# MATH 170A Syllabus

## Course outcomes

For this course, the main subject material is

• Solving Ax=b type problems with direct methods (triangular systems, Cholesky decomposition, banded/sparse systems, Gaussian elimination with and without pivoting, LU decomposition, QR decomposition) and iterative methods (Jacobi and Gauss-Seidel)
• Understanding the theory behind computation (rounding errors, sensitivity, condition numbers, backward error analysis, backward stability)
• Least squares problem (Gram-Schmidt, orthogonal matrices, QR decomposition)
• Basic iterative methods solving for eigenvalues (power method, QR iteration)
• Singular value decomposition

By the end of the course, you should be able to show understanding and mastery of the subject material

• by performing calculations, including knowing which tools to use in which circumstances by writing MATLAB programs to perform these calculations
• by clearly explaining concepts, processes, definitions and theorems
• by proving some results related to the material

## Required material

Textbook: Fundamentals of Matrix Computation, by David Watkins, 3rd edition (2nd edition also ok).

MATLAB: MATLAB (from "matrix laboratory") is a programming language and numerical computing environment often used in applied mathematics and other applications. Many assignments (and even test questions) will be to write short programs for MATLAB.

An intro textbook discussing Matlab can be found here.

There are four main ways to get access to MATLAB:

• In the basement of AP&M there are computer labs with Matlab installed on all the computers.
• You can use the UCSD virtual computer lab (from home or anywhere). Log in with your UCSD credentials.
• You can buy a student copy of the software at the bookstore for \$ 100.

Alternatively, you can download the free open source version called Octave. While Octave and MATLAB are designed to be compatible, there are differences, and Octave is at least marginally slower. If you join a project/company that uses one of these tools, you will need to use the one they use. More places use MATLAB than Octave. However, Octave is free, as part of the GNU project, which can be an advantage.

We will do some 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, but fortunately it's not too complicated.) If you are not comfortable with what a for loop is, or want a short review of basic programming in MATLAB, a good resource is this file.

## How this course is run

Lectures: are held in-person (HSS 1330) as long as the public health situation allows. In case we have to switch to remote instructions, lectures are held synchronously via zoom. Podcasting will be available via UCSD's podcasting system. The recordings should also appear in the Canvas Media Gallery.

Discussion sections:

• A01 and A02: are held synchronously via zoom (links available in Canvas). Recordings of the zoom discussion section are made available to all students in Canvas. You may attend remote discussion sections, even when you are not enrolled for the specific section.
• A03 and A04: are held in-person (WLH 2115) as long as the public health situation allows. If you would like to attend an in-person section, but are enrolled in A01 or A02, please consult with the instructor first.
Note that all discussion sections cover the same material.

Office hours: There are both in-person office hours and remote office hours (via zoom). Please consult the table on the main page. You may attend the office hours of any and all instructors, regardless of discussion section enrollment.

Attendance: is not mandatory for any segment of this course (except for exams, see below). For a good course outcome, it is highly recommended to participate (live or watch the recording afterwards) in the following:

• Lectures, MWF 50 min each,
• One of the discussion sections, M 50 min,

It is furthermore recommended to join the discussions

• on Piazza, which is an online discussion platform,
• in the office hours of the instructor or TA
to further deepen your understanding, and get answers to questions you might have.

## Course work you need to complete

In every lecture we will discuss certain chapters of the textbook, see the course calendar. You are required to read along with the lecture, ideally, read the chapter before the lecture, then it will be easier to follow. Reading does not mean that you have to read and understand all details (though it doesn't hurt to do so). It means you should get a good idea of the topics that are covered in the respective chapter before class, and consult the textbook after class to understand details.

### Homework

Homework will be due Tuesdays of each week by 11 pm. You can find the homework problems as pdf on Canvas under "Files". Late homework will not be accepted.

All standard homework assignments will be turned in via Gradescope.com. Your login is your UCSD email.

All students enrolled in MATH170A have been added to Gradescope. If you have not been added (due to late enrollment, for example), please wait one or two days after enrollment, you will be added automatically.

Assignments should be uploaded in a single pdf file, or as a picture for each question. Please make sure your files are legible before submitting.

For MATLAB coding problems, you need to submit a screenshot of the program you wrote, including a screenshot of the output of the code in case the homework asks you to apply it to some example. Handwritten code, pseudo code or numerical results without code will not result in any credit!

If more than 60% of students fill out CAPEs at the end of the quarter, I will drop everybody's lowest homework score.

### Quizzes

There will be two quizzes during the quarter. Quizzes will be run via Canvas. You will have a window (TBA) to start each of the quizzes. Once a quiz is started, you have 30 min to complete it.
• Quizzes are of the type multiple choice or fill-in-the-blank or similar. They do not require you to upload any written solutions, or intermediate steps.
• You are allowed to use lecture notes, the textbook and homework/discussion section solutions for the quizzes. You are not allowed to use the internet, MATLAB (or any other program), a calculator or any other electronic device (of course, except for your computer to do the quiz).
• Quizzes are unproctored. You have to take quizzes by yourself, and are not allowed to talk/collaborate with other people. Read the academic integrity section for more details.
• I will try to make the questions as precise as possible to avoid confusion. In case you do not understand a question of the quiz, you can ask the instructors during the quiz via a private message on Piazza. Please be aware that depending on the time you take the quiz, instructors might not be available to respond.

### Midterm, final

• There will be one midterm and one final for this class.
• Each one of these exams will be one hour long.
• Exams will take place in the announced time slots.
• The midterm will be unproctored (take it at home). The final is currently planned as in-person.
• As with quizzes, you are allowed to use lecture notes, the textbook and homework/discussion section solutions for the midterms and final. You are not allowed to use the internet, MATLAB (or any other program), a calculator or any other electronic device (of course, except for your computer to get the questions and upload your answers).
• You have to take all exams by yourself, and are not allowed to talk/collaborate with other people. Read the academic integrity section for more details.
• I will try to make the questions as precise as possible to avoid confusion. In case you do not understand a question, you can ask the instructors during the exam (either by raising your hand during in-person exams or via a private post on Piazza during unproctored exams).

### Exams overview

Material refers to all of the material discussed in the lecture, HW and discussion sections from the respective textbook chapters.

Exam Date Time Type Where to find questions Material
Quiz 1 F Oct 8 window: 11 am to 7 pm
30 min quiz time
Remote (unproctored) Canvas 1.1, 1.2, 1.3, 1.7
Midterm F Oct 29 6-7 pm
1 h exam time
Remote (unproctored), or in HSS 1330 Canvas, or on paper 1.8, 1.4, 1.5, 2.1, 3.1, 3.2, 3.3
Quiz 2 F Nov 19 window: 11 am to 7 pm
30 min quiz time
Remote (unproctored) Canvas 3.4, 2.2/2.3, 4.1, 4.2, 4.3, 5.1, 5.2, 5.3
Final W Dec 8 8 - 9 am (last name A-LO),
10 - 11 am (last name LP-Z)
in-person exam in HSS 1330 handed out on paper Everything taught in this class (focus on later chapters)

If academic integrity violations are suspected on any of your assignments, the instructor might ask you to participate in a meeting to explain your solutions. In addition, you may also be reported to the Academic Integrity Office.

To learn how to avoid academic integrity violations in this class, read the academic integrity section.

Your grade will be based on the scores of the homework, two quizzes, one midterm, and one final exam. It will be calculated from taking the maximum of the methods defined below:

Method #1 = (30% HW) + (12.5% Quiz 1) + (12.5% Quiz 2) + (22.5% Midterm) + (22.5% Final)

Method #2 = (30% HW) + (15% for best quiz) + (27.5% Midterm) + (27.5% Final)

There will be no make-up exams. If you miss one of the quizzes, your grade will be computed using method 2. I will use the following approximate scale to compute your grade

A+, A, A- B+, B, B- C+, C, C- F
90+ 80+ 60+ [0,60)

You are guaranteed this scale, that means that your grade will not be worse than specified by the above scale. There might be an adjustment (=improvement) of grades based on the overall class performance. Passing grade for P/NP is C-, i.e. you need at least overall 60% to pass this class.

## 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. We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.