V63.0140-3 Linear Algebra

Instructor: Alex Barnett
email: `barnett at cims.nyu.edu`
tel: 212-998-3296, rm 1122 Warren Weaver Hall (WWH)
Office hours: 4-5pm Tuesdays, 2-3pm Wednesdays.

Grading:

Grade boundaries will be 88 +-2 % for A/B boundary, 78 +-2 % for B/C boundary, and 60 +-5 % for C/D boundary. (D/F will be finalized later). Remember your scoring system is 30% HW, 20% best 3 of 4 quizzes, 20% midterm, and 30% final.

Exams:

General notes on exam and study technique (geared mainly towards final exams).
Quiz 1: Tues Sept 16, Solutions.
Quiz 2: Tues Sept 30, Solutions.
Midterm: Thurs Oct 16 (use this to practise with, and even answers). No equation sheets allowed. Solutions available as handout.
Quiz 3: Tues Nov 4, Solutions.
Quiz 4: Tues Nov 25 Solutions.
Final: Thurs Dec 18, 10-11:50 am, Meyer 122. A single-sided letter paper equation sheet will be allowed (you have to make one yourself!) Use this to practise with (and answers).

Handouts, corrections, and interesting links:

Complete set of WORKSHEETS used in class, in the compact DjVu format (download plugin).
Worked solution to the chemical equation worksheet (part B) from Lecture 4, date 9/11/03.
Online resources for the David Lay book, including transparencies written by a different professor (Lyle Cochran). These can be much more concise than the book.
MIT OpenCourseWare: Linear Algebra has useful practise questions at about our level (but we haven't done 'spaces' yet...).
Essay on teaching by Gilbert Strang, author of one of the best linear algebra books. (He also is one of the inventors of wavelets).
Beautiful interactive linear transformations applets (by David Austin), showing the effect of T(x)=Ax where A is a 2x2 matrix:
- Transformation of a single vector (red vector x can be dragged, the result Ax is shown in grey, the matrix A sits at the top of the screen with its entries given by slider-bars i.e. number lines).
- Transformation of the unit square.
- Transformation of unit grid lines (showing span of the columns of A).
A fixed linear transformation shown with 3d applet. This is the effect of T(x)=Ax where A is 3x2, as discussed in Lecture of 9/30/03.
Vector calculator applet can find linear dependence relations for an arbitrary number of vectors. It can display in 2d and 3d too! Matrix multiplier applet can multiply matrices and matrix calculator applet can invert them and do other operations. You can use to check (but not do) your HW!
Brief history of linear algebra (minus the Chinese in 250 BC).

Homeworks:

Information about our homework grader for this course, Willy Chang.
HW1 due Thurs Sept 11.
HW2 due Thurs Sept 18.
HW3 due Thurs Sept 25 (Note 1.9.12 should instead be 1.9.21).
HW4 due Thurs Oct 2.
HW5 due Thurs Oct 9 (Note 2.3.47 should instead be 2.3.27, and 2.3.10 already done in HW4!).
HW6 due Thurs Oct 23 (Note: last four problems, ie ones from 4.2, will be postponed to HW7).
HW7 due Thurs Oct 30.
HW8 due Thurs Nov 6.
HW9 due Thurs Nov 13 (postpone the last 2 to HW10).
HW10 due Thurs Nov 20 (postpone 6.1.19 to HW11).
HW11 due Thurs Dec 4 (ignore the last three, that is, Section 6.7. We just don't have time for it!).

PS You will be pleased to know my research in physics and medical imaging relies heavily on linear algebra. I am not special - almost any practicing scientist or mathematician would say the same. So... keep studying - it's useful!