123.123.123

More Proofs Stuff

Investigations

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.

Marking Time

Spotting and correcting common errors

components politician triangles queen of hearts check geometric induction

Building Works

Finding and constructing proofs

constructing

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.

this way up

Helpful stuff

truth advice

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

Proofs Examples

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.

 

Direct   Contrapositive   Contradiction

 

Induction   Biconditional   Miscellaneous

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.

diy Return to main Proofs page

Contrapositive

Here are some of the ways we tried to convince students that the contrapositive is a kosher method - mostly without success.

cards contrap cow contrapositive vs contradiction contrap via tables

Email me if you need the answers. (Go to Contact page.)

Click graphics to enlarge

Shirleen Stibbe's OU stuff

Health warning:  This is not official Open University material.  All  errors, misconceptions and misleading statements are my very own