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

This page supplements materials to ``Introduction to Numerical Analysis: Linear Algebra''

Linear algebra and in particular numerical linear algebra is a cornerstone of modern scientific 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

Jan 5

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

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)

Grading

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+

Weblinks:

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.

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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

For additional information, contact the Office for Students with Disabilities:
• 858-534-4382 (Voice)   858-534-9709 (TTY)
• osd@ucsd.edu http://disabilities.ucsd.edu

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.)