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!

Modality : During Fall 2024, nearly all Lecture and Discussion meetings will be held in-person. In the rare event that an instructor or TA is sick or travelling, lectures and meetings may be pre-recorded or remote. The midterms and final will be administered in-person, at the announced times, with an exception only for students with a final exam that conflicts with this course's final exam (see the Syllabus for details).

Canvas : The LMS (learning management system) for this course is Canvas. The Canvas page for this course is combined for all lectures (A00, B00, C00, D00). Canvas will be used in various ways throughout the course, but this course webpage is the main portal for the course.Piazza : We will use Piazza, an online discussion board, as a principal communication tool. It will allow you to post messages and answer posts made by your fellow students, about course content, homework, exams, etc. The instructors and TAs will also monitor and post to Piazza regularly. You can access Piazza from your Canvas site, or directly.

Gradescope : We will use Gradescope to grade your MATLAB homework, midterms, and final exam in this course. You will be able to view your graded assignments and assessments in Gradescope once they are graded and published. You can access Gradescope via Canvas.

Lecture Recordings : Recordings of lectures that are podcasted will be available in the Media Gallery on Canvas as well as on the UCSD podcast website.

Textbook : The required textbook for this course is

*Linear Algebra and its Applications w/ MyMathLab/eBook*(6th Edition), by David C. Lay, Steven R. Lay, and Judi J. McDonald.

You only need to purchase**MyLab access**which gives you both access to the eText and the online homework. MyLab access may be purchased from the UCSD bookstore or directly from Pearson when you log in to MyLab through Canvas. You do not need a physical copy of the textbook. You are encouraged to take advantage of Pearson's "**temporary access without payment for 14 days**," which will let you do the MyLab homework and access the eText for free for two weeks, in case there is a possibility that you will drop the course. You will have the option to purchase access after the two weeks is over, and your homework scores during the trial period will be saved.Discussion Sections are a**required**component of this course. You must attend your scheduled discussion section each week (on time) to receive full credit in the class. The discussion sections will involve community building and active learning, and will play a key role in your success at mastering linear algebra.Supplemental Instruction: : Students will have support from the Academic Achievement Hub's Supplemental Instruction (SI). SI Leaders will be embedded in some of our discussion sections to facilitate active learning, and they will hold SI group study sessions for anyone who wants additional help studying.MyLab Homework : Weekly homework will be assigned through MyLab, the online Pearson homework system. You will find the assignments through the Access Pearson link in Canvas. See the syllabus for more details.MATLAB : One component of our coursework is a series of MATLAB assignments, and a MATLAB quiz at the end. You will submit your MATLAB work through Gradescope. All information relevant to the MATLAB component of Math 18 can be found here.Exams : In this course there will be two midterm exams and one final exam. Dates, times, and locations are posted below. If you cannot take the midterms or the final exam at the scheduled times, you should not enroll in this class. However, the lowest midterm exam score is dropped. The main purpose of this policy is to accommodate for instances when a student cannot attend one of the midterm exams for any reason. However, the final exam score is not dropped.

Name | Role | Office (see Canvas for office hours) | |

Brandon Seward |
Lead Instructor | AP&M 5736 | bseward@ucsd.edu |

Karthik Ganapathy |
Instructor | AP&M 1230 |
kganapathy@ucsd.edu |

Bryan Hu |
Instructor | HSS 5086 |
brhu@ucsd.edu |

Toren D'Nelly-Warady |
Lead TA | HSS 3085 | tdnellywarady@ucsd.edu |

Max Johnson |
Lead TA | HSS 5027 |
mmj002@ucsd.edu |

Dimitri Dine |
TA | HSS 4086B |
ddine@ucsd.edu |

Arseniy Kryazhev |
TA | HSS 5029 |
akryazhev@ucsd.edu |

Sarah Kumar |
TA | HSS 5056 |
sak018@ucsd.edu |

Sharv Laad |
TA | HSS 5024 |
slaad@ucsd.edu |

Mingyu Liu |
TA | HSS 4056 |
mil094@ucsd.edu |

Haotian Qu |
TA | HSS 3044 |
haqu@ucsd.edu |

Rahul Sahjwani |
TA | HSS 5085 |
rsahjwan@ucsd.edu |

Zain Shields |
TA | HSS 4044 |
zshields@ucsd.edu |

Yuanfan Wang |
TA | HSS 3044 |
yuw136@ucsd.edu |

Yingjia Yang |
TA | HSS 4085 |
yiy104@ucsd.edu |

Suichu Zhang |
TA | HSS 5040 |
suz007@ucsd.edu |

Sydney Badescu |
Tutor | AP&M 5218 |
sbadescu@ucsd.edu |

Sahith Cherumandanda |
Tutor | AP&M 5218 |
scherumandanda@ucsd.edu |

Theodore Fung |
Tutor | AP&M 5218 |
tyfung@ucsd.edu |

Jiaxin Guan |
Tutor | AP&M 5218 |
j3guan@ucsd.edu |

Yifan He |
Tutor | AP&M 5218 |
yih068@ucsd.edu |

Margaret Luo |
Tutor | AP&M 5218 |
m5luo@ucsd.edu |

Advait Ramesh |
Tutor | AP&M 5218 |
a3ramesh@ucsd.edu |

Xin Shu |
Tutor | AP&M 5218 |
x1shu@ucsd.edu |

David Stephens |
Tutor | AP&M 5218 |
d1stephens@ucsd.edu |

Jiyoung Choi |
Head MATLAB TA | jichoi@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 | Instructor / TA(s) | Tutor(s) | Date | Time | Location |

Lecture A00 | Brandon Seward | MWF | 10:00am - 10:50am | JEANN AUD | |

Discussion A01 | Dimitri Dine & Mingyu Liu | Sydney Badescu | Th | 12:00pm - 12:50pm | AP&M B402A |

Discussion A02 | Dimitri Dine & Mingyu Liu | Sydney Badescu | Th | 1:00pm - 1:50pm | AP&M B402A |

Discussion A03 | Max Johnson & Sharv Laad | Sydney Badescu | Th | 7:00pm - 7:50pm | RWAC 0121 |

Discussion A04 | Toren D'Nelly-Warady & Sharv Laad | Sydney Badescu | Th | 8:00pm - 8:50pm | RWAC 0121 |

Discussion A05 | Sarah Kumar & Zain Shields | Jiaxin Guan & Margaret Luo | Th | 5:00pm - 5:50pm | PETER 104 |

Discussion A06 | Sarah Kumar & Zain Shields | Jiaxin Guan & Margaret Luo | Th | 6:00pm - 6:50pm | PETER 104 |

Discussion A07 | Yuanfan Wang | Theodore Fung | Th | 5:00pm - 5:50pm | WLH 2113 |

Discussion A08 | Yuanfan Wang | Theodore Fung | Th | 6:00pm - 6:50pm | WLH 2113 |

Discussion A09 | Yuanfan Wang | Theodore Fung | Th | 7:00pm - 7:50pm | WLH 2113 |

Discussion A10 | Yuanfan Wang | Theodore Fung | Th | 8:00pm - 8:50pm | WLH 2113 |

Discussion A11 | Yingjia Yang | David Stephens | Th | 6:00pm - 6:50pm | HSS 2154 |

Discussion A12 | Yingjia Yang | David Stephens | Th | 7:00pm - 7:50pm | HSS 2154 |

Lecture B00 Meetings | Instructor / TA(s) | Tutor(s) | Date | Time | Location |

Lecture B00 | Karthik Ganapathy | MWF | 12:00pm - 12:50pm | PCYNH 109 | |

Discussion B01 | Sharv Laad & Suichu Zhang | Sahith Cherumandanda | Th | 5:00pm - 5:50pm | RWAC 0121 |

Discussion B02 | Sharv Laad & Suichu Zhang | Sahith Cherumandanda | Th | 6:00pm - 6:50pm | RWAC 0121 |

Discussion B03 | Arseniy Kryazhev | Yifan He | Th | 5:00p - 5:50pm | HSS 1315 |

Discussion B04 | Arseniy Kryazhev | Yifan He | Th | 6:00p - 6:50pm | HSS 1315 |

Lecture C00 Meetings | Instructor / TA(s) | Tutor(s) | Date | Time | Location |

Lecture C00 | Karthik Ganapathy | MWF | 1:00pm - 1:50pm | PCYNH 109 | |

Discussion C01 | Mingyu Liu & Suichu Zhang | Jiaxin Guan & Margaret Luo | Th | 7:00pm - 7:50pm | PCYNH 122 |

Discussion C02 | Mingyu Liu & Suichu Zhang | Jiaxin Guan & Margaret Luo | Th | 8:00pm - 8:50pm | PCYNH 122 |

Lecture D00 Meetings | Instructor / TA(s) | Tutor(s) | Date | Time | Location |

Lecture D00 | Bryan Hu | MWF | 3:00pm - 3:50pm | PCYNH 109 | |

Discussion D01 | Haotian Qu & Rahul Sahjwani | Advait Ramesh & Xin Shu | Th | 7:00pm - 7:50pm | PODEM 1A20 |

Discussion D02 | Haotian Qu & Rahul Sahjwani | Advait Ramesh & Xin Shu | Th | 8:00pm - 8:50pm | PODEM 1A20 |

Date | Time | Location | |

Midterm Exam 1 | Friday, October 25 | 7:30pm - 8:20pm | See Canvas for your exam room and seat number |

Midterm Exam 2 | Friday, November 22 | 7:30pm - 8:20pm | See Canvas for your exam room and seat number |

Final Exam | Saturday, December 7 | 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 23 |
Sep 24 |
Sep 25 |
Sep 26 |
Sep 271.1 Systems of Linear Equations |
Sep 28 |

1 | Sept 301.2 Row Reduction and Echelon Forms |
Oct 1 |
Oct 21.3 Vector Equations |
Oct 3Discussion |
Oct 41.4 The Matrix Equation Ax=b |
Oct 5 |

2 | Oct 71.5 Solution Sets of Linear Systems |
Oct 8 |
Oct 91.7 Linear Independence |
Oct 10Discussion First Day Survey Due |
Oct 111.8 Introduction to Linear Transformations Deadline to Add a Course |
Oct 12 |

3 | Oct 141.9 The Matrix of a Linear Transformation |
Oct 15MyLab HW 1 dueMyLab HW 2 due |
Oct 162.1 Matrix Operations MATLAB HW 1 due |
Oct 17Discussion |
Oct 182.2 The Inverse of a Matrix 2.3 Characterizations of Invertible Matrices |
Oct 19 |

4 | Oct 214.1 Vector Spaces and Subspaces |
Oct 22MyLab HW 3 due |
Oct 234.2 Null Spaces, Column Spaces, and Linear Transformations MATLAB HW 2 due |
Oct 24Discussion |
Oct 25Catch-up/Review for Midterm 1 Midterm Exam 17:30 pm - 8:20 pm Deadline to Drop without 'W' |
Oct 26 |

5 | Oct 284.3 Linearly Independent Sets; Bases |
Oct 29MyLab HW 4 due |
Oct 304.5 The Dimension of a Vector Space |
Oct 31Discussion |
Nov 14.4 Coordinate Systems |
Nov 2 |

6 | Nov 43.1 Introduction to Determinants |
Nov 5MyLab HW 5 due |
Nov 63.2 Properties of Determinants 3.3 Cramer's Rule, Volume, and Linear Transformations MATLAB HW 3 due |
Nov 7Discussion |
Nov 85.1 Eigenvectors and Eigenvalues Deadline to drop with 'W' |
Nov 9 |

7 | Nov 11Veteran's Day Holiday |
Nov 12MyLab HW 6 due |
Nov 135.2 The Characteristic Equation |
Nov 14Discussion |
Nov 155.3 Diagonalization |
Nov 16 |

8 | Nov 186.1 Inner Product, Length, Orthogonality 6.7 Inner Product Spaces |
Nov 19MyLab HW 7 due |
Nov 206.2 Orthogonal Sets MATLAB HW 4 due |
Nov 21Discussion |
Nov 22Catch-up/Review for Midterm 2 Midterm Exam 27:30 pm - 8:20 pm |
Nov 23 |

9 | Nov 256.3 Orthogonal Projections |
Nov 26MyLab HW 8 due |
Nov 276.4 The Gram-Schmidt Process |
Nov 28Thanksgiving Holiday |
Nov 29Thanksgiving Holiday |
Nov 30 |

10 | Dec 27.1 Diagonalization of Symmetric Matrices |
Dec 3 |
Dec 4Catch-up/Review for the final MATLAB Quiz opens at 12:00 am |
Dec 5Discussion MATLAB Quiz closes at 11:59 pm |
Dec 6Review for the final MATLAB HW 5 dueMyLab HW 9 due |
Dec 7Final Exam7:00 pm - 9:59 pm |

**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 8, and the first Saturday of exam week;
see above for details.
These exams will be **in-person**. More
information will follow closer to these exams about precise
logistics and policies.

**Exam Versons:** It is standard Math Department practice to utilize different versions of exams, both within each lecture's exam, and between lectures whose exams are at different times. 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. In particular:

- Do not use, or post to "homework help" services such as Chegg. Do not post solutions to homework, the MATLAB quiz, or exam problems in any public forum (such as Piazza).
- Do not collaborate on or copy the MATLAB quiz or exams. (There will be specific instructions about what that means in an Academic Integrity Pledge at the beginning of the MATLAB quiz or exam.)
- Do not use any apps or sites that do the math for you, or connect you with people who will do the math for you. This will not aid in your learning.
- Do not attempt to search for solutions to homework, the MATLAB quiz, or exam problems online or in sources outside of the course content.

**Grading Policies:** Final grades will be calculated as the **maximum** of the following two grading schemes:

**2%****Discussion Section participation**based on on-time, full attendance and full participation of at least 7 discussion sections**6%****MATLAB Assignments****4%****MATLAB Quiz****20%****MyLab Homework****19%****Midterm Exam 1****19%****Midterm Exam 2****30%****Final Exam**

**2%****Discussion Section participation**based on on-time, full attendance and full participation of at least 7 discussion sections**6%****MATLAB Assignments****4%****MATLAB Quiz****20%****MyLab Homework****28%****Best Midterm Exam****40%****Final Exam**

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 |

**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 an alternate final exam time that is available only to students enrolled in another course whose final exam time is in conflict with the final exam time of this class. If you have a conflict with the scheduled final exam time for any other reason, 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:

- Exam Responsibilities An outline of the responsibilities of faculty and students with regard to final exams
- Policies on Examinations The Academic Senate policy regarding final examinations (These are the rules!)

**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). 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

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

**Entering/exiting class:**Please arrive on time and stay for the entire class/section period. If, despite your best efforts, you arrive late, please enter quietly through the rear door and take a seat near where you entered. Similarly, in the rare event that you must leave early (e.g. for a medical appointment), please sit close to the rear exit and leave as unobtrusively as possible.**Noise and common courtesy:**When class/section begins, please stop your conversations. Wait until class/section is over before putting your materials away in your backpack, standing up, or talking to friends. Do not disturb others by engaging in disruptive behavior. Disruption interferes with the learning environment and impairs the ability of others to focus, participate, and engage.**Electronic devices:**Please do not use devices (such as phones, laptops, and tablets) for non-class-related matters while in class/section. No visual or audio recording is allowed in class/section without prior permission of the instructor/TA.**Messaging etiquette:**You are expected to write as you would in any professional correspondence. Email, Piazza, and other written communication should be courteous and respectful in manner and tone. Please do not send/post messages that are curt or demanding.

**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 accommodation towards 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.