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 (see Canvas for office hours) | |
Brendon Rhoades |
Lead Instructor | APM 7250 | bprhoades@ucsd.edu |
John Treuer |
Instructor | APM 1111 |
jtreuer@ucsd.edu |
Nicholas Karris | Lead TA | HSS 5027 | nkarris@ucsd.edu |
Maxwell Johnson | Lead TA | HSS 5207 |
mmj002@ucsd.edu |
Arseniy Kryazhev |
TA | HSS 5209 |
akryazhev@ucsd.edu |
Srinjoy Srimani |
TA | HSS 5204 |
ssrimani@ucsd.edu |
Christopher Xue |
TA | HSS 4016 |
cxue@ucsd.edu |
Haotian Qu |
TA | HSS 3044 |
haqu@ucsd.edu |
Yimeng Zhang |
TA | yiz014@ucsd.edu | |
Yitao Chen |
TA | HSS 3067 |
yic109@ucsd.edu |
Mingyu Liu |
TA | HSS 4056 |
mil094@ucsd.edu |
Zihan Shao |
TA | APM 5412 |
z6shao@ucsd.edu |
Andrew Quach |
Tutor | atquach@ucsd.edu | |
Theo Fung |
Tutor | tyfung@ucsd.edu | |
Michael Hoffman |
Tutor | mjhoffman@ucsd.edu | |
Jiaxin Guan |
Tutor | j3guan@ucsd.edu | |
Fanglei Gao |
Tutor | fagao@ucsd.edu | |
Yifan He |
Tutor | yih068@ucsd.edu | |
Margaret Luo |
Tutor | m5luo@ucsd.edu | |
Xiaomeng Hu |
Senior MATLAB TA | HSS 3070 |
matlabta@math.ucsd.edu |
Christopher Pei |
SI Instructor | czpei@ucsd.edu |
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.
Lecture A00 Meetings | Date | Time | Location |
Lecture A00 (Instructor: Treuer) |
MWF |
9:00am - 9:50am | CENTR 119 |
Discussion A01 (TA: Kryazhev; Tutor: Quach) | Th | 6:00pm - 6:50pm | APM B412 |
Discussion A02 (TA: Kryazhev; Tutor: Quach) | Th | 7:00pm - 7:50pm | APM B412 |
Discussion A03 (TAs: Srimani, Xue; Tutor: Fung) | Th | 5:00pm - 5:50pm | PODEM 1A18 |
Lecture B00 Meetings | Date | Time | Location |
Lecture B00 (Instructor: Rhoades) | MWF | 12:00pm - 12:50pm | JEANN AUD |
Discussion B01 (TAs: Srimani, Xue; Tutors: Fung, Hoffman) | Th | 6:00 - 6:50pm | PODEM 1A20 |
Discussion B02 (TAs: Srimani, Xue; Tutors: Fung, Hoffman) | Th | 7:00 - 7:50pm | PODEM 1A20 |
Discussion B03 (TAs: Srimani, Xue; Tutors: Fung, Hoffman) | Th | 8:00p - 8:50pm | PODEM 1A20 |
Discussion B04 (TAs: Qu, Zhang; Tutor: Guan) | Th | 7:00p - 7:50pm | PODEM 1A18 |
Discussion B05 (TAs: Qu, Zhang; Tutor: Guan) | Th | 8:00p - 8:50pm | PODEM 1A18 |
Discussion B06 (TA: Chen; Tutor: Luo) | Th | 6:00p - 6:50pm | APM 6402 |
Discussion B07 (TA: Chen; Tutor: Luo) | Th | 7:00p - 7:50pm | APM 6402 |
Lecture C00 Meetings | Date | Time | Location |
Lecture C00 (Instructor: Treuer) | MWF | 2:00pm - 2:50pm | YORK 2622 |
Discussion C01 (TA: Karris; Tutor: Gao) | Th | 6:00pm - 6:50pm | APM 7321 |
Discussion C02 (TA: Johnson; Tutor: Gao) | Th | 7:00pm - 7:50pm | APM 7321 |
Discussion C03 (TAs: Liu, Shao; Tutor: He) | Th | 6:00pm - 6:50pm | PETER 102 |
Discussion C04 (TA: Liu; Tutor: He) | Th | 7:00pm - 7:50pm | PETER 103 |
Date | Time | Location | |
Midterm Exam 1 |
Friday, February 2 | 6:00pm - 6:50pm |
A01, A02, A03, C01, C02, C03, C04: GH 242 B01, B02, B03, B07: WLH 2001 B04, B05, B06: CENTR 101 |
Midterm Exam 2 |
Friday, March 1 | 6:00pm - 6:50pm |
A01, A02, A03, C01, C02, C03, C04: GH 242 B01, B02, B03, B07: WLH 2001 B04, B05, B06: CENTR 101 |
Final Exam | Saturday, March 16 |
8:00am - 10:59am | A01, A02, A03: CENTR 119 B01, B02, B03, B04, B05, B06, B07: JEANN AUD C01, C02, C03, C04: LEDDN AUD |
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 |
---|---|---|---|---|---|---|---|
0 |
Jan 1 | Jan 2 | Jan 3 | Jan 4 | Jan 5 | Jan 6 | |
1 |
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
|
Jan 8 | Jan 9 | Jan 10 | Jan 11
Discussion
|
Jan 12 | Jan 13 |
2 |
1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Systems
|
Jan 15
MLK Holiday - No Class
|
Jan 16 | Jan 17 | Jan 18
Discussion
MyLab HW 1 due
|
Jan 19
Deadline to Add a Course
|
Jan 20 |
3 |
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
|
Jan 22 | Jan 23 | Jan 24
MATLAB HW 1 due
|
Jan 25
Discussion
MyLab HW 2 due
|
Jan 26 | Jan 27 |
4 |
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
|
Jan 29 | Jan 30 | Jan 31 | Feb 1
Discussion
MyLab HW 3 due
|
Feb 2
Midterm Exam 1
6:00pm-6:50pm Deadline to Drop without "W"
|
Feb 3 |
5 |
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
|
Feb 5 | Feb 6 | Feb 7
MATLAB HW 2 due
|
Feb 8
Discussion
MyLab HW 4 due
|
Feb 9 | Feb 10 |
6 |
4.5 The Dimension of a Vector Space
4.4 Coordinate Systems
3.1 Introduction to Determinants
|
Feb 12 | Feb 13 | Feb 14 | Feb 15
Discussion
MyLab HW 5 due
|
Feb 16 | Feb 17 |
7 |
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
|
Feb 19
President's Day Holiday - No Class
|
Feb 20 | Feb 21
MATLAB HW 3 due
|
Feb 22
Discussion
MyLab HW 6 due
|
Feb 23 | Feb 24 |
8 |
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
|
Feb 26 | Feb 27 | Feb 28 | Feb 29
Discussion
MyLab HW 7 due
|
Mar 1
Midterm Exam 2 6:00pm-6:50pm
|
Mar 2 |
9 |
6.1 Inner Product, Length, Orthogonality
6.7 Inner Product Spaces
6.2 Orthogonal Sets
|
Mar 4 | Mar 5 | Mar 6
MATLAB HW 4 due
|
Mar 7
Discussion
MyLab HW 8 due
|
Mar 8 | Mar 9 |
10 |
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
7.1 Diagonalization of Symmetric Matrices
|
Mar 11 | Mar 12 | Mar 13
MATLAB HW 5 due
MATLAB Quiz Opens at 12:00am
|
Mar 14
Discussion
MATLAB Quiz Closes at 11:59pm
|
Mar 15
MyLab HW 9 due
|
Mar 16
Final Exam
8:00am-10:59am |
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.
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:
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.
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, 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.