Math 22 Fall 2016: RESOURCES
Theory
- Basics of proofs:
-
Ferry
on several proof methods but not proof by example
(on p.2 the "minus sign with downtick on it's right end" symbol means
logical negation, ie "not the statement")
- Orellana
on good writing and various proof methods
- Scott LaLonde's notes on
contrapositive,
contradiction and induction
-
Introductions to proofs that go way beyond this course but could be useful
as long as you don't let them intimidate you:
Vandervelde,
Hutchins.
-
Applets showing the geometric 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).
- Eigenvalue and eigenvector applets for 2x2 matrices:
Geogebra,
UCLA,
MIT OCW (note the x-coord is plotted negated in the right-side plot!).
- History of Gram-Schmidt orthogonalization process (slides from Steven Leon et al).
Applications
Quizzes
Prior exams
Please keep in mind that the exam topics in the midterms and final may vary.
Ask your instructor if you're unsure whether an old exam question is relevant.
