Here is the course description, stolen from the Rutgers Summer School Catalog

LINEAR ALGEBRA AND APPLICATIONS. (CR.3.)

16:642:550: SEC. E6:80628

N.B. EVE. JUNE 28-AUGUST 5

MTTH 6:15-8:45

BUMBY

HILL CENTER 525

PREREQUISITE: Consent of instructor or graduate director.

Vector spaces, bases, and dimension. Linear operators, quadratic forms, and their matrix representations. Eigenvalues, eigenvectors, diagonalizability, Jordan and other canonical forms. Applications to systems of linear differential equations.

The main source of course material in this department is the World Wide
Web. The department home page is
http://sites.math.rutgers.edu
That page has links to **Course materials**, which shows a page
with links to individual courses. Many courses, including this one, have pointers to several years of course
archives. Here is a link to last summer's
page. This course has been stable for several years.
However, you can expect minor revisions in the supplements, and some
new homework exercises.

Because of a conflict with another scheduled class, the course will
meet in **Hill 705**.

I also have a personal home page that can also
be reached by following the
**Faculty** link on the department page.

I will be available in my office (Hill 438) for questions between 5 and 6 PM on class days.

The pace of the course will be enforced by a short (of duration no more than 45 minutes) exam each week. These exams will be given at the start of the period on Tuesday of the second week, and Monday for subsequent weeks.

Homework will be collected two class meetings after it is assigned. The homework will be graded. The grade will mostly serve to identify additional work that should be done prior to the exam.

July 4 is a holiday, but it falls on Sunday this year. No meetings of this course will be affected.

The last homework was assigned on Monday, July 26. Lectures after this date will deal with chapter 7 and section 3.5 on the fast Fourier transform. These topics do not lend themselves to useful exercises.

There will be a three hour final exam in the last class meeting on Thursday, August 5. On that day, class will start at 6 PM and end at 9 PM. Questions on the final will be similar to those on the class exams. Calculators will be allowed, but no books or papers may be used during the exam.

Prior exposure to Linear Algebra at the Undergraduate level is expected, allowing the course to begin with Section 3.6 of the text. This section gives a quick review of the topics in such a course.

A separate page contains a table showing lecture topics and homework assigned.

These follow the supplements from Summer 2003 fairly closely,
although there are minor improvements in editing. Supplements 5 and 7
have been interchanged. That is, this year's supplement 5 covers the
topic that was supplement 7 last year and *vice versa*. There
is now an attempt to have a uniform appearance. They will appear as
needed.

- S1: Prerequisites, including Intersection of Subspaces. (alternate form of 3Y, p. 198, with an exercise)
- S2: Sign of a Permutation. (extending discussion on pp. 237-238, with an exercise)
- S3: The Cauchy-Binet Formula.(generalization of property 9, p. 217, with two exercises)
- S4: Finding eigenvectors. (more on examples from sections 5.1 - 5.3, with two exercises)
- S5: Matrix exponentials (with three exercises).
- S6: The Perron-Frobenius Theorem (with four exercises).
- S7: A robust method for finding characteristic polynomials (with three exercises).
- S8: Schur's Unitary Triangularization Theorem (and other topics from section 5.6, with five exercises).
- S9: More information about least squares and the pseudoinverse.
- S10: Numerical methods in Linear Algebra. The two exercises will be discussed in lecture.

- Exam 1 on
**Tuesday, July 6**will consist of two problems based on the homework assigned on June 28 and June 29. - Exam 2 on
**Monday, July 12**will consist of two problems based on the homework assigned on July 01 and July 05, emphasizing sections 5.1 through 5.3 and supplement 4, on basic properties of eigenvalues and eigenvectors, diagonalization, and basic applications.**This announcement was corrected on July 11 at approximately 4:15 PM. The original statement did not accurately identify homework 4, all parts of which are included, and erroneously included supplement 3 which is not suitable for an exam.** - Exam 3 on
**Monday, July 19**will consist of two problems based on the homework assigned on July 06 and July 12. This deals with sections 5.4 (as modified by Supplement 5) and 5.5. - Exam 4 on
**Monday, July 26**will consist of two problems based on the homework assigned on July 19 and July 20. This deals with sections 6.1 through 6.4. - Exam 5 on
**Monday, August 2**will consist of two problems based on the homework assigned on July 22 and July 26. This deals with Appendix A, Supplement 9 and sections 3.3 through 3.4.

The grades on the individual weekly exams are not of much significance. However, the three exams and nine homework assignments that have been graded by July 21 give enough to show some indication of progress so far. Each homework problem was worth 1 point, with fractional grades given for solutions that were flagged as being incomplete. There were also some homework problems that have not been submitted. The graph shows a comparison of the two components of class work (homework and class exams). In addition, there is a trend line (the best least squares fit of a linear function to the data) and a line showing the position of total of 80 points out a maximum of almost 100. This is the only major gap in the total score and only three scores are below this total. There is the possibility of a gap developing around 90 since the totals near that value tend to show weakness in one of the two components of the grade. The final exam will allow weakness in the class exams to be corrected. A grade of A will probably require a composite score of 90 percent.

The graph shows a comparison of the two components of class work (homework and class exams). In addition, there is a trend line (the best least squares fit of a linear function to the data) and lines showing the position of totals of 130, 120, and 110 out of a maximum of about 145. Grades above 130 show a good command of the work so far, and should lead to a grade of 'A' for the course, although an exam total below 90 indicates that mastery of some topics needs to be shown on the final. The final may also compensate for some of the grades currently below 130.

The graph shows a comparison of class work (homework and class exams) and the score on the final exam. (The exam score on the vertical axis of an earlier posting seems to have been incorrectly labeled. This has now been corrected.) A view of clusters of grades gives a better picture of work in the course than a simple average. Thirteen grades of A, two grades of B+ and 1 grades of B were assigned. The graph also includes a trend line and the location of totals of 260 and 230 points that mark gaps in the grade distribution that were used to determine the letter grades.

Mail to: bumby@math.rutgers.edu

Last updated: August 07, 2004