# 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).

## 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. 