Comments on Math 221 -- Fall 2000. I was not going to comment on this course but Pit-Mann whom I teaching the course with prompted me to comment. First let me correct an error in Pit's email. The course is not meant for honors majors but for anyone. I have listed the blurb from the course catalog below. I have never taught math 228. My feeling is that 221, as it is, is more theoretical than 228. There are some, but perhaps not enough, proof problems in the homework, quizzes and final. However, it would be nice to make the course more theoretical. This might be difficult as it stands. The students who take this course have only had 125 and 126. They have not had any introduction to proofs. I feel it would be helpful if the students had a "bridging course" to start them on the road to doing proofs. There is more than enough easy topics, complex numbers, roots of unity, some elementary number theory, induction, and some discrete mathematics, that our students need to know and that they can easily learn while learning about proofs. Without such a course, I feel it is near impossible to cover some reasonable piece of linear algebra, learn how to do the needed computations and do proofs. Of course, it could be done. It might be hard on the students and TCE's. As the course is changed one should consider finding a book. The current book, Lay, I think is the best one that we have used in the six years that I have taught the course on and off. There are only a few more good theoretical books and many more less theoretical books. With a good bridging class one could use one of the more theoretical books. When I was looking about for a book the first time I taught this course 6 years ago, I found that many departments had there students take a more computational linear algebra course during the student's second year followed by a very theoretical linear algebra course during their last year. I do not think this option will work as well for us given many of our non-honors math majors go aboard for a semester and very few go on to graduate school. One thing I find odd. Why is 228 worth more credits than 221? Why is there a lab with 228 but not with 221? A lab could make a different in achieving some of the above goals. Peter Cholak ----------- Letter from Pit-Mann: Dear Steve, I am teaching Math 221 Linear Algebra for Math Honors. The curriculum is identical to the Linear Algebra Course to Engineering Students (heavily computational). I feel that since the curriculum is the same why not combine the 2 classes. Otherwise it might be good to reformulate the syllabus. The way I see it, if we want to change the syllabus, then we either make it computer oriented or we make it somewhat more theoretical (i.e., proofs are required and make it more geometric). Either approach has its own merit. Pit-Mann ---------------- From course catalog. 221. Linear Algebra (3-0-3) Open to all students. An introduction to vector spaces, matrices, linear transformations, inner products, determinants and eigenvalues. Emphasis is given to careful mathematical definitions and understanding the basic theorems of the subject. Credit is not given for both MATH 221 and MATH 228. Index 228. Introduction to Linear Algebra and Differential Equations (3-1-3.5) Prerequisite: MATH 225. An introduction to linear algebra and to first- and second-order differential equations. Topics include elementary matrices, LU factorization, QR factorization, the matrix of a linear transformation, change of basis, eigenvalues and eigenvectors, solving first-order differential equations and second-order linear differential equations, and initial value problems. This course is part of a two course sequence that continues with MATH 325. Credit is not given for both MATH 228 and MATH 221. Index 261-262. Honors Algebra I and II (3-0-3) (3-0-3) Prerequisites: MATH 166 A comprehensive treatment of vector spaces, linear transformations, inner products, determinants, eigenvalues, tensor and exterior algebras, spectral decompositions of finite-dimensional symmetric operators, and canonical forms of matrices. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. Index