http://www.math.utah.edu/~korevaar/coord2270-2280: 2270-2280 overview page

### Math 2270 Details

Prerequisites: For Math 2270, students need to have succeeded at first-year Calculus, Mathematics 1210-1220 ( or 1250-1260 or 1270-1280). Although not a formal prerequisite, Math 2270 students would also benfit from the multivariable calculus in either 1260, 1280, or 2210: it is nice to make the connection that affine transformations are the multivariable analog of tangent line approximations, and at the end of the course to discuss the implications of the spectral theorem for multivariable max-min theory based on the Hessian.

Text: Introduction to Linear Algebra, Fourth Edition, by Gilbert Strang. ISBN=978-0-9802327-1-4.

Math 2270 course outline: Cover at least the first seven chapters of the text. This is the standard core material for all good sophomore level linear algebra courses: geometry and algebra of vectors in Rn; linear equations and Gaussian elimination; basic vector space theory; orthogonality; determinants; eigenvalues and eigenvectors; and general linear transformations. Chapter 8 has a selection of relatively in-depth applications. Choose which of these (or others) you wish to study with your class. I especially recommend introducing Fourier series, so that they seem less mysterious in Math 2280. Note that it makes sense to do various of these applications at different points in the course. Also, Math 2270 is now a required course for Computer Science undergraduates as well as for Math majors, and you may wish to tailor your application choices to your audience's as well as your own interests. This is the first year we're using Strang's text (we used to use Bretscher's linear algebra text), and we'll keep track of what works well. Make sure to slow down and fill in details at difficult conceptual junctures of this course.

2270 suggested lectures: The text is written so that each section corresponds roughly to a 50 minute lecture. Since there are 33 sections in the first 7 chapters and roughly 57-58 50-minute class meetings in a (non-summer) semester, you should have plenty of time for supplementary chapter 8 applications, review, class exams, class participation, and for slowing down when necessary. Please keep track of your own course pacing, so that I can enhance my suggestions as we gain experience with this new text. Also note that there is a lot of on-line support for this textbook and course, as described in the Preface. Peter Alfeld's experience from summer 2010 is that some of your students will find this extra material especially useful.

Strang highlights the webpages
http://ocw.mit.edu, http://web.mit.edu/18.06/www/, http://math.mit.edu/linearalgebra/,

Computer projects: These projects will be assigned to enhance the course material. Aim for two or three substantive projects. In addition to the projects, it's sensible to work Maple examples into class lectures and regular homework. Please consult Strang's suggestions, the project ideas that our current instructors have come up with (see links below), use your own ideas, or ask me.

Previous course home pages: Recent instructors of Math 2270 here at Utah who have used the Strang text are Chris Cashen, Dragan Milicic, Peter Alfeld, and Andy Thaler. Chris, Dragan and Andy have pretty complete web pages for the course and I recommend perusing these for ideas about topic presentation, pacing, and project ideas.