Math 170A (Introduction to Numerical Analyis: Linear Algebra)

Course Topics: Introduction to Numerical Analysis: Linear Algebra
Instructor: Prof. Michael Holst (5739 AP&M,; Office Hours: MW 1-2pm)
Term: Winter 2012
Lecture: 12:00p-12:50p MWF, Peterson 103
TA: Shi (Fox) Cheng (5760 AP&M,; Office Hours: Th 2-3pm, F 10-11am)
Discussion: A01: 4-5pm, 5402 AP&M; A02: 5-6pm, 5402 AP&M
Main Class Webpage:
Textbook(s): Fundamentals of Matrix Computations, by D.S. Watkins.
Printable Syllabus: Can be found [ here ].

Analysis of numerical methods for linear algebraic systems and least squares problems. Orthogonalization methods. Ill-conditioned problems. Eigenvalue and singular value computations. Three lectures, one recitation. Knowledge of programming recommended. Prerequisite: Math 20F.

COURSE INFORMATION: Many of the advances of modern science have been made possible only through the sophisticated use of computer modeling. The mathematical foundation of the computer modeling techniques now used in all areas of mathematics, engineering, and science is known as numerical analysis. The Math 170ABC series at UCSD provides an introduction to the exciting field of numerical analysis, which is also sometimes referred to as computational mathematics or scientific computing. Professor Holst has a passion for this particular area of mathematics, and much of his published research is in this area. Math 170A deals primarily with the development and analysis of algorithms (or, numerical methods) for solving problems arising in linear algebra.

GRADES, HOMEWORKS, EXAMS, AND IMPORTANT DATES: Course information, such as homework assignments, due dates, and exam dates, will be maintained on the class webpage. Note that I sometimes make minor changes to the homework assignments as the quarter progresses, based on how much I am able to cover in the lectures. Therefore, CHECK THE WEBPAGE FREQUENTLY. The course will be graded on the homework assignments, two midterm examinations and a final examination, according to the following guidelines:

Written and Computer HW (five homeworks): 30% of grade
Midterm #1 (In class, FRI 2/3, Peterson 103): 15% of grade
Midterm #2 (In Class, FRI 3/2, Peterson 103): 15% of grade
Final (11:30a-2:30p WED 3/21, Peterson 103) 40% of grade

There will be five homework assignments throughout the quarter. The first midterm will be based on homeworks 1 and 2, covering the main parts of Chapters 1-3. The second midterm will be based on homeworks 3 and 4, covering the main parts of Chapters 4-6. The final will be cummulative and based on homeworks 1-4, as well as a small amount of new material from homework 5, covering the main part of Chapter 7. The following policies regarding homeworks and exams will be applied:
  1. All HW assignments will count towards the final grade. I normally do not accept late homeworks, but this quarter I have been slow in getting the assignments posted due to my shoulder surgery. Therefore, this quarter I am being pretty lenient on the due dates for the homeworks, and have instructed Fox to accept late homeworks. However, you need to get the first two homeworks in by the time of the first exam, and you also need to get the third and fourth homeworks turned in before the second midterm; this will just help you better prepare for the midterms.
    UPDATE 3/19/2012: The CAPE respose rate has now exceeded our target of 70% (Section A01 is 76.0%, and Section A02 is 72.73%). As promised, in return for your help with getting a good sample size for the CAPES, I WILL now drop your single lowest homework score. Your grade for the homework will then be the average of just your four best scores. Thanks again to all of you for helping get a good CAPE response; it helps me improve as an instructor.
  2. In order to receive credit on a homework, you must at least attempt the computer parts of the homework assignments (if there are any).
  3. There will be no make-up exams. If you miss a midterm with an excused absence (i.e., illness with a note from a doctor), the other midterm and the final exam will be weighted accordingly.
  4. You are not allowed to use a calculator on midterms or finals.
  5. You are allowed to bring a single 8x11 sheet of paper containing notes on both sides (formulas, whatever you find useful) to each midterm and to the final. My view is that this allows you to focus on learning how to do the problems and understanding the material, rather than on memorizing formulas.
  6. Hint for Midterms and Final: The questions on all three exams should look very familiar. I will make most of the problems on all three exams look very much like the homework problems; in some cases, they will be exactly the same as some of the homework problems, and in other cases, they will be minor variations of homeworks. (I will put at least one slightly more challenging problem on each exam, which is not just a variation of a homework problem; this ensures that everyone will have some challenge on the exam.)

LECTURES: The lectures will follow the textbook quite closely; in particular, we will cover Chapters 1-7, in that order. Homework assignments will be a combination of theoretical and computer problems; this will require some computer programming using MATLAB. The TA will be able to assist you in accessing your computer accounts as well as MATLAB.

Week Topics Covered
Week 1

1.1-1.9: Brief review of background and notation. Introduction -- Gaussian Elimination and Its Variants.

Week 2

2.1-2.9: Sensitivity of Linear Systems.
Homework 1 due Monday 1/30.

Week 3

3.1-3.6: The Least Squares Problems.

Week 4

Review and Midterm: Covering Chapters 1-3.
Homework 2 due Friday 2/10.
Midterm 1 given in class on Friday 2/3. Covers: 1.1-1.7, 2.1-2.2, 3.1-3.3.

Week 5

4.1-4.4: The Singular Value Decomposition.

Week 6

5.1-5.9: Eigenvalues and Eigenvectors I.
Homework 3 due Wednesday 2/22 (Monday 2/20 is a holiday).

Week 7

6.1-6.7: Eigenvalues and Eigenvectors II.

Week 8

Review and Midterm: Covering Chapters 4-6.
Homework 4 due Monday 3/5.
Midterm 2 given in class on Friday 3/2. Covers: 4.1-4.3, 5.1-5.4, 3.4-3.5.

Week 9

7.1-7.9: Iterative Methods for Linear Systems.

Week 10

Review for Final: Covering Main Parts of Chapters 1-6 and 8.
Homework 5 due Friday 3/16.

WED 3/21
Peterson 103

Final Exam: Covers: Main Parts of Chapters 1-6 and 8.
In particular: Covers Homeworks 1-5.
Very specifically: Covers sections 1.1-1.7, 2.1-2.2, 3.1-3.5, 4.1-4.3, 5.1-5.4, 5.6, 6.1-6.2, 8.1-8.4, 8.7.
NOTE: To help you prepare for the final exam, The TA (Fox Cheng) is holding a Review Session and a question-answer (Q/A) session during finals week:
Review: March 18 (Sunday) in APM B412, 3:30pm-5:30pm
Q/A: March 21 (Wednesday) in APM B402A (Calculus lab), 9:30am-10:30am

HOMEWORKS ASSIGNMENTS: The following are the five homework assignments. Each homework consists of exercises listed below, all taken from the book. The exercises are numbered in a slightly unusual way in the book; they are number by Chapter and section (not so unusual), but the exercise number is taken from the "numbered item counter" in the section. For example, Exercise 1.1.8 is the eighth numbered item in Section 1 of Chapter 1; the previous seven number items can be any combination of subsection numbers, equations, theorems, etc. (You should have no trouble finding the exercises; just turn the pages in that chapter until the exercise appears in its chronological order.)

Homework 1 Exercises (Problems covering 1.1-1.7; Midterm 1 is based on these problems):
  1. 1.1.8
  2. 1.1.10
  3. 1.1.25
  4. 1.2.4
  5. 1.3.4
  6. 1.4.15
  7. 1.4.16
  8. 1.5.9
  9. 1.6.4
  10. 1.7.10

Homework 2 Exercises (Problems covering 3.1-3.5, 2.1-2.2; Midterm 1 is based on these problems):
  1. 3.1.5
  2. 3.2.8
  3. 3.2.14
  4. 3.3.7
  5. 3.3.10
  6. 3.4.22 (Not on Midterm 1, but fair game for Midterm 2 and final)
  7. 3.5.23 (Not on Midterm 1, but fair game for Midterm 2 and final)
  8. 2.1.32
  9. 2.2.6
  10. 2.2.24

Homework 3 Exercises (Problems covering 4.1-4.3, 5.1-5.2; Midterm 2 is based on these problems):
  1. 4.1.6
  2. 4.1.15
  3. 4.2.8
  4. 4.2.12
  5. 4.3.8
  6. 4.3.9
  7. 5.1.18
  8. 5.1.19
  9. 5.1.23
  10. 5.2.6
  11. 5.2.17

Homework 4 Exercises (Problems covering 5.3-5.4,5.6; Midterm 2 is based on these problems):
  1. 5.3.6
  2. 5.3.10
  3. 5.3.17
  4. 5.3.34
  5. 5.4.5
  6. 5.4.24
  7. 5.4.25
  8. 5.4.26
  9. 5.4.46
  10. 5.4.56
  11. 5.6.3 (Not on Midterm 2, but fair game for final)
  12. 5.6.4 (Not on Midterm 2, but fair game for final)

Homework 5 Exercises (Problems covering 6.1-6.2,8.1-8.4,8.7; Final Exam will partially cover these problems):
  1. 6.1.1
  2. 6.2.2
  3. 8.1.9
  4. 8.1.12
  5. 8.2.12
  6. 8.2.24
  7. 8.3.12
  8. 8.3.14
  9. 8.4.12
  10. 8.4.21
  11. 8.7.4
  12. 8.7.6