Welcome to this month’s edition of the Aperiodical Carnival of Mathematics! The Carnival is a monthly roundup of exciting mathematical blog posts. Last month, it was hosted by Kartik at Comfortably Numbered and this month, it is my honour to host it here.
But first, I thought I’d start with something new I learned: 149 is the 35th prime number. Ok, so not that interesting in itself but since 941 is also prime they are known as “emirp”s … i.e. prime spelt backwards. HAHAHAHAHAH!! … just fecking brilliant … I didn’t even know that was a “thing”! Why 149?? … this is the 149th edition of the Carnival of Mathematics:
Anthony Bonato gives advice to students about becoming a mathematician in this blog post “So you want to be a mathematician“. Written from a personal perspective and I particularly liked how the beauty of maths comes through: “Mathematicians have the envious job of creating new patterns from nothingness. We get to see the nuts and bolts of how the universe of patterns works. Make that: the multiverse of every possible universe of patterns. When you make a discovery, there is nothing like it. When you prove a theorem it as if you’ve bypassed all the noise of everyday life and peeked into a locked treasure box.”
In Learning Mathematics from Ants , from Life Through A Mathematician’s Eyes you can read about how observing the nature around us can teach us a lot of things about mathematics. The post talks about 3 researches on how we can learn mathematical concepts and methods from ants and how they behave in specific situations. Fascinating stuff!
I love a blog post about maths that provides a “setting” in terms of personal information and Mathematical Enchantments does it perfectly before introducing the maths in this post about Professor Engels Marvellously Improbably Machines . “When the path from a simple question to a simple answer leads you through swamps of computation, you can accept that some amount of tromping through swamps is unavoidable in math and in life, or you can think harder and try to find a different route. This is a story of someone who thought harder” … all I can say is Professor Engel rocks!!
Now this one blew my mind. In “A fishy function” it starts with a lovely scene and then the maths is introduced and ramps up as you read on … not what I expected from the opening paragraph but wow! Just wow! Comfortably Numbered The student behind this post writes on the “about me” page that “there is treasure everywhere, in even the most mundane places, and it isn’t buried deep. It is yours, as long as you take care to look out for it.” What a beautiful thought!
From the Chronicle of Higher Education there is a blog post called Meet the Math Professor Who’s Fighting Gerrymandering With Geometry .If like me, the word “gerrymandering” is new to you … it’s a practice intended to establish a political advantage for a particular party or group by manipulating district boundaries. This is a fab read about Moon Duchin a Tufts university professor and what struck with me was about how to explain difficult concepts to a lay audience and it is really important to constantly remind ourselves as teachers that “Once you achieve a certain level of expertise, it can be hard to find the difficult spots and the reasoning anymore because they’re so familiar to you.”
This one from Mark Dominus where he writes about meeting Erdos (he’s a hero of mine!) made me chuckle! Not sure how I’d have reacted if I’d been given a seat next to him and certainly not sure about the falling asleep bit.
Lance Fortnow and Bill Gasarch celebrate the 15th anniversary of their maths and computing blog and serves a reminder that I must blog more: “Writing keeps him sane.”
Maths with Belle writes a post called “The Waiting Game” about observing a lesson at a school in Tokyo. As a teacher, it’s fascinating to see other teachers reflect on their practice. Anyone that says they haven’t had to think about getting the correct balance between teaching, showing students how things work and allowing them time to think is a liar!!
Joshua Bowman who blogs at Thales Triangles wrote a post entitled “boxes and fractions” I was reminded of how often we don’t generalise things (maybe just me!) in our maths teaching. And in answer to the question about husband and wife pairings : John and Anne Mason spring to mind instantly!
In this post Alon Amit, on his blog Quora introduces the maths through popular “click-bait” memes. Another great lead into some really fun maths.
As they go, the album cover from Joy Division is iconic. There is no band name, no title just this image. In this blog post from Scientific American the origins of the image is discussed. Jan Christiansen includes some amazing links to recordings too!
The long-awaited Smith Report was published and Cambridge Maths wrote a great summary of both the review and also the government response. / It is a balanced summary (for that I am thankful!!) and finishes with a sobering reminder about teacher recruitment and retention: “What is very clear is that current policies just aren’t working. The government has paid out £620 in teacher bursaries in the last 5 years but there is little evidence that those recruited wouldn’t have gone into maths teaching anyway – and there is NO requirement for a recipient to go into teaching at the end of their course. Perhaps a better use of that money would be to make conditions and CPD better for existing teachers so that we don’t lose even more.”
In this post, Dan McQuillan gathers together lots of examples where patterns that appear to hold don’t continue to hold. Thus, it explains why proofs are necessary. But we should not really need this as motivation to want to provide proofs, as proofs are often beautiful and contribute to our understanding. He finishes with a lovely quote from William Thurston: “what we are doing is finding ways for people to understand and think about mathematics… what they really want is usually not some collection of ‘answers’ – what they want is understanding.”
In another post from Cambridge Maths, this time from Darren Macey (**waves**) who explores the variability of sample size when teaching statistics. I have to be honest, statistics “ain’t my bag” because I think they can be used to support arguments in all the wrong way but this post will prove useful in my teaching! It’s been bookmarked!
Judith Knott introduces us to Powers of the Golden Ratio and by answering the question “what do numbers like 1 + √2 and 2 + √5 have in common that 1 + √5 or 4 + √5 don’t?” Introduces us to Pisot numbers. Fascinating stuff!
On a final note … I’m going to leave you with Shakespeare’s Sonnet 149. It is considered one of the “dark lady” sonnets and given that my name, Melanie is derived from the Greek μελανία (melania), “blackness” and that comes from μέλας (melas), meaning “dark” as I was growing up my Mam used to call me her “dark lady” … the sonnet itself is a conflict between reason and infatuation which is how I sometimes feel about Maths. That’s a little deep … I know!! … Forgive me … Normal “taking the piss” service will resume shortly.
I’m also gonna add that if you’re looking for UK only blog posts in relation to maths teaching do check out the Maths Echo Chamber. If you write a maths blog that doesn’t get reblogged then please do contact me ([email protected]) or tweet OldAndrewUK and ask him to add you to the list! (he’ll hate me for doing that!)