Syllabus for Spring Semester, 1996

The course covers chapters 1, 2, and 4 of Kolman, plus a cursory survey of Chapter 5 in the last two weeks of the semester.

Linear algebra is a very different kind of course from Calculus. A typical calculus course primarily focuses on techniques for finding answers to problems. In Linear Algebra, on the other hand, techniques are of secondary importance. The most important goal in Math 311 is to develop a language and a conceptual framework which can be used in many parts of mathematics. In other words, Linear Algebra is a "theory course" rather than a technique course.

One of the most distressing differences between Linear Algebra and Calculus for many students is that Math 311 involves quite a bit of writing. One of the main reasons that some students go into subjects like Mathematics, Physics, and Engineering is that their skills with written language are very poor. At least in Mathematics, they think, there are no essay exams.

Surprise! In this course there are essay exams. It's just that the essays are called proofs.

In Calculus, the focus is on learning formulas and using these formulas to manipulate equations and obtain answers. In Linear Algebra the focus in on learning definitions and using these definitions to manipulate sentences and obtain proofs. Knowing the formal definitions is just as important in Math 311 as knowing formulas is in Calculus.

Aside from the fact that Linear Algebra is a basic conceptual framework used in many parts of mathematics, one of the benefits you should hope for from Math 311 is that your ability to express yourself clearly, precisely, and logically in writing will be considerably improved by the end of the course. You should also expect, however, that you will find learning this a fairly frustrating and painful process.

If you are unable or not willing to express mathematics in words and to write sentences and paragraphs for homework and tests then you should not take Math 311. It is very unlikely that a student can pass this course without learning to do at least some proofs. (Note: On homework assignments, only proofs are graded. Problems involving calculations are assigned purely for your own benefit.)

January 10  Wednesday    First Day 

Jan 15      Monday       KING DAY 

Chapter 1:  Properties of Matrices 

Feb 19      Monday       WASHINGTON's BIRTHDAY 

Feb 23      Friday       First Mid-term?  

Chapter 2:  Linear Independence 

Mar 8      Friday       DROP DEAD LINE 

Mar 22      Friday       Second Mid-term? 

Mar 25 -- Mar 29         SPRING BREAK

Chapter 4:  Linear Transformations 

Apr 5       Friday       GOOD FRIDAY 

Apr 17      Wednesday    Third Mid-term? 

 Chapter 6: Eigenvectors and Eigenvalues  

May 1       Wednesday    LAST DAY 

May 6       Monday 2:15  Final Exam  

                Three Mid-terms @ 100 pts each   = 300 pts  
                Homework roughly 100 pts         = 100 pts     
                Final Exam                       = 200 pts  
                TOTAL                              600 pts 

The grading scale is flexible but past experience suggests that the cut-off for an A is likely to be somewhere around 475 points and the cut-off for a C will be somewhere around 300 points.

Much of the homework and tests will involve writing proofs. It is probably not possible to pass the course by only learning to do calculations.