Math 18: Linear Algebra

Lectures A00 (Anzaldo), B00 and C00 (Ganesan)

Course Information

Modality: During Winter 2025,

All lectures will be delivered in-person, and some will also be podcasted.
All discussion sections will be in-person.
The midterms and final will be administered in-person, at the announced times, with no exceptions.

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). Canvas 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.
Gradescope: We will use Gradescope to grade your MATLAB homework, midterms, and final exam, and to take discussion attendance. You will be able to view your graded assignments and exams 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 and participate in at least 6 of your scheduled discussion sections 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.

MyLab Homework: Weekly homework will be assigned through MyLab, the online Pearson homework system. You will find the assignments through the MyLab 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 during Week 10. 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 and times 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 (see the syllabus for more details). The main purpose of this policy is to accommodate for instances when a student cannot attend one of the midterm exams for any reason. The final exam score is not dropped.

Instructional Staff

Name	Role	Office (see Canvas for office hours)	Email
Leesa Anzaldo	Instructor and coordinator	APM 7432	lbanzaldo@ucsd.edu
Priyanga Ganesan	Instructor	APM 2210	pganesan@ucsd.edu
Lillian McPherson	Lead TA	HSS 3072	lmcpherson@ucsd.edu
Srinjoy Srimani	Lead TA	HSS 5024	ssrimani@ucsd.edu
Sutanay Bhattacharya	TA	HSS 3085	subhattacharya@ucsd.edu
Maxwell Johnson	TA	HSS 5027	mmj002@ucsd.edu
Sarah Kumar	TA	HSS 5056	sak018@ucsd.edu
Cheng Li	TA	HSS 5062	chl119@ucsd.edu
Mingyu Liu	TA	HSS 4056	mil094@ucsd.edu
Zhanbei Liu	TA	HSS 4056	zhl197@ucsd.edu
Weston Miller	TA	HSS 4084	w3miller@ucsd.edu
Rahul Sahjwani	TA	HSS 5085	rsahjwan@ucsd.edu
Yingjia Yang	TA		yiy104@ucsd.edu
Willard Ford	Tutor	APM 5218	wwford@ucsd.edu
Theodore Fung	Tutor	APM 5218	tyfung@ucsd.edu
Jiaxin Guan	Tutor	APM 5218	j3guan@ucsd.edu
Oscar Li	Tutor	APM 5218	o1li@ucsd.edu
Aiyang Lu	Tutor	APM 5218	ail002@ucsd.edu
Margaret Luo	Tutor	APM 5218	m5luo@ucsd.edu
Eric Nguyen	Tutor	APM 5218	ern002@ucsd.edu
Jiyoung Choi	Senior MATLAB TA	HSS 3070	matlabta@math.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.

Class Meetings

Lecture A00 Meetings	Days	Time	Location
Lecture A00 (Instructor: Leesa Anzaldo)	MWF	9:00am - 9:50am	JEANN AUD
Discussion A01 (TAs: Sarah Kumar, Maxwell Johnson; Tutor: Jiaxin Guan)	W	4:00pm - 4:50pm	RWAC 0121
Discussion A02 (TAs: Sarah Kumar, Maxwell Johnson; Tutor: Jiaxin Guan)	W	5:00pm - 5:50pm	PETER 103
Discussion A03 (TAs: Sarah Kumar, Maxwell Johnson; Tutor: Jiaxin Guan)	W	6:00pm - 6:50pm	PETER 103
Discussion A04 (TAs: Sarah Kumar, Maxwell Johnson; Tutor: Jiaxin Guan)	W	7:00pm - 7:50pm	PETER 103
Discussion A05 (TAs: Rahul Sahjwani, Cheng Li; Tutor: Willard Ford)	W	6:00pm - 6:50pm	CENTR 222
Discussion A06 (TAs: Rahul Sahjwani, Cheng Li; Tutor: Willard Ford)	W	7:00pm - 7:50pm	CENTR 222
Discussion A07 (TA: Mingyu Liu; Tutor: Oscar Li)	W	4:00pm - 4:50pm	APM 2402
Discussion A08 (TA: Mingyu Liu; Tutor: Oscar Li)	W	5:00pm - 5:50pm	APM 2402
Discussion A09 (TA: Srinjoy Srimani; Tutor: Oscar Li)	W	6:00pm - 6:50pm	APM 2402
Discussion A10 (TA: Lillian McPherson; Tutor: Oscar Li)	W	7:00pm - 7:50pm	APM 2402
Discussion A11 (TAs: TBA; Tutor: Theodore Fung)	W	7:00pm - 7:50pm	APM 5402
Discussion A12 (TAs: TBA; Tutor: Theodore Fung)	W	8:00pm - 8:50pm	APM 5402

Lecture B00 Meetings	Days	Time	Location
Lecture B00 (Instructor: Priyanga Ganesan)	MWF	1:00pm - 1:50pm	LEDDN AUD
Discussion B01 (TAs: Sutanay Bhattacharya, Zhanbei Liu; Tutors: Aiyang Lu, Eric Nguyen)	W	6:00pm - 6:50pm	FAH 1101
Discussion B02 (TAs: Sutanay Bhattacharya, Zhanbei Liu; Tutors: Aiyang Lu, Eric Nguyen)	W	7:00pm - 7:50pm	FAH 1101

Lecture C00 Meetings	Days	Time	Location
Lecture C00 (Instructor: Priyanga Ganesan)	MWF	3:00pm - 3:50pm	PCYNH 109
Discussion C01 (TA: Yingjia Yang; Tutor: Margaret Luo)	W	5:00pm - 5:50pm	SOLIS 110
Discussion C02 (TA: Yingjia Yang; Tutor: Margaret Luo)	W	6:00pm - 6:50pm	SOLIS 110
Discussion C03 (TA: Weston Miller; Tutor: Margaret Luo)	W	7:00pm - 7:50pm	SOLIS 110
Discussion C04 (TA: Weston Miller; Tutor: Margaret Luo)	W	8:00pm - 8:50pm	SOLIS 110

Exam Information

	Date	Time	Location
Midterm Exam 1	Thursday, January 30	8:00pm - 8:50pm	See Canvas
Midterm Exam 2	Thursday, February 20	8:00pm - 8:50pm	See Canvas
Final Exam	Saturday, March 15	8:00am - 10:59am	See Canvas

Calendar

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	1.1 Systems of Linear Equations 1.2 Row Reduction and Echelon Forms 1.3 Vector Equations	Jan 6 First day of lecture	Jan 7	Jan 8 ~~Discussion~~ CANCELLED	Jan 9	Jan 10	Jan 11
2	1.4 The Matrix Equation Ax=b 1.5 Solution Sets of Linear Systems 1.7 Linear Independence	Jan 13	Jan 14	Jan 15 Discussion	Jan 16	Jan 17 First Day Survey due Deadline to Add a Course	Jan 18
3	1.8 Introduction to Linear Transformations 1.9 The Matrix of a Linear Transformation	Jan 20 Martin Luther King, Jr. Holiday - no class	Jan 21 MyLab HW 1 due MyLab HW 2 due	Jan 22 Discussion MATLAB HW 1 due	Jan 23	Jan 24	Jan 25
4	2.1 Matrix Operations Catch-up/Review for Midterm 1 2.2 The Inverse of a Matrix 2.3 Characterizations of Invertible Matrices	Jan 27 MATLAB HW 2 due	Jan 28 MyLab HW 3 due	Jan 29 Discussion	Jan 30 Midterm Exam 1 8:00pm-8:50pm	Jan 31 Deadline to Drop without "W"	Feb 1
5	4.1 Vector Spaces and Subspaces 4.2 Null Spaces, Column Spaces, and Linear Transformations 4.3 Linearly Independent Sets; Bases	Feb 3	Feb 4 MyLab HW 4 due	Feb 5 Discussion	Feb 6	Feb 7	Feb 8
6	4.5 The Dimension of a Vector Space 4.4 Coordinate Systems 3.1 Introduction to Determinants 3.2 Properties of Determinants	Feb 10 MATLAB HW 3 due	Feb 11 MyLab HW 5 due	Feb 12 Discussion	Feb 13	Feb 14 Deadline to Drop with "W"	Feb 15
7	Catch-up/Review for Midterm 2 3.2 Properties of Determinants (continued) 3.3 Cramer's Rule, Volume, and Linear Transformations	Feb 17 Presidents' Day Holiday - no class	Feb 18 MyLab HW 6 due	Feb 19 Discussion	Feb 20 Midterm Exam 2 8:00pm-8:50pm	Feb 21	Feb 22
8	5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation 5.3 Diagonalization	Feb 24 MATLAB HW 4 due	Feb 25 MyLab HW 7 due	Feb 26 Discussion	Feb 27	Feb 28	Mar 1
9	6.1 Inner Product, Length, Orthogonality 6.7 Inner Product Spaces 6.2 Orthogonal Sets 6.3 Orthogonal Projections	Mar 3	Mar 4 MyLab HW 8 due	Mar 5 Discussion	Mar 6	Mar 7	Mar 8
10	6.4 The Gram-Schmidt Process 7.1 Diagonalization of Symmetric Matrices Catch-up/Review for the final	Mar 10 MATLAB HW 5 due	Mar 11 MyLab HW 9 due	Mar 12 Discussion MATLAB Quiz opens at 12am	Mar 13 MATLAB Quiz closes at 11:59pm	Mar 14 MyLab HW 10 due	Mar 15 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.

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Syllabus

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 6 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.

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 March 17, 2025. 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 Thursday of Week 4, the Thursday of Week 7, and the first Saturday of exam week. The midterms and the final exam will take place in-person.

Exam Versions: There may be different versions of exams given. All versions of any exam will consist of questions from the same range of topics and will be calibrated to the same level of difficulty. 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.

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.

For example:

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.
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. If you accidentally stumble upon a publicly available solution, you should notify your TA and instructor.

Penalties for these offenses 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:

2% Discussion Section participation based on on-time, full attendance and full participation of at least 6 discussion sections
5% MATLAB Assignments
5% MATLAB Quiz
18% MyLab Homework
20% Midterm Exam 1
20% Midterm Exam 2
30% Final Exam

2% Discussion Section participation based on on-time, full attendance and full participation of at least 6 discussion sections
5% MATLAB Assignments
5% MATLAB Quiz
18% MyLab Homework
30% 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

The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, we may lower the cutoffs slightly.

Missed exam policy: There will be no make-up midterm exams; however, by design, the lowest midterm exam grade will be dropped (see the grading policies above for details). 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:

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). 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.

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 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: Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (https://osd.ucsd.edu/). Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department in advance of any exams or assignments.

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.

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