Includes the infamous wrong direct proof, and reminders about the detail required in writing a proof
A question needing L'Hopital's rule, used as a reminder that all criteria need to be checked before using a theorem
Another 'wrong direct' example, and a couple of geometric proofs to practise rigour.
Errors in the formation of an inductive argument.
Two different formats for these breakout sessions:
1) Give the students the chance to be as mean as their tutors in marking wrong answers.
2) Get them to find and prove a result for themselves - which they don't enjoy as much.
Spotting and correcting common errors
Finding and constructing proofs
Triangles: Find a formula for the number of triangles constructed and prove it
Can you believe it? Assess the truth values of statements by a politician.
Construct a proof for a given theorem. (Tutor led)
Sentence first, verdict afterwords: Draw a conclusion from a set of related statements.
Components: Translate several snippets into formal logic notation; use them to prove a given proposition.
General advice on finding and presenting proofs, and a summary of standard strategies.
Summary of logic and proof structures, truth tables and logical equivalences.
Click graphics to view/download
Click graphics to download
These are the (corrected) Tutor's proofs we handed out after we'd discussed the common errors we highlighted in the original presentation. I've grouped them by the method of proof.
Click method to view/download
And you can download a selection of the questions we inflicted on the students in the DIY sessions, by clicking on the hard hat.
Here are some of the ways we tried to convince students that the contrapositive is a kosher method - mostly without success.
Email me if you need the answers. (Go to Contact page.)
Click graphics to enlarge
Health warning: This is not official Open University material. All errors, misconceptions and misleading statements are my very own