|C o o r d i n a t e s (2,6,0)|
Math 260: Linear Algebra
Instructor: Joe Erickson (email@example.com)
Textbook: Introduction to Linear Algebra, 2nd Ed., by Serge Lang
Term: Summer 2013
June 10 - In preparation for Exam #1 pay close heed not just to the homework exercises, but also the examples I have in my Notes. It doesn't hurt to look over the relevant parts of the first exam from last summer, too.
June 8 - If you go to http://joshua.smcvt.edu/linearalgebra and scroll down a little, you will find a free linear algebra textbook by Jim Hefferon along with its accompanying solution manual. You may find it to be a valuable reference in addition to our textbook by Lang and my own notes. Also I plan to assign exercises from the Hefferon book whenever I think Lang needs supplementing. Hefferon's solution manual is said to even include steps to proofs and such, which Lang does not do.
June 6 - Exercise #4 in section 2.3 of the textbook could be written as follows: "Show that if x_1 and x_2 are solutions to the nonhomogeneous system of equations Ax=b, then there exists a solution y to the corresponding homogeneous system Ax=0 such that x_2=x_1+y. Also show that if x_1 is a solution to Ax=b and x_2 is a solution to Ax=0, then x_1+x_2 is a solution to Ax=b." To see a solution to the second part, see the first (and so far only) example in section 2.6 of the Notes.
June 6 - The policy of dropping the lowest of the first three exam scores I don't implement if it actually results in someone getting a worse grade. It is possible! For instance if someone gets 80%, 90%, 90% and 30% on Exams 1, 2, 3, and 4, respectively, dropping the lowest of the first three exams results in an average of (90+90+30)/3 = 52.5% (an "F"). Keeping all the scores results in an average of (80+90+90+30)/4 = 72.5% (a "C"). But if the drop policy is implemented, as it usually is, then each exam not dropped is worth a third of the grade.
June 4 - I've updated the Assignment Sheet to include three exercises in section 2.5 of the Notes (answers are at bottom of page).
June 3 - An example of Gaussian elimination is now in section 2.5 of the Notes.
June 3 - I've done a little reorganizing of the last couple sections of Chapter 2 in the Notes, along with a corresponding shuffling of exercises in the Assignment Sheet. (Same exercises, slightly different order.) I figure no one is likely to be out as far as section 2.5 quite yet, so I seized the chance. At this point the only changes to the Assignment Sheet that I foresee making is to put in exercises that will be included in the Notes themselves. The book doesn't really have any problems involving solving nonhomogeneous systems of equations, oddly, so I'll add exercises in section 2.5 of the Notes. By the way many exercises appear on last summer's exams (in Resources - link below), so they're fully worked out in the keys to those exams.
June 1 - In Chapter 1 of the Notes I have added a few examples: one example in section 1.4 and two in section 1.5. Some proofs were added to Chapter 2, along with some streamlining of notation.
May 31 - Probably the best approach is to read a given chapter in the Lang text first, and then read the corresponding chapter in the Notes. The Notes are there to supplement the text, not replace it. For each section in Lang there is an exercise set, and if you look at the page number where the exercise set begins in Lang, you can find the assignment for that section in the Assignment Sheet by matching page numbers. Section 1.1 in the Notes, about rings and fields, has no analogue in Lang and there is no assignment. But later in the course we will be getting into vector spaces, and it doesn't make sense to talk vector spaces without knowing what a field is.
May 28 - I organize the sections on the Assignment Sheet (link below) in accordance with the Notes (link also below), but most of the exercises on the Assignment Sheet are drawn from the textbook by Lang. So, for a given section of Notes there is usually a corresponding assignment in Lang you should do, although sometimes there are exercises in the Notes themselves. As I said before the Notes only got their start about one year ago, so many sections are still blank. Over the past week I've created another five pages of notes (making the total 130 pages), and made many improvements and revisions. I plan to continue this process as time allows, with the goal of creating at least another 30 pages over the next 12 weeks. I do have many other classes to attend to, however, so time is limited.
May 27 - Orientation for Section E31: Start by reading the syllabus (link below). Then take a look-see at the assignment sheet (link also below). The first exam will be available to take at the Newtown testing center from June 12 to June 18 and will cover sections 1.2-1.5 and 2.1-2.6, so the assignments for those sections should be done by then. That should give you some idea of the pacing. I'll give 2 hours to complete Exam 1, and the testing center will insist on verifying your identification before allowing you to take the exam. If you want to take the exam at the lower or upper county campuses you'll have to let me know well ahead of time, because it'll take at least an extra day for things to get to those places. As for the remaining exams, see the syllabus for dates and sections. The dates of availability for the exams are fairly firm, but check this website for possible changes before heading anywhere to take the exam. Also take note: the lower and upper county testing centers have more restrictive hours than the Newtown testing center! See for yourself: Lower/Upper County Hours & Newtown Hours. Know the hours a testing center is open before you go, because they may change. Exams are paper-and-pencil affairs (no computers). They are printed on a single sheet of paper and are completed with a blue book that the testing center supplies.
May 19 - I should say something about the textbook. Its virtue is that it's cheap, slim, and has almost exactly the right content—and in nearly the right order—for a course like ours. Also it has answers to nearly all the exercises (both even and odd numbered) in the back. Make sure it isn't missing any pages! Also beware: The author, Serge Lang, wrote two different linear algebra books: Introduction to Linear Algebra, in its 2nd edition and the one you want, and Linear Algebra, in its 3rd edition and NOT the one you want! The latter book is somewhat more advanced. I suppose the main disadvantage of the textbook is that the publisher offers no online content to accompany it. But there is this website of my own making, which contains notes (link below) also of my own making which got their start just barely a year ago. The notes are still under construction (currently about 125 pages total), and they are intended to supplement the textbook—not replace it. Old exams along with detailed keys are also to be found here. I'll say more later.
April 6 - The syllabus for the 12-week Summer 2013 distance-learning section of the course (section E31) is now available below!
Math 260 Links