Math 560: Linear Algebra (Fall 2012)

Prof. Dan Bates, MWF 9-9:50, Engineering E104


Linear algebra is ubiquitous throughout the sciences, engineering, and mathematics. It is not uncommon for the deepest theory and hardest computations (both within mathematics and outside) to boil down to linear algebra. Thus, it is essential that future STEM researchers and educators become well-acquainted with the fundamental ideas and computations of this field.

Math 560 is CSU Math's QE (Qualifying Exam) course in linear algebra. This course will be a thorough introduction to the field, aimed more at theory than at computation. Math 561 (Numerical Linear Algebra) is aimed more at computational aspects of linear algebra and will be offered in the Spring. If you take both courses, you will emerge with a sound understanding of the algebra and geometry underlying linear algebra, along with the technical knowledge of what can (and can't) be accomplished with such computations.

As this is a QE course, there is a fixed list of topics that must be covered. You can find that list on page 8 of this document. I will be focusing primarily on training the Math grad students who need this course as a QE course. However, I welcome advanced undergrads (any field) and non-math grad students, as well. My expectations for non-QE students will be different than those for the QE students, as I'll go over on the first day of class.


BOOK: Although this course often uses Lax, I'm going to try using the 4th edition of Friedberg-Insel-Spence instead. I have heard very good things about the latter, particularly in courses such as ours. Since the set of topics for this course was pulled straight from Lax's table of contents, and given that I am bound to follow that set of topics, I will supplement from Lax or Horn-Johnson as necessary. You do not need purchase either Lax or Horn-Johnson, though it might be handy to locate a copy of one or the other in case you want to read about something not in FIS.

Important docs/links

Our syllabus

There will be homework due most Fridays, from the material covered the previous Wednesday, Friday, and Monday (but not the most recent Wednesday). There will be one take-home midterm, and the qualifying exam (as the final exam).

All students (math or otherwise) who are NOT already qualified in Math MUST take the qualifier. For those currently seeking qualification, this is a no-brainer. For the rest of you, this is necessary in case you later choose to join CSU Math as a grad student. If you have concerns about this, please let me know.


Homework

HW 1 (due Friday, 8/31): 1.1/1cd,2a,3b; 1.2/1 (think about justification, but don't write it), 8, 19 (justify!); 1.3/10, 12, 20, 28 (first proof only, but READ second proof statement; all notation needed for this problem can be found on page 22).

HW 2 (due Friday, 9/7): 1.4/3a,10,13; 1.5/2abc,8b,counterexample to 16 (which is false!), read (but don't write up) 9.

HW 3 (due Friday, 9/14): 1.6/2a, 4, 12, 16, 29a; 2.1/4, 9, 20, 28, read (don't do) both 14 and 40.

HW 4 (due Friday, 9/21): 2.2/2efg, 13, 14; 2.3/11, 12, 16a; 2.4/3, 4.

HW 5 (due Monday, 10/1): 2.4/17 (read 5,10); 2.5/3c, 4, 11, 13 (read 9); 2.6/6, 8 (read 17); 3.1/12 (just write down the algorithm; no formal proof needed); 3.2/2abcd, 3.

HW 6 (due Friday, 10/12): (read 3.2/18,19,21,22); 3.3/2c,3c,9,10; 4.2/4,23; 4.4/5,6; 5.1/3d,4c.

HW 7 (due Monday, 10/29): 5.1/8a (for matrices), 15b; 5.2/2ac, 8, 12 (read 18b and the note after it); 5.4/2de, 4, 12.

HW 8 (due Friday, 11/16): 5.4/19 (read 39,41); 6.1/3,4b,10 (read 24, 25); 6.2/2b,6,12 (read 15a,16a); 6.3/12a; 6.4/6a,7b (read 13); 6.5/17 (read 10,11,31); 6.6/3a (read 5,7).

HW 9 (due Friday, 12/7): 7.1/2c; 7.2/2,3abcd; 7.3/2d.