Math 170A

Winter 2026, Lecture A00 (Dumitriu)

Introduction to Numerical Analysis

Calendar
Syllabus
Lecture Notes
MATLAB
Piazza
Academic Integrity Policies
Gradescope

Announcements

Welcome to Math 170A, Lecture A00, Winter 2026!

Course Information

Textbook: The required textbook for this course is

Introduction to Numerical Linear Algebra, by Christoph Borgers; 1st edition.

Subject Material: We will cover parts of chapters 3-6, 8-10, 15-17, 19-20, 22-25 of the text. We will not cover them in the same order as the textbook (see Calendar).

You are greatly encouraged to read the textbook alongside the lectures and other materials we provide.

Coursework: There will be weekly homework assignments due on Fridays (starting with Week 1, see calendar below); they will be posted on the Canvas website for the class. There will be three quizzes, one midterm, and a final exam; dates, times, and locations posted below.

Piazza is an online discussion forum; we will use Piazza. It will allow you to post messages (openly or anonymously) and answer posts made by your fellow students, about course content, homework, exams, etc. You are encouraged to sign up here.

Note: Piazza has an opt-in "Piazza Careers" section which, if you give permission, will share statistics about your Piazza use with potential future employers. It also has a "social network" component, based on other students who've shared a Piazza-based class with you, that comes with the usual warnings about privacy concerns. Piazza is fully FERPA compliant, and is an allowed resource at UCSD. Nevertheless, you are not required to use Piazza if you do not wish.

Gradescope is an online tool for uploading and grading assignments an exams (it is now under the umbrella of TurnItIn). You will turn in your homework and exams through Gradescope, and you will access your graded exams there as well. You can access Gradescope through Canvas.

Instructional Staff

Name	Role	E-mail	Office hours
Ioana Dumitriu	Instructor A00	idumitriu@ucsd.edu	Mon, 5:15-6:45pm (APM 5824); Wed, 11:30-1:30pm (Zoom)
Jiajia Wang	TA, section A01	jiw133@ucsd.edu	Tue, 12-2pm (HSS 4070)
Jake Kosakoff	TA, section A02	jkosakof@ucsd.edu	Thu, 10-12pm (HSS 3062)
Max Johnson	TA, sections A03 and A04	mmj002@ucsd.edu	Thu, 12-4pm (HSS 5027)

Calendar

This is a tentative course outline and might be adjusted during the quarter. The chapters refer to textbook chapters.

Week	Monday	Wednesday	Thursday	Friday
1	Jan 5 3.3, 6.1-6.3 Intro; finite precision arithmetic	Jan 7 3.1+ Big-Oh notation, triangular systems, Gaussian elimination	Jan 8 Discussion Sections	Jan 9 3.1+, 4.1 Gaussian Elimination, LU HW 0 due
2 (Quiz week)	Jan 12 4.1-4.2 LU factorization	Jan 14 4.3-4.5 Permutation matrices, PLU	Jan 15 Discussion Sections Quiz 1	Jan 16 17.1-17.3 Positive definite matrices, Cholesky HW 1 due
3	Jan 19 MLK Day no class	Jan 21 5, 17.4 Banded LU, PLU, Cholesky	Jan 22 Discussion Sections	Jan 23 8.1-8.2, 9.1-9.2 Matrix and vector norms HW 2 due
4 (Quiz week)	Jan 26 9.3-9.4, 10.1 Matrix norms, condition numbers, perturbation theory	Jan 28 10.2-10.4 Perturbation theory	Jan 29 Discussion Sections Quiz 2	Jan 30 16.4-15.1 Gram-Schmidt, orthogonal matrices HW 3 due
5 (Midterm week)	Feb 2 15.1, 15.3, 16.3 orthogonal matrices, Householder reflectors, full QR	Feb 4 Review MIDTERM, 7-8:50pm CENTR 113	Feb 5 Discussion Sections	Feb 6 16.3, 16.5+ Full QR, least squares
6	Feb 9 16.2+ least squares with QR	Feb 11 23+ Singular value decomposition (SVD)	Feb 12 Discussion Sections	Feb 13 24.2, 24.4-24.5 Spectral norm, condition number, low-rank approximation HW 4 due
7 (Quiz week)	Feb 16 Presidents' Day no class	Feb 18 24.1, 24.3 Least squares with SVD, pseudoinverse	Feb 19 Discussion Sections Quiz 3	Feb 20 19.1 Eigenvalues; direct vs iterative methods HW 5 due
8	Feb 23 19.2, 19.4 Eigenvalues, diagonalization, similarity	Feb 25 20.1-20.2 Power method	Feb 26 Discussion Sections	Feb 27 22.4-22.5 Hessenberg form, QR iteration HW 6 due
9 (Quiz week)	Mar 2 23.3 SVD, via eigenvalues	Mar 4 25.1+ Iterative methods for linear systems	Mar 5 Discussion Sections Quiz 4	Mar 6 25.1 Jacobi method
10	Mar 9 25.2 The Gauss-Seidel method	Mar 11 25.1-25.2 Analysis of Jacobi and Gauss-Seidel	Mar 12 Discussion Sections	Mar 13 Final Review HW 7 due
11 (Finals week)				Mar 20 Final Exam 3:00-6:00pm CENTR 216

Lecture Notes

The Canvas site has lecture notes, both ``before" and ``after" lecture.

Syllabus

Prerequisites: MATH 18 or MATH 31AH and MATH 20C or MATH 31BH and CSE 20 or MATH 15A or MATH 31CH or MATH 109, or consent of instructor. Familiarity with a programming language is very helpful; familiarity with MATLAB would be helpful.

Lectures: Attending the in-person lectures and watching the podcast / recording when in-person attendance is not possible is a fundamental part of the course. You are responsible for material presented in the lectures 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 lectures.

Discussion sections: Participation in discussion sections is greatly encouraged. Make use of the time that your TAs offer! Attend the discussions to see more examples, work through problems, and talk to your TAs in a small-group setting.

Homework: Homework assignments will be posted on Canvas and will be due at 11:59pm on the indicated due date. You must turn in your homework through Gradescope. A PDF or picture is required to upload; if (and only if) you have clean and neat handwriting, it is permitted to turn in pictures/scans of homework done on paper. Assignments should be in a single PDF file before being uploaded, or as a picture for each question. It is allowed and even encouraged to discuss homework problems with your classmates and your instructor and TA, but your final write up of your homework solutions must be your own work.

Lowest score: There will be 8 homework sets, but the first one will only be graded for completion. Only the 7 proportionally highest scores will be counted towards your grade.

Midterm and Final Exams: Both the midterm and the final will be in-person and will take place on the date and at the time indicated on the calendar. There will be no makeup opportunities for either, except in the most serious of circumstances.

You will be allowed to use a single sheet of notes, 8.5x11 or similar, double-sided, handwritten for the midterm, and two such sheets (total: 4 pages) for the final.
You will be allowed (but should not need) a scientific calculator (i.e., with one line of display and only very basic functions).
No other notes, textbooks, resources, calculators, or human help of any kind will be allowed.
See the Academic Integrity policies below for additional information.
It is your responsibility to ensure you do not have conflicts involving the final examination.

Quizzes: They will be held at the date and time stated above, in the Discussion Sections; each will take 20 minutes. They will be multiple-choice (fill-in bubble).

You will not be allowed any notes, but will be allowed (though should not need) a scientific calculator (i.e., with one line of display and only very basic functions).
There will be no makeups for quizzes, but the grading scheme allows for dropping the lowest-performing one and transferring the credit to the final.
See the Academic Integrity policies below for additional information.

Administrative Links: 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 Quizzes will be graded automatically by Canvas, and they are multiple-choice. No regrades will be possible or necessary.
Your Midterm, Final, and homework will be graded using Gradescope. You will be able to request regrades directly from your TA or grader through Gradescope for a specified window of time. Be sure to make your request within the specified window of time; no regrade requests will be accepted after the deadline. Note: Your grader will consider your regrade request only if you have explained clearly, thoroughly, and politely why you think an error in grading was made.

Grading: Your cumulative average will be the best of the following two weighted averages:

14% Homework, 4% for each of the 4 quizzes, 25% Midterm, 45% Final Exam
14% Homework, 4% for each of top 3 quizzes, 25% Midterm, 49% Final Exam

Your course grade will be determined by your cumulative average at the end of the quarter. Grading will not be curved, but adjustments will be made as necessary to account for unexpected difficulty of tests. You will need roughly 90% to get A- or above, roughly 80% to get a B- or above, and roughly 60% to get a C- or above. This is guaranteed, meaning that you will not get a worse grade than specified above. However, you will not get a pass (or P) unless you get a C- or above score, so aim for at least 60%.

Community Principles

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.
Messaging etiquette: You are expected to write as you would in any professional correspondence. E-mail, 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.

Accommodations:

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 letter to faculty (please make arrangements to contact your instructor privately) and to the OSD Liaison in the Math Department (Holly Proudfoot, hproudfoot@ucsd.edu) in advance so that accommodations may be arranged. You will find more information here.

Academic Integrity Policies

UC San Diego's code of academic integrity outlines the expected academic honesty of all students and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due (listing your collaborators on homework assignments, noting books or papers containing information you used in solutions, etc.), and treating your peers respectfully in class.

Most of the rules governing exams are explained above. Additional rules will be communicated as necessary, with at least 48 hours of advance notice, by email or through Canvas Announcements. Participation in any of the exams implies that you agree to respect all communicated rules.

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.

About Gradescope

We will be using Gradescope for the grading of both homework and exams.

You can access Gradescope directly through your Canvas Math 170A page, by click on the "Gradescope" link in the tab on the left.
If you have not yet been added to the course (Course ID 1209927), you can add yourselves via the code YBRN55. IMPORTANT: use your UCSD email! If you don't use the proper UCSD credentials, your grades will not be sync'ed once you are officially enrolled!
Please make sure your files are legible before submitting, and also to assign the pages you want graded for each problem.
Most word processors can save files as a pdf.
There are many tools to combine pdfs, such as here, and others for turning jpgs into pdfs, such as here.

About Matlab

MATLAB (from "matrix laboratory") is a programming language and numerical computing environment widely used in applied mathematics, engineering, computer science and sciences in general. Many assignments (and even some test questions) will be to write short programs for Matlab. One thing to know about Matlab: the command ‘help’ is your best friend! Use to look up what functions do and the syntax.

We will do basic MATLAB programming in this course. While we will talk about the MATLAB specific programming details during class, I will expect that you know some programming basics, including what a "for loop" is. (The for loop is about the most complicated programming concept we'll use, and fortunately it's not too complicated.)

There are three main ways to get access to Matlab:

Go to this link and use your UCSD credentials to either download a copy of MATLAB onto your computer, or to use MATLAB online (the code you write will be saved into your online account).
You can use a UCSD virtual computer lab (from home or anywhere). You log in with your UCSD credentials. Info here; search for "virtual computing labs".
You can buy a student copy of the software at the bookstore.

For a review of basic programming in MATLAB, a good resource for intro MATLAB can be found on Professor Bruce Driver's website, here.