WitCH 120: Unanalytic Continuation

Ten years ago, Numberphile came out with a now famous/infamous video featuring physicist Tony Padilla, in which Padilla “proves” that 1 + 2 + 3 + … = -1/12. It was quickly followed by a second, “what we really mean” video and some rebuttal notes by Padilla. At the time, Burkard and I (too) softly hammered Numberphile for this, in one of our final Age columns. A few years later, Burkard hammered Numberphile much harder, in an early Mathologer video.* Now, Numberphile has come out with two new videos: The return of -1/12, featuring Berkeley mathematician Tony Feng; and Does -1/12 protect us from infinity, with Padilla.

I have my views, but this a WitCH (thus summarising my views). So it’s your job. The two new videos are below. Go for it.

*) See also my post defending Burkard’s uncollegial hammering of Numberphile, an earlier WitCH on Numberphile (and Too Much Woo), a post on my general dislike of mathematics documentaries and on video as a medium for maths ed, and a video containing my proof that 1 + 2 + 3 (no dots) equals -1/12 (48:45 and 55:00). 

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A Sum of “Complex” Numbers

We really want to get on to other things, but this needs to be done. Below is pretty much a complete cataloging of Nelson‘s use of the adjective “complex” in the five recent WitCHes (here, here, here, here and here). To be clear, there is tons more wrong, and bad, in the selected excerpts in the WitCHes: the proper WitCH updating, currently scheduled for late 2029, will be long and painful. But the use of “complex” warrants particular attention. It reflects VCAA’s complex madness, and we doubt that it is a coincidence. Continue reading “A Sum of “Complex” Numbers”

WitCH 119: Poly Want a Cracker?

Last one. These are excerpts from the final section of Nelson‘s complex numbers chapter. Similar to the previous WitCHes, I’ve tried to not be manipulative material in selecting the material except, of course, in selecting the worst bits: the worked examples not indicated are standard, and in general the working is tedious but ok; a monotonous but essentially correct proof of the conjugate root theorem is included in the text.

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WitCH 118: The Chaos Factor

I was gonna go with The Sot-Weed Factor, but that was too cute a title, even for me.

We’re now getting to the VCAA-related material, which prompted this whole series. The last two sections of Nelson‘s complex numbers chapter are on factors and roots of polynomials. Below are excerpts on factorisation. (For the sake of interpretation, note that: the factor and remainder theorems are stated reasonably clearly, but of course with no hint of a proof; these two theorems are followed by two standard “worked examples”; the working of all the worked examples is painfully earnest and slow, but is close enough to correct.)

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WitCH 116: Polar Bare

This is our second WitCH on Nelson‘s chapter on complex numbers. As with our first WitCH, we have not excluded any definitions or arguments or explanations from the text that would fill apparent (and actual) gaps in the selected material; the rest of the subchapter consists of routine examples and less problematic (but far from unproblematic) exposition. Continue reading “WitCH 116: Polar Bare”

WitCH 115: Not So Complex

Last year we took a multiwhack at VICmaths, Nelson’s Year 12 Specialist Mathematics textbook, specifically at Nelsons chapter on logic and proof: see here, here, here, here, here and here. This post is the beginning of a second multiwhack, this time at Nelsons chapter on complex numbers. Continue reading “WitCH 115: Not So Complex”

Witch 113: Smoothing Over the Cracks

This one is a combo WitCH. The main concern is a multiple choice question from last week’s Methods Exam 2. The question may not be an “error” in the newspaper sense, but it is bad. To appreciate some (but far from all) of its badness, however, we need to see VCAA’s solution. We won’t likely see that solution, however however, for months, if ever; transparency is not VCAA’s strong suit (Section 7).

To deal with this, we’ve teamed up last week’s MCQ with a similar MCQ from the 2021 Exam 2, together with VCAA’s solution to that earlier question from the exam report. Last week’s question appears first. Continue reading “Witch 113: Smoothing Over the Cracks”

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).

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