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Math 560: Linear Algebra Fall 2012 Time/place: MWF 9:00–9:50 a.m. in Engineering E104 Course website: www.math.colostate.edu/∼bates/courses/F12/560 Text: Linear Algebra by Friedberg, Insel & Spence, 4th edition (ISBN 0-13-008451-4). Instructor info: Prof. Dan Bates, bates@math.colostate.edu, Weber 221 (1-1037) Office hours for 560: Thursday, 12-1, but please let me know beforehand if you are planning to come in. If I am not expecting anyone, I may not be there. My schedule is extremely tight this semester, so I have very few times when I can meet with students in my classes. If Thursday 12-1 is bad for you, try email. If that isn’t working for you, then we can try to set up a time that will work for both of us. Prerequisites: Basic calculus (derivatives, mostly). This is a basic graduate course in the Math Department, so prerequisites are minimal. Topics to be covered: See the schedule below. These are exactly the topics required by the Math Department for this QE course. Structure of the class: This will be a fairly standard lecture class, though I welcome your comments and ideas! Please feel free to speak up (within reason). There will be homework due most weeks (typically on Fridays), a take-home midterm (date TBD), and a 2-hour QE final exam. The final will be cumulative on exactly the topics listed on the QE syllabus. The unofficial rule in the department is that everybody (other than those Math grad students beyond Part I) must take the qualifier. Feel free to work together on the homework, BUT you MUST turn in your own write-up! Plagiarism is entirely unacceptable. I am generally a generous grader, but I have no patience for plagiarism and will give a 0 for the first assignment/exam on which I spot it, followed by an F for the course for a second offense. Grading: Each homework problem will have the same value (10 points), regardless of difficulty. The homework will be worth 50% of your course grade. The midterm and final will each be worth 25%. Feedback: I am always happy to hear it, even if it is negative. I am happy to adapt my teaching style a bit if it will make the course work better for you. Final Note: You should know that I have insulin-dependent diabetes and may therefore need to sit down and take it easy occasionally. There is also the very slight risk that I could have very low blood sugar at some point, causing me to pass out. If that happens (the probability of this is very low), I will need somebody to call 911. Please don’t worry: I haven’t passed out yet and don’t intend to! Even if I do pass out, I am not in any significant danger. (Tentative!!!) Schedule Date M 8/20 W 8/22 F 8/24 M 8/27 W 8/29 F 8/31 M 9/3 W 9/5 F 9/7 M 9/10 W 9/12 F 9/14 M 9/17 W 9/19 F 9/21 M 9/24 W 9/26 F 9/28 M 10/1 W 10/3 F 10/5 M 10/8 W 10/10 F 10/12 M 10/15 W 10/17 F 10/19 M 10/22 W 10/24 F 10/26 M 10/29 W 10/31 F 11/2 M 11/5 W 11/7 F 11/9 M 11/12 W 11/14 F 11/16 M 11/19 W 11/21 F 11/23 M 11/26 W 11/28 F 11/30 M 12/3 W 12/5 F 12/7 H 12/13 Topic syllabus, introduction to LA vector spaces subspaces, direct sums linear equations, span linear combinations, linear (in)dependence linear (in)dependence No class – Labor Day! bases, dimension linear transformations (LTs), null space, range (same) matrix of an LT LT composition, matrix multiplication invertibility (same) change of bases duality (same) Gaussian elimination rank, inverses (same) linear solving, quickly transpose, projections, similarity determinants (same) properties and Cramer’s Rule multilinear functions eigenvalues, eigenvectors (same) + diagonalizability (same) invariant subspace, Cayley-Hamilton generalized eigenvectors inner products, norms, and Halloween! (same)&Gram-Schmidt (orthogonal complements, etc.) (same) adjoints normal, self-adjoint operators orthogonal operators projections, spectral theorem SVD No class - Fall Break! No class - Fall Break! No class - Fall Break! QR, Schur (same) Jordan canonical form normed linear spaces (same) Review for Final Exam FINAL EXAM, 7:30–9:30 a.m. (yuck) Sections (FIS, unless otherwise noted) 1.1 1.2 1.3 1.4 1.4, 1.5 1.5 1.6, Lax pp. 4–7 2.1 2.1 2.2 2.3 2.4 2.4 2.5 2.6, Lax pp. 8–13 2.6, Lax pp. 8–13 3.1 3.2 3.2 3.3,3.4 Lax pp. 21–24 4.1,4.2 4.1,.42 4.3,4.4 4.5 5.1 5.2 5.2 5.4 Lax pp. 52–56 (maybe 57–61) 6.1 6.2 6.2 6.3 6.4 6.5 6.6 6.7, Trefethen Horn & Johnson or Trefethen (same) 7.1,7.2 Ch. 14 of Lax (same)