# 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 slider-bars 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 x-coord is plotted negated in the right-side plot!).
• History of Gram-Schmidt orthogonalization process (slides from Steven Leon et al).

## Prior exams

Our Midterm 1 (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.