Course orientation #

Syllabus #

File: 140-syllabus.pdf

Notes during orientation #

Regular quizzes
2 exams
Modules has prerecorded lectures
Homework assignments not graded
Can watch videos during Zoom meeting, or prior
Generally 1 quiz per lecture (calendar at end of syllabus), given at the first class after the last day of the lecture
Turn in work as single PDF file

Methods of proof #

File: 140-methods_of_proof.pdf

Recap on methods of proof.

Direct method #

A method we use to prove a statement directly. If we want to prove “if \( p \) then \( q \) ”, we try to prove it directly by assuming if \( p \) is true, then \( q \) is true.

Proof by Counter Example #

A method we use when a general statement is stated, and we want to disprove it. If someone says “all triangles have the same length sides”, all we have to do is come up with a triangle that doesn’t have the same length sides.

Proof by Contradiction #

We assume that the negation of the statement is true, so we assume that \( p \wedge \neg q \) is true through contradiction.

\[\begin{aligned} p \to q \equiv \neg(p \wedge \neg q) \end{aligned}\]

A contradiction is generally a false statement.

Proof by Contrapositive #

The contrapositive of \( p \to q \) is \( \neg q \to \neg p \) .

“If I wake up early, then I go to school.” The contrapositive of this would be “if I don’t go to school, I didn’t wake up early.”

To prove by contrapositive you try to prove \( \neg q \to \neg p \) .