Johannes Brust (Instr.) Zhichao Wang (TA) jjbrust@ucsd.edu zhw036@ucsd.edu Office/student hrs: Office/student hrs: M,W: 9a-10:30a (APM 1111) R:8a-10a (HSS 5012)

## Welcome to Math 170A (Lecture A, Winter 2023)

Linear algebra and in particular numerical linear algebra is a cornerstone of modern scientifc computing. As such this class involves a valuable amount of numerical reasoning in connection with practical methods. One may use the materials to further learn about nonlinear numerical analysis in Math 170B or even use them as tools to numerically solve problems from research, industry and applications accross a variety of different subjects.

Because of this, algorithms and computer implementations are important components of the class. The examples and textbook are in [Matlab] (available for free to UCSD students), yet in principle you are free to choose a language you like.

### Memo to the student:

Remember, this class is here to help succeed in learning the subject.

• Homework problems will help prepare for Quiz, Midterm and Final questions
• •Being active in Lecture, Discussion and office hours will help to learn
• •Ask for help when you need help to learn the materials

# Announcements

 Jan 5 Lectures on Monday Jan. 9th and Wednesday Jan. 11th are recorded.

# Syllabus

All times in Pacific Time

Lectures: MWF, 8a-8:50a in HSS 1330

Discussions:
A01: 5p-5:50p in DIB 121
A02: 6p-6:50p in DIB 121

## Schedule

(Note: Schedule and policies may be updated throughout the quarter)

Week Monday Tuesday Wednesday Thursday Friday
1
09 Jan
1.1: Mat. mult.
10 Jan 11 Jan
1.2: Lin. sys.
12 Jan 13 Jan
1.3: Triang. sys.
HW 1
2
16 Jan
Holiday (MLK)
17 Jan 18 Jan
1.7: Gauss elim., LU
19 Jan 20 Jan
1.8: Gauss elim., pivot
HW 2
3
23 Jan
1.4: Pos. def., Chol.
24 Jan 25 Jan
1.5: Bnd. pos. def.
26 Jan
Quiz 1
27 Jan
2.1: Norms
HW 3
4
30 Jan
3.1&3.2: LS & Orth.
31 Jan 01 Feb
3.2: Orth.
02 Feb 03 Feb
3.3: LS soln.
HW 4
5
06 Feb
3.4: Gramm-Schmidt
07 Feb 08 Feb
Review
09 Feb 10 Feb
Midterm (8a-8:50a)
6
13 Feb
2.2&2.3: Cond. & Perturb.
14 Feb 15 Feb
4.1&4.2: SVD I
16 Feb 17 Feb
4.3: SVD II
HW 5
7
20 Feb
Holiday (Pres.)
21 Feb 22 Feb
5.1: Diff. eq. sys.
23 Feb
Quiz 2
24 Feb
5.2: Eigvals./vecs.
HW 6
8
27 Feb
5.3: Power methd.
28 Feb 01 Mar
5.4: Sim. trans.
02 Mar 03 Mar
5.5: Hessenb./tridiag.
HW 7
9
06 Mar
5.6: Francis's Alg.
07 Mar 08 Mar
5.8: SVD III
09 Mar
Quiz 3
10 Mar
8.1: Iter. methds.
HW 8
10
13 Mar
8.2: Classic Iter. methds.
14 Mar 15 Mar
8.3: Conv. Iter. methds.
16 Mar 17 Mar
Review
11
20 Mar
Final exam (8a-11a)

## Materials

 Textbook: Fundamentals of Matrix Computations (3rd ed.), David S. Watkins (2nd ed. is also be acceptable, however section numbering and some content differs) Content: We will cover relevant parts of chapters 1,2,3,4,5 and 8 Homework: We will use 8 HW sets (to learn and practice the subject) Assessment: 8 Homework, 3 Quizzes, 1 Midterm, and 1 Final exam Quizzes available for 24 hours via Canvas Midterm and Final exams are in person Quiz 1 (start: R. Jan. 26, 12pm -- end: F. Jan. 27, 12pm), (Content: Secs. 1.1,1.2,1.3,1.7,1.8,1.4) Midterm (F. Feb. 10, 8am -- 8:50am, HSS 1330), (Content: all sections covered) Quiz 2 (start: R. Feb. 23, 12pm -- end: F. Feb. 24, 12pm), (Content: Secs. 2.2,2.3,4.1,4.2,4.3) Quiz 3 (start: R. Mar. 9, 12pm -- end: F. Mar. 10, 12pm), (Content: Secs. 5.1,5.2,5.3,5.4,5.5,5.6) Final (M. Mar. 20, 8:00am -- 10:59am), (Content: comprehensive)

Weighted final scores from the best of two approaches:

 30% Homework + 25% Quizzes + 45% Midterm & Final OR 30% Homework + 15% Best Quiz + 55% Midterm & Final

Letter grades from weighted final scores and the best of two options

• (Option A):
•  A+ A A- B+ B B- C+ C C- D F 97 93 90 87 83 80 77 73 70 60 60>

• (Option B):
• A curve where the median corresponds to B-/C+

# Resources

 Canvas (Course page) Gradescope (Examination system) Piazza (Portal to ask questions) Matlab (Computing software)

## Homework:

The homwork and solutions are uploaded via the Canvas page.

 (Due/ Sections) Homework 1, [HW1] (due Jan. 13, Secs. 1.1,1.2) Homework 2 (due Jan. 20) Homework 3 (due Jan. 27) Homework 4 (due Feb. 3) Homework 5 (due Feb. 17) Homework 6 (due Feb. 24) Homework 7 (due Mar. 3) Homework 8 (due Mar. 10)

### Instructions (homework):

 • Total of 8 HW sets. Cumulative HW grade based on the best 7 out of 8. • HW 1 -- 8 submitted to Gradescope by Friday 11:00 pm Pacific Time. (Note: To be prepared for unforeseen technical difficulties, we will accept homework submitted within 24 hours from the due date, i.e., Saturday 11:00 pm, without a penalty.) • In view of the above arrangement, NO late homework will be accepted. • You can work with classmates, but need to write down your own version. Copying solutions from others is not accepted and is considered cheating. • Include an brief explanation of how a method works and an image (screenshot) of the code and results for programming problems.

## Notes:

Please notice that outside factors, including the need for a certain grade for admission/retention in any academic program, scholarship or transfer credit, graduation requirements or personal desire for a specific grade DO NOT appear in the determination of course grades. Effort, improvement, class attendance and participation will all dramatically improve your grade in the course in that they will enable you to learn the materials. They will NOT, however, actively participate in the calculation of course grades.
Remember that your instructor or TA are there for you if you need help in learning the course content.

Accommodations: Students requesting accommodations and services due to a disability for this course are asked to provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD), prior to eligibility for requests. Receipt of AFAs in advance is necessary for appropriate planning for the provision of reasonable accommodations. OSD Academic Liaisons also need to receive current AFA letters. Students can find department-specific information on exam accommodations on the following Math Department webpage: http://www.math.ucsd.edu/programs/undergraduate/exam_accommodations.php

Academic Dishonesty:  Academic dishonesty is considered a serious offense at UCSD.  Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.  It is in the student's very best interest to maintain academic integrity. (Click here for more information.)