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MATH 170A, lecture A

Winter 2021

Disclaimer: This is the website of lecture A. Lecture B runs in parallel and is taught by Ioana Dumitriu. Before continuing on this website, please make sure you are actually enrolled in lecture A.

Announcements

  • Final on Mar 17. Please see the syllabus for details on material and time window. Also read the Canvas announcement.
  • Feb 16: We have quiz 3 on Friday, Mar 5. The material is chapter 4.3, 5.1, 5.2, 5.3, 5.4, QR iteration (essentially lectures 18-23). Please read the more detailed Canvas announcement on quiz 3.
  • Feb 12: We have quiz 2 on Friday, Feb 19. The material is chapter 3.2, 3.4, 2.2, 2.3, 4.1, 4.2 (essentially lectures 12, 14-17).
  • Jan 29: We have midterm 1 on Friday, Feb 5. The material is chapter 1.4, 2.1, 3.1-3.3 (including Feb 1 lecture). Please read the more detailed Canvas announcement on the midterm.
  • Jan 25: No live lecture. Please watch the recording in Canvas Media Gallery instead. Also, office hour is canceled. Instead, I am holding office hour on Thursday, Jan 28, 10-11 am (see zoom meetings on Canvas).
  • Jan 17: We have our first quiz on Friday, Jan 22. Please see the syllabus for details on material.
  • Jan 6: We will be using Piazza for course-related questions. Enroll here .
  • Jan 1: Welcome to MATH 170A! Please make sure to read all of the course information on this website before the first lecture on Jan 4.

Course information

  • Course type: This class is completely remote. Lecture, discussion sections and office hours are held via zoom. Recordings of all lectures and discussion sections will be made available to enrolled students. See details in the syllabus.
  • Catalog description: Analysis of numerical methods for linear algebraic systems, least squares problems, orthogonalization methods, eigenvalues and singular value decomposition.
  • Prerequisites: MATH 18 or MATH 20F or MATH 31AH (i.e. some version of linear algebra), and MATH 20C (calculus 3). Familiarity with basic programming (i.e. for-loops) is assumed, familiarity with MATLAB would be very helpful (see the syllabus for details).
  • Textbook: Fundamentals of Matrix Computation, by David Watkins, 3rd edition (2nd edition also ok). Lecture notes will be available as well. The lecture notes are an addition to the textbook, they do not replace it.

Instructors

Name Role Email Section Office hour
Caroline Moosmüller Instructor cmoosmueller (at) ucsd (dot) edu A00 MW 10-11 am
and by appointment
Hangran Zhang TA haz355 (at) ucsd (dot) edu A01, A02 Tu 4-6 pm
Lin Zheng TA liz176 (at) ucsd (dot) edu A03, A04 Tu 1:30 - 3:30 pm
Noah Applegate Study group leader napplega (at) ucsd (dot) edu Study group

Synchronous class meetings

Lectures, discussion sections and office hours will be held synchronously via zoom (links available on Canvas). Recordings of all lectures and discussion sections will be made available on Canvas.

Note that all discussion sections cover the same material, so it is enough to join one of the discussion sections.

You may attend the office hours of any and all instructors, regardless of discussion section enrollment.

Attendance is not mandatory, but highly recommended!

Meeting type Instructor Date Time Place
Lecture A00 Caroline Moosmüller MWF 9-9:50 am Zoom LTI PRO tab in Canvas
Discussion A01 Hangran Zhang Tu 8-8:50 am Zoom LTI PRO tab in Canvas
Discussion A02 Hangran Zhang Tu 9-9:50 am Zoom LTI PRO tab in Canvas
Discussion A03 Lin Zheng Tu 10-10:50 am Zoom LTI PRO tab in Canvas
Discussion A04 Lin Zheng Tu 11-11:50 am Zoom LTI PRO tab in Canvas
Study group Noah Applegate Th 4-5:20 pm Canvas
Office hour Caroline Moosmüller MW 10-11 am Zoom LTI PRO tab in Canvas
Office hour Lin Zheng Tu 1:30-3:30 pm Zoom LTI PRO tab in Canvas
Office hour Hangran Zhang Tu 4-6 pm Zoom LTI PRO tab in Canvas

Lecture notes

Mar 12: Final review

Mar 10: Chapter 8.1-8.3: iterative methods, Gauss-Seidel method

Mar 8: Chapter 8.1-8.3: iterative methods, Jacobi method

Mar 5: QR iteration flop count
Intro to MATH 170B

Mar 3: Chapter 5.5: Upper Hessenberg matrices, QR iteration
Review for quiz 3

Mar 1: QR iteration intro

Feb 26: Chapter 5.3: Power method example, Chapter 5.4: Similarity transforms

Feb 24: Chapter 5.3: Power method

Feb 22: Chapter 5.2: More on eigenvalues/vectors

Feb 19: Chapter 4.3: pseudo inverse, Chapter 5.1: Eigenvalues intro

Feb 17: Chapter 4.3: Least squares with SVD
Quiz 2 review

Feb 12: Chapter 4.2: more SVD

Feb 10: Chapter 2.2/3: condition number, perturbations and Chapter 4.1: SVD

Feb 8: Chapter 2.2/3: condition number, perturbations

Feb 5: Chapter 3.2: proof of full QR, Chapter 3.4: reduced QR

Feb 3: Review for midterm

Feb 1: Chapter 3.2: Projectors, reflectors, proof of QR

Jan 29: Chapter 3.1/2/3: Solve least squares, projectors

Jan 27: Chapter 3.1/2/3: Intro least squares, orthogonal matrices, QR

Jan 25: Chapter 2.1: Norms

Jan 22: Chapter 1.4: Cholesky decomposition, Chapter 2.1: Norms

Jan 20: Chapter 1.4: Cholesky decomposition
Office hour: review for quiz 1

Jan 15: Chapter 1.7: LU decomposition, Chapter 1.8: Gauss elimination with pivoting

Jan 13: Chapter 1.7: Gauss elimination (continuation)
Code (Gauss_solve.m)

Jan 11: Chapter 1.3: Lower triangular system flop count, Chapter 1.7: Gauss elimination
Code (lowertriagsolve.m)

Jan 8: Chapter 1.2: Finish ODE example, Chapter 1.3: triangular systems

Jan 6: Chapter 1.1: Big-Oh notation, Chapter 1.2: linear systems motivation

Jan 4: Chapter 1.1: Matrix multiplications

Discussion section problems

Week 10: Discussion section will go over some of the problems of the sample final. To prepare, try to solve the problems on the sample final, see homework.

Week 9: pdf with problems

Week 8: pdf with problems

Week 7: pdf with problems

Week 6: pdf with problems

Week 5: Discussion section will go over some of the problems of the sample midterm. To prepare, try to solve the problems on the sample midterm, see homework.

Week 4: pdf with problems

Week 3: pdf with problems

Week 2: pdf with problems

Week 1: Discussion sections will go over basic MATLAB programming. To prepare for discussions, write a short MATLAB program that computes the inner product using a for-loop.