Math 4242, Fall 2016: Linear Algebra with …

1 Math 4242, Fall 2016 , Grinberg: SyllabusSeptember 21, 2016 Math 4242, Fall 2016 : Linear Algebra with applications (4 credits) Syllabus Darij Grinberg, VinH update: September 21, 2016 Time & PlaceSection 070: MW 14:30 15:45 [Lind Hall 302]Section 080: MW 17:00 18:15 [Ford Hall B10]Homework will usually be due on Wednesday at 23:00 (by email) or earlier inclass (you choose).Textsrequired:I will write lecture notes accompanying the classes: ~dgrinber/4242 notes will contain at least the (examinable) mathematical material (but prob-ably no applications ). Apart from these notes, there will be no required , it seems that the lecture notes are lagging behind class (I am having lesstime than I hoped to have) and might end up incomplete at the end. I am thusaiming for a mixture of my own notes and references to others freely-avaliablenotes (mostly Lankham/Nachtergaele/Schilling).

2 Recommended: P. Olver & C. Shakiban,Applied Linear Algebra , Prentice Hall, might be the best place to learn about the applications . Jim Hefferon, Linear Algebra , 2016 . (Scroll down to The next edition )Free text which does many things very well. The main drawback is that it lacksthe theory of bilinear forms. Isaiah Lankham, Bruno Nachtergaele, Anne Schilling, Linear Algebra As anIntroduction to Abstract Mathematics, 2016 . (Download ~anne/linear_ )An introductory text that appears to do the abstract side (vector spaces, linearmaps) early on and in some detail. Its treatment of determinants is also exemplary. Sergei Treil, Linear Algebra Done Wrong, 2015. (Download ~treil/papers/ )Another free text focussing on the more analytic side. This one requires somemore mathematical maturity from the 4242, Fall 2016 , Grinberg: SyllabusSeptember 21, 2016 These are all fairly new sources, and some might be currently under revi-sion.

3 For any unclarities with and questions about these texts, consult or the authors (or both).Office Hours (these have changed!)Tuesday 13:00 16:00, in my office (Vincent Hall 203B).Thursday 10:00 13:00, in my office (Vincent Hall 203B).ContactAll material regarding the course (including homeworks) can be found on ~dgrinber/4242/. Best way to reach meis email (preliminary)This is still preliminary, although a little bit more informed than what I hadat the onset of this term. Topics inside parentheses are the most likely to besacrificed if I run out of time. Butthe midterm dates are are in Olver/Shakiban, although (as I said) the book is not actuallyrequired and will not always be SepQ,R,C,Q, matrix SepInverses, triangular matrices, Linear SepGauss, determinants, a little bit of Linear , ( )26 SepVector spaces, dimension, kernel, OctMidterm I10 OctThe four subspaces, bilinear , OctCholesky, quadratic optimization, least OctOrthogonal bases and matrices, Oct(Orthogonal polynomials and projections) NovMidterm II14 NovLinear , NovEigenvalues, , NovSymmetric matrices, (singular values), Jordan , , Dec( Linear iteration, Markov chains, iterative solvers, QR) , DecMidterm IIIW orkload and gradingThe grade will be computed based on three midterms (totalling to 70% of thefinal grade)

4 And between 9 and 12 homework sets (totalling to 30% of the finalgrade, but the two lowest scores will be dropped).Collaboration on homework is allowed, as long as:2 Math 4242, Fall 2016 , Grinberg: SyllabusSeptember 21, 2016 youwriteup the solutions autonomously and in your own words (in par-ticular, this means that you have tounderstandthem), and youlist the names of your collaborators(there will be no penalties forcollaboration, so you don t lose anything doing this!).On the midterms, of course, you have to work alone. You can bring a calcula-tor, recommended books and notes (including your own notes) to the should be submitted either in person during class, or by (Note: dgrinber , not dgrinberg !) Calculators andcomputer Algebra systems may be used, but are not necessary (and you areresponsible for any errors they make, or you make at using them).

5 Exams can be missed in force majeure situations (illness, jury duty, etc.),but you should notify me of these as early as possible. Late homework is notaccepted in any situation; instead, submit whatever you have done and keep inmind that the 2 lowest pset scores will be also the following university policies.