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!
Name | Role | Office | Office hours (see Canvas for Zoom links) | |
Leesa Anzaldo |
Lead Instructor | APM 1240 | Remote: Mon 7pm-8pm, Wed 7pm-8pm, Sun 12pm-1pm In-person: Wed 9am-10am |
lbanzaldo@ucsd.edu |
Marco Carfagnini |
Instructor | APM 6305 |
In-person: Wednesday 1:20pm-3:20pm in APM 6303 |
mcarfagnini@ucsd.edu |
Quang Bach |
Instructor | APM 1250 |
Remote: TuTh 3pm-4pm, Saturday 10:30am-12:30pm |
qtbach@ucsd.edu |
Johannes Brust |
Instructor | APM 1111 |
Remote: Mon and Fri 3:30pm-4:40pm In-person: Wed 3:30pm-4:30pm |
jjbrust@ucsd.edu |
Cameron Cinel | Lead TA | Remote: Tuesday 2-3 PM, Wednesday 2-4 PM |
ccinel@ucsd.edu | |
Jon Stephens |
Lead TA | HSS 5005 |
In-person: Tuesday/Thursday 12:30pm-2pm |
jcstephens@ucsd.edu |
Vitor Borges da Silva |
TA | HSS 5044 |
In-person: Tuesday 3:30pm-5:30pm |
vborgesdasilva@ucsd.edu |
Runqiu Xu |
TA | HSS 4037 |
In-person: Monday 4-6pm |
r4xu@ucsd.edu |
Haoyu Zhang |
TA | HSS 4047 |
In-person: Monday/Wednesday 1pm-3pm |
haz053@ucsd.edu |
Yuchen Wu |
TA | APM 6414 |
In-person: Thursday 3:30pm-5:30pm |
yuw181@ucsd.edu |
Minyoung Jeong |
TA | APM 5712 |
In-person: Tuesday 5pm-7pm |
m1jeong@ucsd.edu |
Haotian Qu |
TA | Remote: Tuesday 6pm-8pm |
haqu@ucsd.edu | |
Nathan Wenger |
TA | HSS 5029 |
Remote: Monday/Thursday 1:30-2:30 |
nwenger@ucsd.edu |
Nicholas Zhao |
TA | HSS 4084 |
Hybrid: Friday 10am-2pm |
nizhao@ucsd.edu |
Toren D'Nelly-Warady |
TA | APM 2313 |
In-person: Wednesday, Thursday 10am-11am in HSS 5012 |
tdnellywarady@ucsd.edu |
Lizzy Coda |
TA | HSS 5012 |
In-person: Monday 5pm-7pm |
ecoda@ucsd.edu |
Shuncheng Yuan |
TA | APM 5412 |
Remote: Monday 6:00-8:00pm |
syuan@ucsd.edu |
Sutanay Bhattacharya |
TA | APM 6414 |
In-person: Wednesday 2pm-4pm |
subhattacharya@ucsd.edu |
Itai Maimon |
Senior MATLAB TA | |
matlabta@math.ucsd.edu |
We will also have support from the Academic Achievement Hub's Supplemental Instruction. SI Leaders will be embedded in some of 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).
In the following scheduled meeting times, physical locations are listed where relevant. Zoom meeting coordinates can be found in Canvas.
Lecture A00 Meetings | Date | Time | Location |
Lecture A00 (Instructor: Anzaldo) |
MWF |
11:00am - 11:50am | JEANN AUD |
Discussion A01 (TA: Borges da Silva) | Tu | 10:00am - 10:50am | HSS 4025 |
Discussion A02 (TA: Borges da Silva) | Tu | 11:00am - 11:50am | HSS 4025 |
Discussion A03 (TA: Xu) | Tu | 12:00pm - 12:50pm | HSS 4025 |
Discussion A04 (TA: Xu) | Tu | 1:00pm - 1:50pm | HSS 4025 |
Discussion A05 (TA: Xu) | Tu | 2:00pm - 2:50pm | HSS 4025 |
Discussion A06 (TA: Xu) | Tu | 3:00pm - 3:50pm | HSS 4025 |
Discussion A07 (TA: Zhang) | Tu | 4:00pm - 4:50pm | HSS 4025 |
Discussion A08 (TA: Zhang) | Tu | 5:00pm - 5:50pm | HSS 4025 |
Discussion A09 (TA: Zhang) | Tu | 6:00pm - 6:50pm | HSS 4025 |
Discussion A10 (TA: Zhang) | Tu | 7:00pm - 7:50pm | HSS 4025 |
Discussion A11 (TA: Wu) | Tu | 8:00am - 8:50am | PCYNH 120 |
Discussion A12 (TA: Wu) | Tu | 9:00am - 9:50am | PCYNH 120 |
Discussion A13 (TA: Jeong) | Tu | 12:00pm - 12:50pm | CENTR 217A |
Discussion A14 (TA: Jeong) | Tu | 1:00pm - 1:50pm | CENTR 217A |
Discussion A15 (TA: Qu) | Tu | 2:00pm - 2:50pm | Remote |
Discussion A16 (TA: Qu) | Tu | 3:00pm - 3:50pm | Remote |
Discussion A17 (TA: Qu) | Tu | 4:00pm - 4:50pm | Remote |
Discussion A18 (TA: Qu) | Tu | 5:00pm - 5:50pm | Remote |
Discussion A21 (TA: Wenger) | Tu | 12:00pm - 12:50pm | Remote |
Discussion A22 (TA: Wenger) | Tu | 1:00pm - 1:50pm | Remote |
Discussion A23 (TA: Wenger) | Tu | 2:00pm - 2:50pm | Remote |
Discussion A24 (TA: Wenger) | Tu | 3:00pm - 3:50pm | Remote |
Lecture B00 Meetings | Date | Time | Location |
Lecture B00 (Instructor: Carfagnini) | MWF | 12:00pm - 12:50pm | LEDDN AUD |
Discussion B01 (TA: Zhao, SI: Henstridge) | Tu | 2:00pm - 2:50pm | WLH 2113 |
Discussion B02 (TA: Zhao, SIs: Shukla, Wang, Venerio) | Tu | 3:00pm - 3:50pm | WLH 2113 |
Discussion B03 (TA: Zhao, SIs: Shukla, Wang, Venerio) | Tu | 4:00pm - 4:50pm | WLH 2113 |
Discussion B04 (TA: Zhao, SIs: Shukla, Wang) | Tu | 5:00pm - 5:50pm | WLH 2208 |
Discussion B05 (TA: D'Nelly-Warady, SIs: Shukla, Venerio) | Tu | 6:00pm - 6:50pm | SOLIS 111 |
Discussion B06 (TA: D'Nelly-Warady, SIs: Shukla, Venerio) | Tu | 7:00pm - 7:50pm | SOLIS 111 |
Lecture C00 Meetings | Date | Time | Location |
Lecture C00 (Instructor: Bach) | MWF | 2:00pm - 2:50pm | WLH 2005 |
Discussion C01 (TA: Coda, SIs: Puneet, Nguyen) | Tu | 9:00am - 9:50am | Remote |
Discussion C02 (TA: Coda, SIs: Puneet, Nguyen, Patil) | Tu | 10:00am - 10:50am | Remote |
Discussion C03 (TA: Yuan, SIs: Henstridge, Nguyen, Gupta) | Tu | 11:00am - 11:50am | Remote |
Discussion C04 (TA: Yuan, SIs: Henstridge, Puneet, Gupta) | Tu | 12:00pm - 12:50pm | Remote |
Discussion C05 (TA: Cinel, SIs: Henstridge, Patil) | Tu | 1:00pm - 1:50pm | Remote |
Lecture D00 Meetings | Date | Time | Location |
Lecture D00 (Instructor: Brust) | MWF | 5:00pm - 5:50pm | LEDDN AUD |
Discussion D01 (TA: Bhattacharya, SIs: Patil, Hu) | Tu | 9:00am - 9:50am | RWAC 0115 |
Discussion D02 (TA: Bhattacharya, SI: Hu) | Tu | 10:00am - 10:50am | RWAC 0115 |
Discussion D03 (TA: Borges da Silva, SIs: Hu, Wu) | Tu | 8:00am - 8:50am | HSS 4025 |
Discussion D04 (TA: Borges da Silva, SI: Wu) | Tu | 9:00am - 9:50am | HSS 4025 |
Discussion D05 (TA: Stephens, SI: Wu) | Tu | 10:00am - 10:50am | PCYNH 120 |
Date | Time | Location | |
Midterm Exam 1 |
Friday, October 21 | 7:00pm - 8:50pm |
A00: PETER 108 and 110 B00: LEDDN AUD C00: MOS 0113 D00: CTL 0125 |
Midterm Exam 2 |
Thursday, November 10 | 8:00pm - 9:50pm |
A00: PETER 108 and 110 B00: MOS 0113 C00: SOLIS 107 D00: CTL 0125 |
Final Exam | Saturday, December 3 |
7:00pm - 9:59pm | 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 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
---|---|---|---|---|---|---|
0 |
Sep 19 | Sep 20 | Sep 21 | Sep 22 | Sep 23
1.1 Systems of Linear Equations
|
Sep 24 |
1 |
Sep 26
1.2 Row Reduction and Echelon Forms
|
Sep 27
Discussion
|
Sep 28
1.3 Vector Equations
|
Sep 29 | Sep 30
1.4 The Matrix Equation Ax=b
|
Oct 1 |
2 |
Oct 3
1.5 Solution Sets of Linear Systems
|
Oct 4
Discussion
|
Oct 5
1.7 Linear Independence
|
Oct 6
First Day Survey due
|
Oct 7
1.8 Introduction to Linear Transformations
MATLAB HW 1 due
Deadline to Add a Course
|
Oct 8 |
3 |
Oct 10
1.9 The Matrix of a Linear Transformation
MyLab HW 1, 2 due
|
Oct 11
Discussion
|
Oct 12
2.1 Matrix Operations
|
Oct 13 | Oct 14
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
|
Oct 15 |
4 |
Oct 17
4.1 Vector Spaces and Subspaces
MyLab HW 3 due
|
Oct 18
Discussion
|
Oct 19
Catch-up/Review
|
Oct 20 | Oct 21
4.2 Null Spaces, Column Spaces, and Linear Transformations
Midterm Exam 1
7:00pm-8:50pm Deadline to Drop without "W"
|
Oct 22 |
5 |
Oct 24
4.3 Linearly Independent Sets; Bases
MyLab HW 4 due
MATLAB HW 2 due
|
Oct 25
Discussion
|
Oct 26
4.5 The Dimension of a Vector Space
|
Oct 27 | Oct 28
4.4 Coordinate Systems
|
Oct 29 |
6 |
Oct 31
3.1 Introduction to Determinants
3.2 Properties of Determinants
MyLab HW 5 due
|
Nov 1
Discussion
|
Nov 2
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
|
Nov 3 | Nov 4
5.1 Eigenvectors and Eigenvalues
MATLAB HW 3 due
Deadline to Drop with "W"
|
Nov 5 |
7 |
Nov 7
5.2 The Characteristic Equation
MyLab HW 6 due
|
Nov 8
Discussion
|
Nov 9
Catch-up/Review
|
Nov 10
Midterm Exam 2
8:00pm-9:50pm |
Nov 11
Veterans Day Holiday - no class
|
Nov 12 |
8 |
Nov 14
5.3 Diagonalization
MyLab HW 7 due
|
Nov 15
Discussion
|
Nov 16
6.1 Inner Product, Length, Orthogonality
6.7 Inner Product Spaces
|
Nov 17 | Nov 18
6.2 Orthogonal Sets
MATLAB HW 4 due
|
Nov 19 |
9 |
Nov 21
6.3 Orthogonal Projections
MyLab HW 8 due
|
Nov 22
Discussion
|
Nov 23
6.4 The Gram-Schmidt Process
|
Nov 24
Thanksgiving Holiday - no class
|
Nov 25
Thanksgiving Holiday - no class
|
Nov 26 |
10 |
Nov 28
7.1 Diagonalization of Symmetric Matrices
|
Nov 29
Discussion
|
Nov 30
Catch-up/Review
MyLab HW 9 due
MATLAB Quiz opens at 12am
|
Dec 1
MATLAB Quiz closes at 11:59pm
|
Dec 2
Review
MATLAB HW 5 due
|
Dec 3
Final Exam
7:00pm-9:59pm |
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 8 out of the 10 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. For remote discussions, this also includes having mics and cameras on 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 Thursday 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.
Exam Versions: In cases of legitimate, well-documented, and unavoidable conflicts, 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 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:
Grading Policies: Final grades will be calculated as the maximum of the following two grading schemes:
A+ | A | A- | B+ | B | B- | C+ | C | C- |
97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 |
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.
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 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 three days after the scores are posted, and it will stay open for three days. 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, hproudfood@ucsd.edu) 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.