Last one. This is the final in our sequence of WitCHes on the *Logic and Proof* chapter of *VicMaths*, Nelson’s Specialist Mathematics Year 12 text; the previous WitCHes are here and here and here and here (and a PoSSW here). This WitCH is on the final section, *Proof by mathematical induction*. The worked examples are all similar in form to that given below. The exercises seem ok except for one, which is almost almost good, but which definitely isn’t good (and for which no solution is provided).

# Tag: proof

## New Cur 29: Negative Definite

We’ve already written about the lack of proof in the Australian curriculum. The problem is much more fundamental than that, however: there is a lack of clear mathematical constructs to even prove things about.

Continue reading “New Cur 29: Negative Definite”

## Witch 111: Positively Contra

Almost there. This is a continuation of the previous WitCHes, here and here and here, on the *Logic and Proof* chapter of *VicMaths*, Nelson’s Specialist Mathematics Year 12 text. It is the penultimate section, *Proof by contrapositive and contradiction*. Most of the worked examples are OK (including Example 18, a correct and reasonably well-written proof “by contrapositive” that if n^{2} is divisible by 3 then n is divisible by 3). But, there are issues, notably in the exercises.

## Witch 110: Misdirection

## Witch 109: Bad Language

This is a continuation of a previous WitCH (and PoSWW) on the *Logic and Proof* chapter of *VicMaths*, Nelson’s Specialist Mathematics Year 12 text. The previous WitCH comprised the first part of Section 3.1, titled *Conjectures*, together with some associated exercises. The remainder of 3.1 covered conjectures proper, including examples and counterexamples and the like:

Yes …

On to 3.2, titled *The Language of Proof*. Below are the, um, highlights from this section. We’ve restrained ourselves and not included associated exercises.

## Witch 107: Infer a Pounding

This has a lot in it: it’s more of a coven than a WitCH. We couldn’t see what else to do.

As with our recent PoSWW, this WitCH comes from the Logic and Proof chapter of *VicMaths*, Nelson’s Specialist Mathematics Year 12 text. This is a new VCE topic, for which the summary from VCAA’s study design (Word, idiots) is,

This summary is also given as the prompt of Nelson’s chapter. Then, the extended excerpt here is Nelson’s introduction to the chapter, together with a few of the associated exercises + answers. (The textbook then continues with its coverage of “conjecture” and so forth.)

Readers who lose sight of land may wish to refer to a solid introduction to argument to get their bearings.

## PoSWW 39: A One-Sided Triangle

As for our most recent WitCH, this one comes from *VicMaths*, Nelson’s Specialist Mathematics Year 12 text. It is an exercise and solution from the Logic and Proof chapter (covering a new VCE topic). Continue reading “PoSWW 39: A One-Sided Triangle”

## New Cur 27: The Proof Is in the Plodding

A month or so ago, we posted on Euclid et al, asking about the proper role of proof in a mathematics curriculum. The question and subsequent discussion was purely theoretical of course, since proof barely exists in the Australian Curriculum. Here’s the proof. Continue reading “New Cur 27: The Proof Is in the Plodding”

## Witch 99: PseudoPseudoCode

And one more step into Exam 2. To be honest, we couldn’t give a stuff about this garbage topic, other than to note that introducing it into VCE is complete madness. But, clearly some people feel there are specifics to hammer. So, hammer away. (Hammerers may wish to refer to this or this or this or this (Word, idiots), all courtesy of VCAA.)

## Witch 98: Contrapositive Definite

Having finished going through the Specialist Exam 1 sample questions, we started on Exam 2. We didn’t get far: