6:50pm FAH 1101
Discussion A03 (TAs: Patchell, Saha; Tutor: Allada) Th 7:00pm - 7:50pm MOS 0204
Discussion A04 (TAs: Patchell, Saha; Tutor: Allada) Th 8:00pm - 8:50pm MOS 0204
Discussion A05 (TAs: Patchell, Saha; Tutors: Allada, Guan) Th 5:00pm - 5:50pm FAH 1101
Discussion A06 (TA: Karris; Tutor: Nguyen) Th 8:00pm - 8:50pm APM B402A
Discussion A07 (TAs: Benson, Kryazhev; Tutor: Guan) Th 7:00pm - 7:50pm PETER 103
Discussion A08 (TAs: Benson, Kryazhev; Tutor: Guan) Th 8:00pm - 8:50pm PODEM 1A18
Lecture B00 Meetings Date Time Location
Lecture B00 (Instructor: Agrawal) MWF 10:00am - 10:50am WLH 2005
Discussion B01 (TA: Xiao) Th 3:00pm - 3:50pm APM B402A
Discussion B02 (TA: Xiao) Th 4:00p - 4:50pm APM B402A
Discussion B03 (TA: Xiao; Tutor: Nguyen) Th 5:00p - 5:50pm APM B402A
Discussion B04 (TA: Zhao; Tutor: Gu) Th 6:00p - 6:50pm APM B402A
Lecture C00 Meetings Date Time Location
Lecture C00 (Instructor: Agrawal) MWF 12:00pm - 12:50pm PCYNH 106
Discussion C01 (TAs: Li, Zhao; Tutor: Gu) Th 5:00pm - 5:50pm PODEM 1A19
Discussion C02 (TA: Xiao) Th 7:00pm - 7:50pm APM B402A
Discussion C03 (TAs: Li, Zhao; Tutor: Gu) Th 7:00pm - 7:50pm PODEM 1A19
Lecture D00 Meetings Date Time Location
Lecture D00 (Instructor: Pardo Guerra) MWF 3:00pm - 3:50pm CSB 002
Discussion D01 (TAs: Johnson, Mathers; Tutor: Luo) Th 7:00pm - 7:50pm PODEM 1A18
Discussion D02 (TA: Mathers; Tutor: Luo) Th 8:00pm - 8:50pm DIB 121

Exam Information

Date Time Location
Midterm Exam 1
Friday, October 27 6:00pm - 6:50pm
A00PETER 108 and TBA
B00PETER 110
C00MOS 0114
D00CSB 002
Midterm Exam 2
Friday, November 17 6:00pm - 6:50pm
A00PETER 108 and TBA
B00PETER 110
C00MOS 0114
D00CSB 002
Final Exam Saturday, December 9
3:00pm - 5:59pm TBA


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 Lecture topics for the week Monday Tuesday Wednesday Thursday Friday Saturday
1.1 Systems of Linear Equations
Sep 25 Sep 26 Sep 27 Sep 28
First day of class for Lecture A00
Sep 29
First day of class for Lectures B00, C00, D00
Sep 30
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax=b
Oct 2 Oct 3 Oct 4 Oct 5
Oct 6 Oct 7
1.5 Solution Sets of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
Oct 9 Oct 10 Oct 11 Oct 12
Oct 13
First Day Survey due
Deadline to Add a Course
Oct 14
1.9 The Matrix of a Linear Transformation
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
Oct 16
Oct 17
MyLab HW 1 due
MyLab HW 2 due
Oct 18 Oct 19
Oct 20 Oct 21
4.1 Vector Spaces and Subspaces
Catch-up/Review for Midterm 1
4.2 Null Spaces, Column Spaces, and Linear Transformations
Oct 23 Oct 24
MyLab HW 3 due
Oct 25
Oct 26
Oct 27
Midterm Exam 1
Deadline to Drop without "W"
Oct 28
4.3 Linearly Independent Sets; Bases
4.5 The Dimension of a Vector Space
4.4 Coordinate Systems
Oct 30 Oct 31
MyLab HW 4 due
Nov 1 Nov 2
Nov 3 Nov 4
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
Nov 6 Nov 7
MyLab HW 5 due
Nov 8
Nov 9
Nov 10
Veterans Day Holiday - no class
Nov 11
5.1 Eigenvectors and Eigenvalues
Catch-up/Review for Midterm 2
5.2 The Characteristic Equation
Nov 13
Deadline to Drop with "W"
Nov 14
MyLab HW 6 due
Nov 15 Nov 16
Nov 17
Midterm Exam 2
Nov 18
5.3 Diagonalization
6.1 Inner Product, Length, Orthogonality
6.7 Inner Product Spaces
Nov 20 Nov 21
MyLab HW 7 due
Nov 22
Nov 23
Thanksgiving Holiday - no class
Nov 24
Thanksgiving Holiday - no class
Nov 25
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
Nov 27 Nov 28
MyLab HW 8 due
Nov 29 Nov 30
Dec 1 Dec 2
7.1 Diagonalization of Symmetric Matrices
Catch-up/Review for the final
Dec 4 Dec 5 Dec 6
MATLAB Quiz opens at 12am
Dec 7
MATLAB Quiz closes at 11:59pm
Dec 8
MyLab HW 9 due
Dec 9
Final Exam

Reading:  Reading the sections of the textbook corresponding to each lecture is critical. Homework 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 in-person or viewing the lecture podcast, 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 7 out of the 9 discussion sections during the quarter. Full participation is required in order to earn credit for attendance. This includes contributing to group work and group discussions and staying engaged with the discussion material at all times.

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: after three incorrect attempts, you will be offered a "Similar question" which is the same problem but with different numbers. 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 last day of instruction. 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. No late MATLAB assignments will be accepted. However, the lowest MATLAB assignment score will be dropped. There will be no make-up MATLAB quiz.

Exams: The midterm exams and final exam are scheduled for the Friday of Week 4, the Friday of Week 7, and the first Saturday of exam week; see above for details. The midterms and the final exam 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.

Collaboration Guidelines: You are allowed and even 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 the MATLAB quiz or exams. Moreover, "homework assistance" online sites such as Chegg are NEVER allowed for use in this class on homework, the MATLAB quiz, 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: Final grades will be calculated as the maximum of the following two grading schemes:

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 exam policy: There will be no make-up midterm exams; however, by design, the lowest midterm exam grade will be dropped. Nevertheless: you should make every effort to take the exams; this policy is meant only to accommodate true emergencies.

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 MyLab homework and the MATLAB quiz will be autograded; your exams and MATLAB homework will be graded using Gradescope. If you find errors in the grading of your written work, you will have an opportunity to request a regrade through Gradescope. A regrade window will open the day after the scores are posted, and it will stay open for one week for each midterm and a few days for the final (depending on how quickly the exam is graded). During this time window you will be able to leave careful, thoughtful comments about where you feel a grading error was made. No regrade requests will be considered after the specified window closes. 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 your 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.