Intersections by Anila Quayyum Agha.
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Why do $0!$ and $a^0$ equal $1$?
The last two weeks my first year mathematicians and I have covered Taylor series.This means that several times I’ve had the conversation that goes “What’s $0!$?” “It’s $1$.” “Oh, erm, right. Why again?” “Because it works.” This may not be a completely satisfactory answer!
One of my students, Callum Mulligan, tweeted this question.
Why does 0! = 1 better yet, why does a^0 = 1 I must see a proof! #Mission #Unanswered #MathRage
— Callum Mulligan (@Calified) February 1, 2014
Saying “by definition” or “because it makes a bunch of stuff work” won’t cut it. So how to answer this question? To give a somewhat intuitive understanding of why this should be the case to a first year undergraduate. It may be obvious, but it wasn’t immediately obvious to me how to explain this, so I share some thoughts here.
Puzzlebomb – February 2014
Puzzlebomb – Issue 26 – February 2014
The solutions to Issue 26 can be found here:
Puzzlebomb – Issue 26 – February 2014 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.
Open Problems in Mathematics, a new open access journal
Here’s a nice idea: a journal for people to write about open problems, with the aim of inspiring someone to have a go at solving them. Open Problems in Mathematics is a new open-access journal set up by Krzysztof Burdzy and a few others, and it’s online now.
Proof News: Designs exist!
The year in proofs has started with a big result in combinatorics: the existence conjecture for designs. As usual, weightier minds than ours have comprehensively explained the result, so I’ll just give a brief summary of the problem and then some links.
An Approach That Uses Computers a Bit to Ask Questions on Numbers and Stuff in Big School
Here I attempt to write the abstract for my thesis, ‘A Partially-automated Approach to the Assessment of Mathematics in Higher Education’, “using only the ten hundred words people use the most often“.
Carnival of Mathematics #106 – December 2013
Happy New Year! And welcome to the first Carnival of Mathematics of 2014. The Carnival is a monthly roundup of blog posts on or related to mathematics, from all over the internet. Posts are submitted by authors and readers, and collated by the host, whose blog it’s posted on. This month, the Carnival has pulled in here at The Aperiodical, and we’re all ready with our party hats for the celebration of mathematical blogging that implies.