Recursion & Induction
Self-reference, recurrence relations, nested structure.
This is the house that Jack built
This is the house that Jack built.
This is the malt that lay in the house that Jack built.
This is the rat that ate the malt
That lay in the house that Jack built.
This is the cat
That killed the rat that ate the malt That lay in the house that Jack built. This is the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the maiden all forlorn That milked the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the man all tattered and torn That kissed the maiden all forlorn That milked the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the priest all shaven and shorn That married the man all tattered and torn That kissed the maiden all forlorn That milked the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the cock that crowed in the morn That woke the priest all shaven and shorn That married the man all tattered and torn That kissed the maiden all forlorn That milked the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the farmer sowing his corn That kept the cock that crowed in the morn That woke the priest all shaven and shorn That married the man all tattered and torn That kissed the maiden all forlorn That milked the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built. This is the horse and the hound and the horn That belonged to the farmer sowing his corn That kept the cock that crowed in the morn That woke the priest all shaven and shorn That married the man all tattered and torn That kissed the maiden all forlorn That milked the cow with the crumpled horn That tossed the dog that worried the cat That killed the rat that ate the malt That lay in the house that Jack built.
There Was an Old Lady Who Swallowed a Fly
There was an old lady who swallowed a fly. I don’t know why she swallowed a fly - perhaps she’ll die!
There was an old lady who swallowed a spider, That wriggled and wiggled and tickled inside her; She swallowed the spider to catch the fly; I don’t know why she swallowed a fly - perhaps she’ll die!
There was an old lady who swallowed a bird; How absurd to swallow a bird! She swallowed the bird to catch the spider…
There was an old lady who swallowed a cat; Fancy that to swallow a cat! She swallowed the cat to catch the bird…
There was an old lady who swallowed a dog; What a hog, to swallow a dog! She swallowed the dog to catch the cat…
There was an old lady who swallowed a cow; I don’t know how she swallowed a cow! She swallowed the cow to catch the dog…
There was an old lady who swallowed a horse… She’s dead, of course!
Old MacDonald Had a Farm
Old MacDonald had a farm, E-I-E-I-O, And on his farm he had a cow, E-I-E-I-O, With a moo moo here and a moo moo there, Here a moo, there a moo, everywhere a moo moo, Old MacDonald had a farm, E-I-E-I-O.
(…and a pig, a duck, a horse, a sheep, each new animal added to all the ones before…)
Five Little Ducks
Five little ducks went out one day, Over the hills and far away. Mother duck said, “Quack, quack, quack, quack.” But only four little ducks came back.
(…four, three, two, one… down to none, and then…)
Mother duck said, “Quack, quack, quack, quack.” And all of her five little ducks came back.
There Was a Crooked Man
There was a crooked man, and he walked a crooked mile, He found a crooked sixpence against a crooked stile; He bought a crooked cat, which caught a crooked mouse, And they all lived together in a little crooked house.
Series, Sequences & Enumeration
Functions on the naturals, sums, finite domains.
As I Was Going to St Ives
As I was going to St. Ives, I met a man with seven wives, Each wife had seven sacks, Each sack had seven cats, Each cat had seven kits: Kits, cats, sacks, and wives, How many were there going to St. Ives?
One, two buckle my shoe
One, two, buckle my shoe; Three, four, knock at the door; Five, six, pick up sticks; Seven, eight, lay them straight; Nine, ten, a big fat hen; Eleven, twelve, dig and delve; Thirteen, fourteen, maids a-courting; Fifteen, sixteen, maids in the kitchen; Seventeen, eighteen, maids in waiting; Nineteen, twenty, my plate’s empty.
Continuous Dynamics & Calculus
Position and time, derivatives, kinematics, ODEs.
Itsy bitsy spider
The itsy bitsy spider climbed up the waterspout.
Down came the rain
And washed the spider out.
Out came the sun
And dried up all the rain
And the itsy bitsy spider climbed up the spout again.
Mary had a Little Lamb
Mary had a little lamb,
Little lamb, little lamb.
Mary had a little lamb,
Its fleece was white as snow.
And everywhere that Mary went,
Mary went, Mary went,
Everywhere that Mary went,
The lamb was sure to go.
It followed her to school one day,
School one day, school one day.
It followed her to school one day,
Which was against the rules.
It made the children laugh and play,
Laugh and play, laugh and play.
It made the children laugh and play
To see a lamb at school.
“Why does the lamb love Mary so?
Mary so, Mary so?
Why does the lamb love Mary so?”
The eager children cry.
“Why, Mary loves the lamb, you know,
Lamb, you know, lamb, you know,
Mary loves the lamb, you know,“
The teacher did reply.
Rock-a-bye-baby
Rock a bye baby on the tree top, When the wind blows the cradle will rock, When the bough breaks the cradle will fall, And down will come baby, cradle and all.
Jack jumped over the candlestick
Jack be nimble,
Jack be quick,
Jack jump over the candlestick.
Hey Diddle Diddle
Hey diddle diddle,
The cat and the fiddle,
The cow jumped over the moon;
The little dog laughed
To see such sport,
And the dish ran away with the spoon.
Row, Row, Row Your Boat
Row, row, row your boat, Life is but a dream. Merrily, merrily, merrily, merrily, Gently down the stream.
It’s Raining, It’s Pouring
It’s raining, it’s pouring,
The old man is snoring,
He went to bed and bumped his head,
And couldn’t get up in the morning.
Conservation, Transfer & State Machines
Conserved quantities, transitions between states, Markov chains.
The Queen of Hearts
The Queen of Hearts She made some tarts, All on a summer’s day. The Knave of Hearts He stole those tarts. And he took them clean away. The King of Hearts Called for the tarts. And beat the knave full sore. The Knave of Hearts Brought back the tarts. And vowed he’d steal no more.
Baa baa black sheep
Baa, baa, black sheep,
Have you any wool?
Yes, sir, yes, sir,
Three bags full;
One for the master,
And one for the dame,
And one for the little boy
Who lives down the lane.
Rain Rain Go away, come again
Rain, rain, go away,
Come again another day.
Set Theory & Cardinality
Membership, partition, counting elements, the topology of a set.
Little Bo Peep
Little Bo-Peep has lost her sheep And doesn’t know where to find them. Leave them alone and they’ll come home, Bringing their tails behind them.
Three blind mice
Three blind mice, three blind mice, See how they run! They all run after the farmer’s wife, And she cut off their tails with a carving knife, Did you ever see such a thing in your life As three blind mice!
Little Miss Muffet
Little Miss Muffet Sat on a tuffet, Eating her curds and whey; There came a big spider, Who sat down beside her And frightened Miss Muffet away.
Logic, Predicates & Irreversibility
Boolean classification, the excluded middle, non-invertible maps.
The Grand Old Duke of York
The grand old Duke of York, He had ten thousand men; He marched them up to the top of the hill, And he marched them down again. And when they were up, they were up, And when they were down, they were down, And when they were only halfway up, They were neither up nor down.
Humpty Dumpty
Humpty Dumpty sat on a wall, Humpty Dumpty had a great fall. All the king’s horses and all the king’s men Couldn’t put Humpty together again.
Cyclic, Modular & Periodic Structure
Cyclic groups, clocks, rounds, rotation, periodicity.
Hickory Dickory Dock
Hickory dickory dock, The mouse ran up the clock. The clock struck one, The mouse ran down, Hickory dickory dock.
Solomon Grundy
Solomon Grundy, Born on a Monday, Christened on Tuesday, Married on Wednesday, Took ill on Thursday, Grew worse on Friday, Died on Saturday, Buried on Sunday, That was the end Of Solomon Grundy.
Monday’s Child
Monday’s child is fair of face, Tuesday’s child is full of grace, Wednesday’s child is full of woe, Thursday’s child has far to go, Friday’s child is loving and giving, Saturday’s child works hard for a living, And the child that is born on the Sabbath day Is bonny and blithe, and good and gay.