Math 170A

Fall 2023, Lectures A00 (Dumitriu) and B00 (Huang)

Introduction to Numerical Analysis

Calendar
Syllabus
MATLAB
Piazza
Academic Integrity Policies
Gradescope

Announcements

Welcome to Math 170A, Lectures A00 and B00, Fall 2023! Our lectures are coordinated, which means we will be using the same Canvas site, website, Gradescope and Piazza sites; it also means we will have the same homework and exams. All information here is valid for both lectures A00 and B00.

Course Information

Textbook: The required textbook for this course is

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

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	Wed, 11-12pm, AP&M 5824; Thu, 4:30-6:30pm (Zoom)
Lei Huang	Instructor B00	leh010@ucsd.edu
Jiyoung Choi	Teaching Assistant A01 and A02	jichoi@ucsd.edu
Haixiao Wang	Teaching Assistant A03 and A04	h9wang@ucsd.edu
Shuncheng Yuan	Teaching Assistant B01 and B02	syuan@ucsd.edu
Xiaomeng Hu	Teaching Assistant B03 and B04	x8hu@ucsd.edu

Calendar

This is a tentative course outline and might be adjusted during the quarter. The chapters refer to textbook chapters.
If you see a + next to a lecture, the lecture contains MORE information than the respective chapter.

Week	Monday	Tuesday	Wednesday	Thursday	Friday
0					Sep 29 3.3, 6.1-6.3 (finite precision, big-Oh)
1	Oct 2 3.1+ (triangular systems, Gaussian elimination)		Oct 4 3.1+, 4.1 (Gaussian elimination, LU factorization)		Oct 6 4.1-4.2 (LU factorization) HW 0 due
2	Oct 9 4.3-4.5 (permutation matrices, PLU factorization)		Oct 11 17.1-17.3 (positive definite matrices, Cholesky)		Oct 13 5, 17.4 (banded LU, PLU, Cholesky) HW 1 due
3 (Quiz week)	Oct 16 8.1-8.2, 9.1-9.2 (matrix and vector norms)	Oct 17 Quiz 1 (Canvas)	Oct 18 9.3-9.4, 10.1 (matrix norms, condition number, perturbation theory)		Oct 20 10.2-10.4 (perturbation theory) HW 2 due
4	Oct 23 16.4, 15.1 (Gram-Schmidt, orthogonal matrices)		Oct 25 15.1, 15.3, 16.3 (orthogonal matrices, Householder reflectors, full QR)		Oct 27 16.3, 16.5, + (full QR, least squares setup) HW 3 due
5 (Midterm week)	Oct 30 16.2+ (least squares with QR)		Nov 1 Review for Midterm	Nov 2 MIDTERM 8-9:50pm A00: PETER 108 B00: PETER 108	Nov 3 23+ (the singular value decomposition, SVD)
6	Nov 6 24.2, 24.4-24.5 (spectral norm, condition number, low-rank approximation)		Nov 8 24.1, 24.3 (least squares with SVD, pseudoinverse)		Nov 10 Veterans' Day NO CLASS HW 4 due
7 (Quiz week)	Nov 13 19.1 (eigenvalues; direct vs. indirect methods)	Nov 14 Quiz 2 (Canvas)	Nov 15 19.2, 19.4 (eigenvalues, diagonalization, similarity)		Nov 17 20.1-20.2 (the power method) HW 5 due
8	Nov 20 22.4-22.5 (Hessenberg form, QR iteration)		Nov 22 23.3 (computing the SVD via eigenvalues)		Nov 24 Thanksgiving Break NO CLASS
9 (Quiz week)	Nov 27 Catch-up HW 6 due	Nov 28 Quiz 3 (Canvas)	Nov 29 25.1+ (iterative methods)		Dec 1 25.1 (Jacobi)
10	Dec 4 25.2 (Gauss-Seidel)		Dec 6 25.1-25.2 (complexity and convergence of Jacobi and Gauss-Seidel)		Dec 8 Review for FINAL, which is on DEC 9 HW 7 due

Syllabus

Prerequisites:

MATH 18 or MATH 31AH, and
MATH 20C or MATH 31BH, and
CSE 20 or MATH 15 or MATH 109 or MATH 31CH.
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 (note Homework 0-5 and Homework 7 are due on Fridays, while Homework 6, due to the Thanksgiving Break, is due on the next Monday).

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. If you worked in a group, you must specify that and write down all group members' names on the first page of your homework.

Lowest score: There will be 8 homework sets; 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; the midterm will take place on the date indicated, in the evening. The final will be administered on the date, and at the place and time indicated in the schedule of classes. The dates are listed in the calendar. There will be no makeup opportunities for either, except in the most serious of circumstances.

For the Midterm, you will be allowed to use a single sheet of notes, 8.5x11 or similar, double-sided, handwritten.
For the Final, you will be allowed two sheets of notes, 4 pages total, as above.
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.

The quizzes will be run via Canvas. They will be multiple-choice and randomized.
You will have a 24-hour window to start the quizzes; once started, the quizzes will take 30 minutes.
The grades will be posted at the end of the 24-hour window.
You will be allowed to use lecture and discussion session notes, the textbook, and solutions to homework.
No other notes, textbooks, online resources, software (e.g., MATLAB), calculators, or human help of any kind will be allowed.
I will try to make the questions as clear as possible; if you do not understand a question, send a private message via Piazza. Please be aware that, depending on when you take the quiz, the instructors and TAs may not be available to answer.
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:

20% Homework, 5% for each of the 3 quizzes, 25% Midterm, 40% Final Exam
20% Homework, 5% for each of top 2 quizzes, 25% Midterm, 45% Final Exam

Your course grade will be determined by your cumulative average at the end of the quarter. Grading will not be curved. 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%.

Etiquette

In addition, here are a few of my expectations for etiquette.

Zoom meetings audio/video: You will be seeing and hearing me and your TAs. By default, I prefer to see you or at least hear you during Zoom meetings. If you do not feel comfortable with video, you are welcome to turn it off; and if you are also uncomfortable with audio, you can use the "chat" feature. The downside to this is that there may be considerable delay in answering your questions if you only use "chat", as I may not get to scan the "chat" as easily as answering verbal questions. In addition, Zoom has a feature called "raise your hand"; I greatly encourage you to use that to attract my attention, and to talk when I call your name. I will do my best to give you each your turn. Also, if you will turn off your video, please do not use odd or offensive images as background.
Noise and common courtesy during Zoom meetings: It is best to keep your microphone on "mute", and unmute it only when you speak; that way, there's less interference.
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 cell phones, laptops, tablets, iPods) 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 (whether by camera, cell phone, or other means).
E-mail etiquette: You are expected to write as you would in any professional correspondence. E-mail communication should be courteous and respectful in manner and tone. Please do not send e-mails that are curt or demanding.

Accommodations:

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 (OSD) which is located in University Center 202 behind Center Hall. The AFA letter may be issued by the OSD electronically or in hard-copy; in either case, please make arrangements to discuss your accommodations with me in advance (by the end of Week 2). We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see 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.

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, the Gradescope entry code is YD2XJW. IMPORTANT: use your UCSD email!
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:

UCSD students can download it for free from this link.
For a review of basic programming in MATLAB, a good resource for intro MATLAB can be found on Professor Bruce Driver's website, here.
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 $99.
You can also access MATLAB in one of our physical computing labs.