Marissa Os ato  Humanities Core Course  12 June 2006 


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Osato 1  Marissa Osato Humanities Core Course 12 June 2006  Art in the Internment Camps: Designing the Japanese American Identity  At the heart of the bustling metropolis of downtown Los Angeles there exists a hidden place of tranquil beauty and reflection – a traditional Japanese garden in the middle of Little Tokyo.  This garden, composed of customary Japanese flowers, streams, and rock carvings, is part of the Japanese American Cultural and Community Center, a center for the sharing and promotion of Japanese and Japanese American cultural arts with surrounding communities.  A plaque dedicated to the garden reads: In the middle cascades, the stream divides, expressing the conflicts experienced by the second generation Nisei, who volunteered out of America's concentration camps during World War II to prove their loyalty to the United States of America. The stream gradually becomes a gentle murmur, ending in a serene pond, symbolic of the hope for a peaceful world for the Sansei and the ensuing generations. Reading this reminded me of my own grandparents – Nisei Japanese Americans who were interned in the Poston III, Arizona camp in 1942.  Although there has been much public contention regarding the injustices and constitutional violations committed by the internment process, my grandparents never exhibited any resentment towards the American society that incarcerated them.  In fact, when reflecting on her experiences in Poston, my grandmother often
  • a photograph described by allen eaton explains a collection of intricately painted stones representing japanese folktale characters 
  • reflecting on her experiences in poston
  • personal exploration and communal unity
  • of ethnicity and the psychological effects of internment on japanese americans
  • and communal needs for a renewal of spirit
  • the artwork and art­related activities practiced during imprisonment reflected a significant turning point for the japanese american community – this art became a symbol of the acculturation of histories and ideologies that shaped the hybrid identity of the japanese american citizen
  •   the painted detail and delicate carving of these birds suggests the incredible meticulousness and patience with which they were made



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Computing Fundamentals 2
Lecture 5
Combinatorial Analysis
Lecturer: Patrick Browne
Room K408
Based on Chapter 16.
A Logical approach to Discrete Math
By David Gries and Fred B. SchneiderCombinatorial Analysis
• Counting
• Permutations
• Combinations
• The Pigeonhole Principle
• ExamplesCombinatorial Analysis
• Combinatorial analysis deals with
permutations of a set or bag and
combinations of a set, which lead to
binomial coefficients and the Binomial
Theorem.Rules of Counting
• Rule of sums: The size of the union on n
finite pair wise disjoint sets is the sum of
their sizes.
• Rule of product: The size of the cross
product of n sets is the product of their
• Rule of difference: The size of a set with a
subset removed is the size of the set
minus the size of the subset.Product Rule Example
• If each license plate contains 3 letters and
2 digits. How many unique licenses could
there be?
• Using the rule of products.
• 26 x 26 x 26 x 10 x 10 = 1,757,600
Permutation of a set
• A permutation of a set of elements is a linear
ordering (or sequence) of the elements e.g.
• {1,4,5}
• Permutation A : 1, 4, 5
• B : 1, 5, 4
• An anagram is a permutation of words.
• There are
n • (n – 1) • (n - 2) .. 1

permutations of a set of n elements.
• This is factorial n, written n!Calculating Factorial
module FACT {
-- Two notations for factorial
op _! : Nat -> NzNat {prec 10}
op fact : Nat -> NzNat
var N : Nat
-- Notation 1
eq 0 ! = 1 .
ceq N ! = N * (N - 1) ! if N > 0 .
-- Notation 2
eq fact(0) = 1 .
ceq fact(N) = N * fact(N - 1) if N > 0 .
open FACT
red 4 ! .
red fact(4) .Permutation of a set
• Sometimes we want a permutation of size
r from a set of size n.
• (16.4) P(n,r) = n!/(n-r)!
• The number of 2 permutations of BYTE is
• P(4,2) = 4!/(4-2)! = 4 • 3 = 12

• P(n,0) = 1
• P(n,n-1) = P(n,n) = n!
• P(n,1) = nCalculating Permutations and
Combinations of sets
mod CALC{
op permCalc : Int Int -> Int
op combCalc :
vars N R : Int
-- Compute permutation where order matters abc =/= bac
-- A permutation is an ordered combination.
-- perm calculates how many ways R items can be selected from N items
eq permCalc(N , R) = fact(N) quo fact(N - R) .
-- combination of N things taking R at a time
-- Note extra term in divisor.
eq combCalc(N , R) = fact(N) quo (fact(N - R) * fact(R)) .}
open CALC
-- Permutation from 10 items taking 7 at a time
red permCalc(10,7) . – gives 604800
-- Combination from 10 i
red combCalc(10,7) . – gives 120Permutation with repetition of a set
• An r-permutations is a permutation that allows
repetition. Here are all the 2-permutation of the
letters in SON:
• Given a set of size n, in constructing an r-
permutation with repetition, for each element we
have n choices.
• (16.6) The number of r permutations with
repetition of a set of size n is n , repetition is
allowed in the permutation not in the original set.