Tips and Tricks for Specialist Mathematics

I just received the following email from Mystery Student, Alex:

Hi marty,

I’m currently taking Spec 3&4 and just had a couple of questions reading this post.

For testing linear dependence, you recommended using a ‘3×3 determinant’. I was just a bit confused, and I’m always looking for areas to improve my knowledge, blah blah blah.

Do you have any other areas that make questions more efficient that are glossed over by VCAA or textbooks?

Thanks a bunch 🙂

I answered Alex briefly on the determinant question, but there are obviously readers much better informed than me about helpful tips and tricks for Specialist. And, in any case, such questions are best replied to by the crowd.

So, please make your suggestions in the comments below, including answering Alex’s specific question.

If the post takes off then I’ll perhaps try to categorise and summarise the suggestions in updates to the post. Also, if people think a companion Methods Tips post is worthwhile I’m happy to do that (although the worth of that is less obvious to me).

Witch 112: Cooking Induction

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).

Continue reading “Witch 112: Cooking Induction”

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 n2 is divisible by 3 then n is divisible by 3). But, there are issues, notably in the exercises.

Continue reading “Witch 111: Positively Contra”

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.

Continue reading “Witch 109: Bad Language”

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.

Continue reading “Witch 107: Infer a Pounding”

Witch 106: Plane Silly

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.

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WitCH 105: Flippin’ Ridiculous

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”