Cody, Benjamin, Sean, Cameron, Aaron, and Jordan each had a different amount of money. They all went to the mall and brought their money. At the mall, each person spent a fraction of the money they started out with. They started out with: $72, $24, $66, $18, $48, and $60. At the mall one spent 1/3 of their money, one spent 1/3 of their money, one spent 5/6 of their money, one spent 1/6 of their money, one spent 2/3 of their money, and one spent 1/2 of their money.

How much money did each person spend at the mall?

How much money does each person have left?

1. Benjamin spent more than 1/6 of his money.

2. Cameron spent less than 5/6 of his money.

3. Cody did not spend 1/2 of his money.

4. Jordan spent less than 1/2 of his money.

5. Jordan spent $24.

6. Sean has $15 left after spending money at the mall.

7. Cody spent $33.

8. The person that started out with $24, has $8 left after shopping.

9. Cameron has $40 left after spending money at the mall.

10. Cameron did not spend 2/3 of his money.

11. The person that started out with $60, has $40 left after shopping.

12. Benjamin did not spend 1/6 of his money.

13. Aaron did not spend 1/3 of his money.

14. Benjamin has $8 left after spending money at the mall.

What would life be without mathematics? As Marlon Brando put it… 

This gif animation illustrates the most popular of the cyclic octonion multiplication tables #math

I’m reading Introduction to Octonion algebra

(1) Can Math Be Beautiful?

What is it about Euclid’s infinite primes that rocks Simon Singh’s world? What makes math different from the rest of the sciences? Listen as he and mathematician Marcus du Sautoy explain why, to them, math is a language of beauty, creativity, and immortality—for its unshakable proofs allow you to truly stand solidly on the shoulders of giants.

http://worldsciencefestival.com/videos/can_math_be_beautiful

Simon Singh: “When you heard that proof [Euclid’s proof for the infinity of prime numbers] for the first time, did it not rock your world? … It’s not about how clever Euclid was — It’s about how beautiful it is that in four lines of argument you can grapple with infinity.”

Euclid, in few lines, showed that the there is infinitely many primes. The beauty and elegance resides in its simplicity.

In mathematics, we use infinity quite often. It is very useful in Calculus, Real Analysis, http://en.wikipedia.org/wiki/Infinity#Mathematics

There’s also Mathematics without infinity, which I’m not familiar with.

**Leibniz, one of the co-inventors of infinitesimal calculus, speculated widely about infinite numbers and their use in mathematics. To Leibniz, both infinitesimals and infinite quantities were ideal entities, not of the same nature as appreciable quantities, but enjoying the same properties.

Whether infinity exists in our physical universe, is an open question.

Read more here http://en.wikipedia.org/wiki/Infinity

(2) Mysteries of the Mathematical Universe

http://worldsciencefestival.com/videos/mysteries_of_the_mathematical_universe

The poincaré conjecture Explained: #math 

In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. The Poincaré Conjecture tries to answer how multi-dimensional shapes behave in space.

Henri Poincaré was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics.

The Poincaré Conjecture overview:

http://www.youtube.com/watch?v=AUoaTrQTM5o

Grigori Perelman and the Poincaré Conjecture

http://www.youtube.com/watch?v=NEVWCBOBIXM

Grigori Yakovlevich Perelman (born on 13 June 1966) is a Russian mathematician, who has made landmark contributions to Riemannian geometry and geometric topology. In particular, he proved Thurston’s geometrization conjecture. This solves in the affirmative the famous Poincaré conjecture, posed in 1904. Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv.org. The proof followed the program of Richard Hamilton.

#mathchat - No one who is interested in an equitable society can fail to be irked by unfairness in wealth distribution – but it is not unexpected

The economist Edward N Wolff, of New York University, has pointed out that, as of 2007, the top 1% of households in America owned 34.6% of all privately held wealth, and the next 19% had 50.5% of the wealth. This means that just 20% of the people owned 85% of the wealth, leaving only 15% for the bottom 80% of the people. No one who is interested in an equitable society can fail to be irked by this unfairness.

http://www.guardian.co.uk/commentisfree/2011/nov/11/occupy-movement-wealth-power-law-distribution?CMP=twt_gu

Geometry and Billiards #mathchat 
Geometry and physics are essential parts of the game of pool/billiards. 

Baby Got Stats #edchat #Statistics 

Lyrics :

Baby Got Stats

Lyrics by Dorry Segev

To the music of “Baby Got Back” by Sir Mix-A-Lot

(spoken by 2 epi grad students)

Oh my god, Becky, look at his log file.. it is so big,

he looks like one of those biostats grad students.

But, you know, who understands biostats?

They only hired him because he looks like a total geek, ok?

I mean, his log file is like 200 pages.

I can’t believe he even calculated, like, what’s a Schoenfeld residual?

I mean – gross. Look! He’s just so… smart!

I like good stats and I cannot lie.

You other brothers can’t deny

that when you get some data, and you put it in STATA,

and it spits out a beta of 10 you get sprung..

and you’re thinkin’ “No way – gonna send that to JAMA today!”

Couldn’t be any greater, an unbiased estimator.

Oh data, I wanna get with ya, regress and fit ya.

Scott Zeger tried to warn me, but those odds ratios get me so horny!

Ooh add a spline term, you say you wanna perfect fit?

Just add a quadratic… with STATA it’s automatic.

I seen her 2-tail, kickin’ it on the log scale,

no leaf, no stem, got it going with GLM.

I’m tired of magazines saying exact tests are the things.

Take the average grad student, she will say: “I like your logit way”

So fellas, fellas, did you download the DTA?

Reshape it, reshape it, reshape it with LDA.

Baby got stats

I like my R-squared’s big.. the AUC I dig. I just can’t help myself,

analyzin’ like an animal, now here’s my scandal:

I wanna sit at home and sum, double-up, sum-of-squares!

I ain’t talkin’ exact test, large sample assumption is the best.

I want a high coefficient, so find a cohort study.

If the data’s muddy, I’ll clean it up with my buddy.

Put a paper in Nature or Cell, takes 7 years to do it well…

You can tell everyone I’m a geek, but I write my grants in a week.

A word to you epi sistas.. I wanna get with ya, I won’t overfit ya.

But it’s gonna be great when we’re playin’ with Cox models all night long,

STATA got it goin’ on!

A lot of people gonna be served..

They don’t check for proportional hazards, but I got me a log log curve.

And I shout, without a doubt, don’t make me take my DO file out!

So ladies, ladies, using methods from the 80’s?

Well don’t resign, get STATA 9, and your thesis will be fine.

Baby got stats

Yeah baby, when it comes to models,

Epi ain’t got nothing to do with my selection.

2x2 tables?

Yeah, only if it’s AJE (*American Journal of Epidemiology)

So your girlfriend rolls a Honda, runs a study in Rwanda,

but all I want is the data in the back of her Honda.

My anaconda don’t want none unless your p is 0.01!

You can do stepwise or subsets, or even AIC.

Some brothers analyze survival, tell you censoring just don’t count.

But I find them, and remind them: competing risks are behind them.

So they teach STATA in class, and the real world uses SAS,

but remember that STATA is nearly free,

and for SAS you pay a yearly fee.

Scatterplots i do adore, but i can do much more.

You want prediction, I’ll create it, bootstrap and validate it.

A 650 geek went too far, tried to do it all in R,

He had game but he didn’t perfect it, and Annals had to reject it.

So ladies if your budget’s tight, ask me to do your stats tonight,

You’ll have a valid sample size, and get your Nobel prize

Baby got stats

(you have no bias but you have no life)

(word to your data)

Previous post: 

http://benvitale-digits-of-pi.tumblr.com/post/12502354906/part-4-words-that-start-and-end-with-the-same-letters

List of words starting with “D”

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-d.html

4-Letter Words Starting With “D” 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/4-letter-words-starting-with-d.html

My aim is to find 4-letter words that start and end with “D”, add them up and perhaps get 44, being the concatenation of 4 and 4.

In mathematics, concatenation is the joining of two numbers by their numerals. That is to say, the concatenation of numbers a and b is denoted a||b. In this case 44 = 4||4.

dabb, dabs, dace, dada, dade, dado, dads, daff, daft, dago, dais, dale, dalf, dame, damn, damp, dams, dana, dane, dang, dank, dare, darg, dark, darn, darr, dart, dase, dash, data, date, daub, dauk, daun, dauw, dave, dawe, dawk, dawn, days, daze, dbms, dead, deaf, deal, dean, dear, deas, debs, debt, deck, deco, dede, deed, deem, deep, deer, dees, deev, deft, defy, degu, deil, deis, deja, dele, delf, deli, dell, deme, demi, demo, demy, dens, dent, deny, dept, dere, derf, derk, derm, dern, desk, dess, deus, deux, deva, deve, devi, dews, dewy, deye, deys, dhow, diag, dial, diam, dian, dias, dibs, dice, dich, dick, dict, dido, didy,died, diem, dies, diet, digs, dika, dike, dill, dime, dims, dine, ding, dink, dins, dint, dips, dipt, dire, dirk, dirl, dirt, disc, dish, disk, dite, ditt, diva, dive, dizz, djin, doab, doat, dock, docs, dodd, dodo, doer, does, doff, doge, dogs, dogy, doit, dojo, doko, dole, dolf, doll, dolt, dome, doms, dona, done, dong, doni, dons, doom, doop, door, dope, dopy, dorm, dorn, dorp, dorr, dors, dory, dose, doss, dost, dote, doth, dots, doty, douc, dour, dout, dove, dowl, down, dows, doxy, doze, dozy, drab, drad, drag, dram, drat, draw, dray, dree, dreg, drek, drew, drey, drib, drie, drip, droh, drop, drow, drub, drug, drum, drys, duad, dual, duan, dubb, dubs, duce, duck, duct, dude, duds, duel, dues, duet, duff, dugs, duke, dull, duly, dumb, dump, dune, dung, dunk, duns, dunt, duos, dupe, dura, dure, durn, duse, dusk, dust, duty, dyad, dyas, dyed, dyer, dyes, dyke, dyne,

A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, J = 10, 
K = 11, L = 12, M = 13, N = 14, O = 15, P = 16, Q = 17, R = 18, S = 19, 
T = 20, U = 21, V = 22, W = 23, X = 24, Y = 25, Z = 26

dead = 4 + 5 + 1 + 4 = 14 
deed = 4 + 5 + 5 + 4 = 18 
died = 4 + 9 + 5 + 4 = 22
dodd = 4 + 15 + 4 + 4 = 27 
drad = 4 + 18 + 1 + 4 = 27 
duad = 4 + 21 + 1 + 4 = 30 
dyed = 4 + 25 + 5 + 4 = 38

There are no words such the sum of their digits is 44.

A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, 

J = 10, K = 11, L = 12, M = 13, N = 14, O = 15, P = 16, Q = 17, 

R = 18, S = 19, T = 20, U = 21, V = 22, W = 23, X = 24, Y = 25, 

Z = 26 

(1) Words starting with the letter “A” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter.html

(2) Words starting with the letter “B” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-b.html

(3) Words starting with the letter “C” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-c.html

(4) Words starting with the letter “D” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-d.html

(5) Words starting with the letter “E” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-e.html

(6) Words starting with the letter “F” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-f.html

(7) Words starting with the letter “G” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-g.html

(8) Words starting with the letter “H” : 

http://ben-vitalis-math-ed-videos.blogspot.com/2011/11/letter-h.html

Additional restriction : If, for example, I look for a word that starts and ends with the 5th letter of the alphabet, I’ll restrict the search for words that have 5 letters.

With words that start and end with “A”, only the word A = 1 follows the rule.

With the letter “B”, N/A

With the letter “C”, none.

With the letter “D”, I need to research.

With the letter “E”, I found that ….

envie = 5 + 14 + 22 + 9 + 5 = 55 

etude = 5 + 20 + 21 + 4 + 5 = 55

exile = 5 + 24 + 9 + 12 + 5 = 55 

These 3 words, “envie”, “etude” and “exile”, all start with the 5th letter of alphabet, and each of them contains 5 letters, and add up to 55.

I haven’t finished the search, I’ll continue later with words that start and end with the letters “F”, “G” and “H”.