Math 22 Summer 2017: 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 sliderbars i.e.
number lines).

Transformation of the
unit
square.

Transformation of
unit grid
lines (showing span of
the columns of A).

Review of theory results for abstract vector spaces.

Eigenvalue and eigenvector applets for 2x2 matrices:
Geogebra,
UCLA,
MIT OCW
(note the xcoord is plotted negated in the rightside plot!).

History of
GramSchmidt orthogonalization process
(slides from Steven Leon et al).
Applications
Quizzes
Prior exams
Our Midterm 1 (solutions with grading rubric).
Our Midterm2 (solutions with grading rubric).
Old 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.
See bottom of this page.