Ideas for math/algorithms writing for young people

[Complexity]

I love what I do research on (mostly developing new algorithms for challenging problems, especially some in graph theory).

I've slowly writing up the results of 25 years of research and wanting to find some interesting ways of sharing it.

I've also wanted to write an invitation to math, algorithms, etc. for teens.

A year or so ago, I decided to combine these efforts into a book (possibly a series). I've been working on this off and on, soon to be on for a sustained period.

I've got an abundance of material centering on a few graph theory problems and a variety of my algorithms for my solution. My favorite problem, by far, is the k-clique exists problem (aka 'clique'), for which I've developed six or seven new algorithms. I'm also love the maximum cliques, maximal cliques, graph isomorphism, graph-oriented Ramsey theory, and universal traversal sequences problems, to name a few.

Now, this list of problems sounds opaque and intimidating to most people, but each problem can easily be explained to and understood by a child and much of the thought behind the algorithm develoment can be followed well by a teenager (or so it is my fond hope).

I want to get into the problems and my algorithms for those problems. I also want to show how various algorithms have unfolded through the following of metaphors, how some algorithms are better than others and under what circumstances, how I wandered around, occasionally spending time on dead ends, often finding some new or interesting things, and very occasionally reinventing the wheel.

There are several aspects of creativity, method, abstraction, formality, flow, habits, state of mind, attitude, persistence, and most of all play that I want to explore.

I want to share why I love this stuff, hoping that some readers may be enticed into investigating it and possibly embracing it.

There are several topics that I have in mind, but I'm interested in your answers to some of the following questions. Perhaps I'll find some other ways of expanding this sort of work.

What do you think a teenager would be interested in reading about (for various ages of teenager)?

What would you be interested in reading about? (Most of us haven't grown up that much.)

Do you have any suggestions, comments, encouragements, or cautions with regard to this endeavour?

I wrote many posts here a few years ago related to these problems and they were well received. That experience and the reactions that I received helped to prod me into actually working on this rather than merely thinking about it.

Thank you in advance for your comments, suggestions, and advice.

 

[BigAl]

I love what I do research on (mostly developing new algorithms for challenging problems, especially some in graph theory).

I've slowly writing up the results of 25 years of research and wanting to find some interesting ways of sharing it.

I've also wanted to write an invitation to math, algorithms, etc. for teens.

Maybe this is tangential to your query but an early 60s issue of CACM had a paper that described how to teach school kids old enough to have been taught how to do square roots on paper how a computer works at the machine language level. I paraphrase from memory;

The teacher prepares the "program" to do square roots by iteration on a couple dozen 3x5 cards. Each card has a Cell # (an address) and an instruction .

The accumulator and PC are kept on the blackboard and a student plays the roll of the arithmetic unit and updates the AC and PC as instructed.


The cards are handed out to the students at their desks.

The student with cell #1 reads his card and the person at the blackboard (the "ALU") updates the accumulator and PC as needed. The PC is incremented or replaced (as a result of a goto or an if) and read aloud and the kid with that card # reads his card.

The person at the blackboard does the logic as needed and calls out the next PC number until the halt instruction is executed.
​

"Group Participation Computer Demonstration", CACM, Vol 6#9, Sept 1963. Google in 2009 tells me this 1963 paper is online for those that have an ACM password.

http://portal.acm.org/citation.cfm?id=367647&coll=portal&dl=ACM

 

[Floyt]

I was drawn in (as a tween, to be sure) by the Carrollian whimsy of Hofstadter's Gödel, Escher, Bach - problems of logic and iterative computation embedded in witty conversations. I also liked the "original", Dodgson's series of maths problem short-shorts collected in "A Tangled Tale". If your talents go into the direction of weaving an entertaining story or set-piece around the topic you want to communicate, you might go that way. A time-honoured method

 

[Dancing David]

I think the algorithm for the generation fo squares is really cool, and it makes sense in so many ways, I would start with the easy ones to draw them in:

1²=1
2²=1+3=4
3²=4+5=9
4²=9+7=16

You start with 1 add 3, then 5 then 7, and so on.

 

[Complexity]

Maybe this is tangential to your query but an early 60s issue of CACM had a paper that described how to teach school kids old enough to have been taught how to do square roots on paper how a computer works at the machine language level. I paraphrase from memory;

The teacher prepares the "program" to do square roots by iteration on a couple dozen 3x5 cards. Each card has a Cell # (an address) and an instruction .

The accumulator and PC are kept on the blackboard and a student plays the roll of the arithmetic unit and updates the AC and PC as instructed.


The cards are handed out to the students at their desks.

The student with cell #1 reads his card and the person at the blackboard (the "ALU") updates the accumulator and PC as needed. The PC is incremented or replaced (as a result of a goto or an if) and read aloud and the kid with that card # reads his card.

The person at the blackboard does the logic as needed and calls out the next PC number until the halt instruction is executed.
​

"Group Participation Computer Demonstration", CACM, Vol 6#9, Sept 1963. Google in 2009 tells me this 1963 paper is online for those that have an ACM password.

http://portal.acm.org/citation.cfm?id=367647&coll=portal&dl=ACM

I wish I'd been exposed to that as a kid, and I was a kid when that was written about. It took me a long time to finally 'land' in computer science.

 

[Complexity]

I was drawn in (as a tween, to be sure) by the Carrollian whimsy of Hofstadter's Gödel, Escher, Bach - problems of logic and iterative computation embedded in witty conversations. I also liked the "original", Dodgson's series of maths problem short-shorts collected in "A Tangled Tale". If your talents go into the direction of weaving an entertaining story or set-piece around the topic you want to communicate, you might go that way. A time-honoured method

Oh, I wish! Hofstadter had incredible nerve to attempt it (emulating Carroll), but he also had the skill and talent to pull it off with style.

Finding my voice for this has been one of the harder things I've had to do. Still not sure where it will settle.

 

[Complexity]

I think the algorithm for the generation fo squares is really cool, and it makes sense in so many ways, I would start with the easy ones to draw them in:

1²=1
2²=1+3=4
3²=4+5=9
4²=9+7=16

You start with 1 add 3, then 5 then 7, and so on.

I've spent a lot of time playing with the n-th powers of integers and the differences of n-th powers of integers (curse you, Fermat!).

Found a very cool pair of identities that make me happy.

 

[Dancing David]

Cool!