invindex.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

% this file inverts index.tex (omitting \see and \also)
i: Euler, Leonhard
iii--vi: Knuth, Donald Ervin
iii: Graham, Ronald Lewis
iii: Patashnik, Oren
iv: Graham
iv: Patashnik
v: Bulwer-Lytton, Edward George Earle Lytton, Baron
v: Halmos, Paul Richard
v: Hammersley, John Michael
v: Stanford University
vi: Graham
vi: Halmos
vi: Melzak, Zdzislaw Alexander
vi: P\'olya, George (= Gy\"orgy)
vi: Patashnik
vi: Stone, Marshall Harvey
vi: \v{C}ech, Eduard
vi: calculus
vi: concrete mathematics, defined
vii: Euler
vii: Gau{\ss} (= Gauss), Karl (= Carl) Friedrich
vii: Gottschalk, Walter Helbig
vii: Haar, Alfr\'ed
vii: Kilroy, James Joseph
vii: Leibniz, Gottfried Wilhelm, Freiherr von
vii: Stanford University
vii: graffiti
vii: philosophy
viii--ix: typefaces
viii: American Mathematical Society
viii: Beeton, Barbara Ann Neuhaus Friend Smith
viii: Boas
viii: Durst, Lincoln Kearney
viii: Knuth
viii: Murdock, Phoebe James
viii: Palais, Richard Sheldon
viii: Renz, Peter Lewis
viii: Swanson, Ellen Esther
viii: Whidden, Samuel Blackwell
viii: Woolf, William Blauvelt
viii: Zapf, Hermann
viii: answers
viii: cheating
viii: exercises, levels of
viii: levels of problems
viii: problems, levels of
ix: AMS Euler
ix: Aaronson, Bette Jane
ix: Addison-Wesley
ix: Broder
ix: Brown University
ix: Brown, Roy Howard
ix: CUNY (= City University of New York)
ix: Chung, Fan-Rong King
ix: Columbia University
ix: Dupr\'e, Lyn Oppenheim
ix: Euler
ix: Gordon, Peter Stuart
ix: Graham
ix: Graham, Cheryl
ix: Knuth
ix: Knuth, Nancy Jill Carter
ix: Mayr, Ernst
ix: National Science Foundation
ix: Naval Research
ix: Office of Naval Research
ix: Patashnik
ix: Patashnik, Amy Markowitz
ix: Princeton University
ix: Rice University
ix: Stanford University
ix: Yao, Andrew Chi-Chih
ix: Yao, Foong Frances
ix: Zeilberger, Doron
ix: fans
ix: graffiti
ix: puns
ix: rewards, monetary
x--xi: notation
xi: parenthesis conventions
xi: quotation marks
  1--20: recurrences
  1--4: Hanoi, Tower of
  1--4: Tower of Hanoi
  1: Brahma, Tower of
  1: God
  1: Lucas, Fran\c cois \'Edouard Anatole
  1: Tower of Brahma
  2: Allardice, Robert Edgar
  2: Fraser, Alexander Yule
  2: downward generalization
  2: empty case\sub for Tower of Hanoi
  2: generalization\sub downward
  2: name and conquer
  2: notation
  2: null case\sub for Tower of Hanoi
  2: small cases
  2: thinking\sub big
  3: basis of induction
  3: closed form
  3: induction
  3: induction\sub basis of
  3: mathematical induction
  3: mathematical induction\sub basis of
  3: solution
  4--8: lines in the plane
  4--8: regions
  4: Brahma
  4: Tower of Brahma
  4: inductive leap
  4: pizza
  4: proof
  5: Steiner, Jacob
  5: convex regions
  5: small cases
  6: Euler
  6: Gau{\ss} (= Gauss)
  6: Gau{\ss} (= Gauss)\sub trick
  6: arithmetic progression\sub sum of
  6: bowling
  6: recurrences\sub unfolding
  6: sums\sub of consecutive integers
  6: triangular numbers
  6: unfolding a recurrence
  7--8: zig
  7: Gau{\ss} (= Gauss)
  7: closed form
  7: induction
  7: mathematical induction
  7: proof
  8--17: Josephus\sub problem
  8: $\sim$: is asymptotic to
  8: Ahrens, Wilhelm Ernst Martin Georg
  8: Herstein, Israel Nathan
  8: Josephus, Flavius
  8: Kaplansky, Irving
  8: Mathews, Edwin Lee (= 41)
  8: Seaver, George Thomas (= 41)
  8: war
  9: small cases
 10--11: basis of induction
 10--11: induction
 10--11: mathematical induction
 11--13: binary notation (radix~$2$)
 11--13: radix notation
 11: generalization
 11: philosophy
 12: Josephus
 12: cyclic shift
 12: fixed points
 12: nu function: sum of digits\sub binary (radix $2$)
 12: sideways addition
 13--16: Josephus\sub recurrence, generalized
 13: generalization
 14--15: repertoire method
 15--16: binary notation (radix~$2$)
 15--16: radix notation
 16: P\'olya
 16: generalization
 16: philosophy
 16: war
 17--20: Hanoi\sub variations on
 17--20: Tower of Hanoi\sub variations on
 17: Venn\sub diagram
 17: horses
 17: induction\sub failure of
 17: lines in the plane
 17: mathematical induction\sub failure of
 17: regions
 18: horses
 18: induction\sub backwards
 18: mathematical induction\sub backwards
 19--20: Josephus
 19: cheese slicing
 19: lines in the plane
 19: planes, cutting
 19: regions
 19: repertoire method
 19: zig
 19: zig-zag
 20: Josephus\sub subset
 20: Venn\sub diagram
 20: convex regions
 20: periodic recurrences
 20: polygons\sub Venn diagrams with
 20: recurrences\sub periodic
 21--25: sums\sub notations for
 21--66: summation
 21--66: sums
 21: $\ldots\,$: ellipsis
 21: Mathews
 21: Seaver
 21: ellipsis ($\cdots@$)
 21: ellipsis ($\cdots@$)\sub advantage of
 21: term
 21: three-dots ($\cdots@$) notation
 21: three-dots ($\cdots@$) notation\sub advantage of
 22--25: $\sum$-notation
 22--25: Sigma-notation
 22--25: prime numbers\sub sum of reciprocals
 22: $i$
 22: Fourier, Jean Baptiste Joseph
 22: bound variables
 22: free variables
 22: index set
 22: index variable
 22: square root\sub of $-1$
 22: summand
 23: $\approx$: approximates
 23: Mertens\sub constant
 23: properties
 24--25: Iverson\sub convention
 24--25: boundary conditions on sums\sub made easier
 24--25: bracket notation\sub for true/false values
 24--25: zero, not considered harmful
 24--25: zero\sub strongly
 24: Finetti, Bruno de
 24: Iverson, Kenneth Eugene
 24: Kronecker\sub delta notation
 24: de Finetti, Bruno
 24: efficiency, different notions of
 24: empty sum
 24: sums\sub empty
 25--29: recurrences\sub and sums
 25--29: sums\sub and recurrences
 25: ellipsis ($\cdots@$)\sub advantage of
 25: ellipsis ($\cdots@$)\sub disadvantage of
 25: three-dots ($\cdots@$) notation\sub advantage of
 25: three-dots ($\cdots@$) notation\sub disadvantage of
 26--27: Hanoi
 26--27: Tower of Hanoi
 26: $\pi$ ($\approx3.14159$)
 26: arithmetic progression\sub sum of
 26: pi ($\approx3.14159$
 26: repertoire method\sub for sums
 27--29: summation\sub factors
 28--29: quicksort
 28--29: sorting\sub quicksort
 28: Hoare, Charles Antony Richard
 29: harmonic numbers
 29: violin string
 30--31: arithmetic progression\sub sum of
 30--31: changing the index of summation
 30--31: summation\sub changing the index of
 30: Gau{\ss} (= Gauss)\sub trick
 30: arithmetic progression
 30: associative law
 30: commutative law
 30: distributive law
 30: index set
 31: Alice
 31: Carroll, Lewis (= Dodgson, Rev.~Charles Lutwidge)
 31: Iverson\sub convention
 31: commutative law\sub relaxed
 32--33: geometric progression\sub sum of
 32--33: perturbation method
 32: geometric progression
 32: name and conquer
 33: calculus
 33: derivative operator\sub with generating functions
 34--41: double sums
 34--41: interchanging the order of summation
 34--41: multiple sums
 34--41: summation\sub interchanging the order of
 34--41: sums\sub multiple
 34: Iverson\sub convention
 34: index variable
 34: properties
 35: distributive law
 36--41: summation\sub over triangular arrays
 36--41: triangular array, summation over
 36: candy
 36: factorization of summation conditions
 36: rocky road
 36: vanilla
 37: rocky road
 38: Chebyshev, Pafnuti{\u\i} L'vovich
 38: Chebyshev\sub monotonic inequalities
 39: $\#$: cardinality
 39: bijection
 39: changing the index of summation
 39: summation\sub changing the index of
 41--46: squares, sum of consecutive
 41--46: sums\sub of consecutive squares
 41: harmonic numbers\sub sums of
 41: sums\sub of harmonic numbers
 42: Abramowitz, Milton
 42: Hansen, Eldon Robert
 42: Sloane, Neil James Alexander
 42: Stegun, Irene Anne
 42: Stengel
 42: computer algebra
 42: reference books
 42: square pyramidal numbers
 42: sums\sub of consecutive $m$th powers
 43--44: perturbation method
 43: Wapner, Joseph Albert
 43: induction
 43: inductive leap
 43: mathematical induction
 44--45: repertoire method\sub for sums
 44: sums\sub of consecutive integers
 45--46: integration
 45: approximation\sub of sums by integrals
 45: sums\sub approximation of, by integrals
 46: double sums\sub considered useful
 46: philosophy
 47--49: derivative operator
 47--55: $\Delta$: difference operator
 47--55: difference operator
 47--56: $\delta$
 47--56: calculus\sub finite and infinite
 47--56: finite calculus
 47: falling factorial powers
 47: operators
 47: operators\sub derivative ($D$)
 47: operators\sub difference ($\Delta$)
 48--49: indefinite summation
 48: Euler
 48: Fundamental Theorem of Calculus
 48: Pochhammer, Leo
 48: Pochhammer\sub symbol
 48: anti-derivative operator
 48: anti-difference operator
 48: empty product
 48: empty sum
 48: falling factorial powers\sub difference of
 48: integration
 48: operators\sub anti-derivative ($\int$)
 48: operators\sub anti-difference ($\sum$)
 48: rising factorial powers
 48: sums\sub empty
 49--50: definite sums, analogous to definite integrals
 49--50: summation\sub definite
 49: notation\sub extension of
 50--53: falling factorial powers\sub summation of
 50: $\ldots\,$
 50: ellipsis ($\cdots@$)\sub advantage of
 50: telescoping
 50: three-dots ($\cdots@$) notation\sub advantage of
 51: cubes, sum of consecutive
 51: falling factorial powers\sub related to ordinary powers
 51: squares
 51: sums\sub of consecutive cubes
 51: sums\sub of consecutive squares
 52: exponents, laws of
 52: falling factorial powers\sub negative
 52: negative factorial powers
 52: notation\sub extension of
 53--54: ln: natural logarithm\sub discrete analog of
 53--54: logarithms\sub discrete analog of
 53--54: natural logarithm
 53: falling factorial powers\sub difference of
 53: harmonic numbers\sub analogous to logarithms
 54--56: indefinite summation\sub by parts
 54--56: summation\sub by parts
 54: anti-difference operator
 54: chain rule
 54: exponential function, discrete analog of
 54: geometric progression\sub sum of
 54: integration\sub by parts
 54: quicksort
 54: sorting\sub quicksort
 55: $E$: shift operator
 55: operators\sub shift ($E$, $K$, $N$)
 55: shift operator
 56--62: infinite sums
 56--62: summation\sub infinite
 56--62: sums\sub infinite
 56: harmonic numbers\sub sums using summation by parts
 56: sums\sub of harmonic numbers
 56: thinking\sub not at all
 57: divergent sums
 57: least upper bound
 57: paradoxical sums
 57: sums\sub paradoxical
 58: Grandi, Luigi Guido
 59: "self reference"
 59: conditional convergence
 59: convergence\sub conditional
 59: doubly infinite sums
 59: graffiti
 59: infinite sums\sub doubly
 59: sums\sub doubly infinite
 60--62: absolute convergence
 60--62: convergence\sub absolute
 60--62: sums\sub absolutely convergent
 60: distributive law
 60: divergent sums
 60: index variable
 61: associative law
 61: commutative law
 61: double sums\sub infinite
 61: index set
 61: least upper bound
 61: multiple sums
 61: sums\sub multiple
 62: harmonic series, divergence of
 63: cubes
 63: double sums\sub faulty use of
 63: duality\sub between rising and falling powers
 63: exponents
 63: falling factorial powers\sub negative
 63: falling factorial powers\sub related to rising powers
 63: negative factorial powers
 63: repertoire method\sub for sums
 63: rising factorial powers\sub negative
 63: rising factorial powers\sub related to falling powers
 63: summation\sub by parts
 63: sums\sub of consecutive cubes
 64: $\Im$: imaginary part
 64: $\Re$: real part
 64: $\prod$-notation
 64: Jacobi, Carl Gustav Jacob
 64: Lagrange (= de la Grange)\sub identity
 64: absolute convergence
 64: absolute value of complex number
 64: associative law
 64: commutative law
 64: complex numbers
 64: convergence\sub absolute
 64: distributive law