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).
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 n2 is divisible by 3 then n is divisible by 3). But, there are issues, notably in the exercises.
This is a continuation of the previous WitCHes, here and here, on the Logic and Proof chapter of VicMaths, Nelson’s Specialist Mathematics Year 12 text. Again, we’ve stuck to the highlights, and we’ve resisted the temptation to include some (pretty weird) exercises.
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:
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.
This one, which has been discussed a bit here, comes from the 2023 NHT Methods Exam 2. It is a little strange. There are aspects of the question we like, or at least there are some interesting ideas underlying the question. Nonetheless there is no shortage of crap, and so here we are.
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.
We’re snowed, and we have a couple posts in the works that simply won’t behave. So, we’ll just keep the ball rolling with a WitCH, and have you commenters do the work for now. The following is the introduction to planes (a new VCE topic) in VicMaths, Nelson’s Specialist Mathematics Year 12 text.
It’s hard to be believe we haven’t already done this one, since it’s been irritating us for years. But in any case it really irritated us again yesterday during a tute, and so here we are.
The following introduction and example, chosen largely but not entirely at random, is from Cambridge’s Specialist Mathematics 3 & 4. Continue reading “WitCH 105: Flippin’ Ridiculous”