Announcements

• Solutions to homework 4 and midterm 2 are available now.

• THE FINAL is scheduled on Wed, March 19 at Center Hall 119 between 11:30am-2:30pm. The emphasis will be on the later topics not included in the midterms, specifically Chapters 3,5,6. Everything on the course calendar (except sections 3.3 and 7.1 which are not covered in class) are included. About %30-40 of the questions will be related to the earlier topics.  The final will be closed-book, but you can use up to 5 double-sided pages of notes. Calculators will not be allowed.
  • Study Guide for the Final
  • Additional Questions for the Final

• Additional office hours before the final
  • E. Mengi on Sun, Mon, Tue (March 16th, 17th, 18th) between 1pm-3pm at APM 5763
  • R. Haut on Tue (March 18th) between 11am-1pm at APM 6436
• Review session for the final
  • A. Stout on Mon (March 17th) starting at 12:30pm at the calculus lab in the basement of the APM building.

Calendar

Monday	Wednesday	Friday
Week 1	Jan 7 Organization & 1.1	Jan 9 1.1 & 1.2	Jan 11 1.2
Week 2	Jan 14 1.3 & 1.4	Jan 16 1.5 & 1.6	Jan 18 1.7 & 1.8
Week 3	Jan 21 Martin Luther King Day	Jan 23 1.8 & 1.9	Jan 25 2.1 Hw-1 due by 3pm
Week 4	Jan 28 2.2	Jan 30 Review Midterm 1 at 7pm at York 2622	Feb 1 2.3 & 2.5
Week 5	Feb 4 2.5 & 4.1	Feb 6 4.2	Feb 8 4.3

Week 6	Feb 11 4.4 & 4.5	Feb 13 4.5 & 4.7 Hw-2 due by 3pm	Feb 15 4.6
Week 7	Feb 18 President’s Day	Feb 20 3.1 & 3.2	Feb 22 3.2 & 3.3
Week 8	Feb 25 5.1 & 5.2	Feb 27 Review Midterm 2 at 7pm at York 2622 Hw-3 due by 3pm	Feb 29 5.2 & 5.3
Week 9	Mar 3 6.1 & 6.2	Mar 5 6.2 & 6.3	Mar 7 6.4
Week 10	Mar 10 6.5	Mar 12 7.1	Mar 14 Review Hw-4 due by 3pm

Important Enrollment Dates

• January 18  ; Last day to add classes
• February 1  ; Last day to drop without W on transcript
• March 7 ; Last day to withdraw

Final

• March 19, Wednesday from 11:30am to 2:30pm

Lecture Notes

The lecture notes will normally be available here at the end of each week. However, if the attendance drops below a certain level, I may no longer post them here and possibly distribute them in the class.

• Lecture 1 – Systems of Linear Equations
• Lecture 2 – Solving a System of Linear Equations
• Lecture 3 – Existence and Uniqueness Questions Regarding a Linear System
• Lecture 4 – Matrix Vector Representations of a Linear System, Span of a Set of Vectors
• Lecture 5 – Solution Set of a Linear System
• Lecture 6 – Linear Independence
• Lecture 7 – Geometric Interpretations of the Span and Linear Independence
• Lecture 8 – Linear Transformations

Past Exams

Below are the exams of the section of Math 20F that I taught in Spring 2007.

• Midterm 1  —  Solutions
• Midterm 2  —  Solutions
• Final

Resources

• On-Campus resources :
  • Calculus Tutoring

• Encyclopedias on the web : On these sites you can find brief descriptions of most of the topics we will cover.
  • Wikipedia – the scientific encyclopedia 
  • Wolfram Mathworld

Syllabus

Catalog Name :
Math 20F, Linear Algebra

Credits :
4 credits

Prerequisites :
Math 20C or equivalent with a grade of C- or better

Description :
The following topics will be covered:

• Sytems of Linear Equations
• Matrices and Operations on them
• Vector Spaces and Subspaces
• Column, Null Spaces and Rank of a Matrix
• Linear Transformations
• Determinants
• Orthogonal Subspaces, Gram Schmidt and Least Squares
• Real Eigenvalues and Eigenvectors
• Matrix Factorizations

We will restrict ourselves to linear algebra with real numbers. For instance we will only consider linear equations with real coefficients, vector spaces with real scalars, matrices with real entries. Usually generalizations to complex cases are straightforward.

Course Webpage:

(You are expected to check the webpage regularly.)

Textbook :
Linear Algebra and its Applications by David C. Lay – 3rd Edition

For the exams you are responsible for all of the sections on the course calendar.

Grading Policy :
Your grade will be based on your performance in the four homeworks, matlab computer labs (see the information about the computer labs on the right for how your matlab score will be determined), two midterms and final. We will use one of the following two schemes (whichever yields the higher score) to calculate your overall score out of 100.

• %10x(Matlab score)  +  %20x(Average of best 3 homeworks)  + %20xMidterm 1  +  %20xMidterm 2  +  %30xFinal
• %10x(Matlab score)  +  %20x(Best of Midterm 1 and Midterm 2)   +  %20x(Average of best 3 homeworks)  +  %50xFinal

Remember always that this is a curved-class. We will use curve in favor of you. This means that if the class average is high, then we will use the standard scale below.

D	C	B	A
60<= score <70	70<= score <80	80<= score <90	90<= score <100

But more likely we will have to use a different scale so that you can get better grades than the above scale suggests.  For instance if your overall score is 80 but if you are in the upper %10 of the class, you should normally receive an A. Unless the class-average is high, what matters in the end will be your rank in the class and your average as compared to the class-average. Please don’t get discouraged if you find an exam difficult; possibly it was a difficult exam for the majority of the class.

Midterms :
The midterms will be held from 7pm to 8:50pm on January 30th and February 27th at York 2622.

• Midterm 1 (Jan 30, Wednesday) : Sections 1.1-9 are included
• Midterm 2 (Feb 27, Wednesday) : Sections 2.1-3, 2.5, 4.1-7 are included.

Typically there will be five questions on each of the midterms. Both of the midterms will be open-book exams. There will be no make-up midterms; if you miss a midterm, the weight of the final will be increased to %50. One of the midterms will be discarded if your final grade is better than your lowest midterm grade. In this case the weight of the final will be %50 of your overall score.

Final :
Final is scheduled on March 19th, Wednesday from 11:30am to 2:30pm. Please make sure that you have no other final scheduled at this time. (neither you would like to have multiple finals, especially three or more, on this date.)  The final will be a closed-book exam. It covers all of the topics on the  course calendar. There will be no make-up final under no circumstances.

Homeworks :
Homeworks are due by 3pm on the indicated dates on the  course calendar. You will have to drop them off to the homework box reserved for our class on the 6th floor of the APM building. Homework boxes are on the right on the 6th floor as soon as you leave the elevator. One of the boxes will be labeled as Math20F (Lecture C-Homeworks). Normally late homeworks will not be accepted. If you have a valid excuse to return it late, please see me and not drop it off to the homework box late. (Homeworks dropped off late will be discarded.) Additionally there will be suggested questions from the textbook, which will be solved during the discussion sections. These questions are not going to be collected or graded.  Their sole purpose is to get you prepared for the exams. Please check the  homework page to access the latest homeworks and suggested questions posted.

Calculators :
Use of a calculator such as TI-85 or TI-86 when solving the homeworks or suggested questions is recommended. Calculators are not allowed during the exams.

Lectures :
Attendance to the class is not required. However, the most efficient way to learn is sitting in the class. Because this gives you the opportunity to interact in case something is not clear. What is covered in the class will be compatible with the textbook. But the lectures will be brief and we will touch on only the most essential concepts.

Discussion Sections :
Discussion sections meet every Tuesday. Your TAs will be solving some of the homework and suggested questions. Here you will find more time to raise individual questions. This provides a good opportunity to practice with your friends and knowledgable TAs.

Computer Labs :
Computer labs will be held every Thursday at the same time as your discussion sections. You will be using the mathematical computing software Matlab. Some of the techniques you will learn in the class are tedious for hand calculations. Matlab will let you perform these techniques efficiently. For instance as we shall see, finding the eigenvalues of a matrix is equivalent to finding all of the roots of a polynomial, which is a very difficult computational problem. Today there are efficient techniques for eigenvalue computation devised for computers from which Matlab benefits.

Only the best six Matlab assignments count. There will be a Matlab final during the 10th week’s computer lab. Your matlab score will be calculated as

• %80x(Average of the best 6 Matlab hws) + %20x(Matlab final)

Your Matlab score contributes %10 to your overall score…

Academic Dishonesty :
Please realize that you are a student in one of the prestigious colleges in California. We expect you to behave accordingly during the lectures and exams. In the case of any unethical act during the lectures or exams, necessary steps will be taken.