invindex.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

 64: infinite sums
 64: partial fraction expansions\sub for easy summation and differentiation
 64: perturbation method
 64: product notation
 64: real part
 64: summation\sub factors
 64: summation\sub infinite
 64: sums\sub absolutely convergent
 64: sums\sub infinite
 65: $\bigwedge$-notation
 65: Riemann's zeta function
 65: cribbage
 65: double sums\sub faulty use of
 65: greatest lower bound
 65: minimum
 65: sums\sub of consecutive integers
 65: zeta function
 66: Acton, John Emerich Edward Dalberg, Baron
 66: Goldbach\sub theorem
 66: Golomb\sub self-describing sequence
 66: perfect powers
 66: self-describing sequence
 67--69: ceiling function
 67--69: floor function
 67: INT function
 67: Iverson
 67: calculators
 67: notation\sub ghastly
 67: pocket calculators
 68--69: duality\sub between floors and ceilings
 68: $\Longleftrightarrow$: if and only if
 68: Iverson\sub convention
 68: ceiling function\sub converted to floor
 68: ceiling function\sub graph of
 68: floor function\sub converted to ceiling
 68: floor function\sub graph of
 68: graphs of functions\sub floor and ceiling
 69: duality
 70: $\phi$ ($\approx1.61803$): golden ratio
 70: $\pi$ ($\approx3.14159$)
 70: $e$ ($\approx2.71828$)\sub as canonical constant
 70: Reingold, Edward Martin
 70: binary logarithm
 70: binary notation (radix~$2$)
 70: carries\sub across the decimal point
 70: fractional parts
 70: integer part
 70: lg: binary logarithm
 70: logarithms\sub binary
 70: phi ($\approx1.61803$)\sub as canonical constant
 70: pi ($\approx3.14159$\sub as canonical constant
 70: radix notation\sub length of
 71--72: prove or disprove
 71: $\Longrightarrow$: implies
 71: McEliece, Robert James
 71: philosophy
 71: skepticism
 72--73: exercises
 72--73: levels of problems
 72--73: problems
 72--73: properties
 72: Einstein, Albert
 72: necessary and sufficient conditions
 72: philosophy
 73--74: $\dts\,$: interval notation
 73--74: closed interval
 73--74: counting\sub integers in intervals
 73--74: half-open interval
 73--74: intervals
 73--74: open interval
 73: Hoare
 73: Ramshaw, Lyle Harold
 73: Toledo, Ohio
 73: baseball
 74--76: roulette wheel
 74: Colombo, Cristoforo (= Columbus, Christopher)
 74: Concrete Math Club
 74: Murphy's Law
 74: greed
 74: mnemonics
 74: wheel
 75: Iverson\sub convention
 75: boundary conditions on sums\sub can be difficult
 75: philosophy
 75: vocabulary
 75: wheel\sub big
 76: $O$-notation
 76: Big Oh notation
 76: asymptotics\sub of wheel winners
 76: asymptotics\sub usefulness of
 77--78: partitions, of the integers
 77--78: spectra
 77: Rayleigh, John William Strutt, 3rd Baron
 77: calculators
 77: irrational numbers\sub spectra of
 77: multisets
 77: pocket calculators
 78--81: recurrences\sub floor/ceiling
 78: Knuth\sub numbers
 79--81: Josephus\sub problem
 79--81: Josephus\sub recurrence
 79: algorithms\sub divide and conquer
 79: divide and conquer
 79: halving
 79: merging
 79: sorting\sub merge sort
 80: Armstrong, Daniel Louis (= Satchmo)
 81--82: remainder after division
 81--85: mod: binary operation
 81: Josephus\sub numbers
 81: Odlyzko, Andrew Michael
 81: Wilf, Herbert Saul
 81: quotient
 82--83: mod $0$
 82: modulus
 83--85: distribution\sub of things into groups
 83--85: partition into nearly equal parts
 83: distributive law\sub for mod
 83: fractional parts\sub related to mod
 83: mumble function
 83: notation\sub need for new
 84: mumble function
 85: Armageddon
 85: war
 86--94: sums\sub floor/ceiling
 86: boundary conditions on sums\sub can be difficult
 87--89: summation\sub asymptotic
 87: Bohl, Piers Paul Felix [= Bol', Pirs Georgievich]
 87: Sierpi\'nski, Wac{\l}aw
 87: Weyl, Claus Hugo Hermann
 87: distribution\sub of fractional parts
 87: fractional parts\sub uniformly distributed
 87: step functions
 88--89: discrepancy
 88: mumble function
 88: name and conquer
 89--94: arithmetic progression\sub floored
 91: Whitehead, Alfred North
 91: philosophy
 92: greatest common divisor
 94: Mathews
 94: Seaver
 94: reciprocity law
 95: "self reference"
 95: Dirichlet\sub box principle
 95: Egyptian mathematics
 95: Fibonacci, Leonardo
 95: Fibonacci\sub algorithm
 95: Josephus\sub problem
 95: algorithms\sub Fibonacci's
 95: box principle
 95: downward generalization
 95: exercises
 95: fractions\sub unit
 95: generalization\sub downward
 95: levels of problems
 95: nearest integer
 95: problems
 95: rounding to nearest integer
 95: unit fractions
 96: ceiling function\sub converted to floor
 96: duality\sub between floors and ceilings
 96: floor function\sub converted to ceiling
 96: irrational numbers\sub spectra of
 96: open interval
 96: partitions
 96: spectra
 97: $\phi$ ($\approx1.61803$): golden ratio
 97: Josephus\sub numbers
 97: Knuth\sub numbers
 97: discrepancy
 97: doubly exponential recurrences
 97: phi ($\approx1.61803$)\sub in solutions to recurrences
 97: recurrences\sub doubly exponential
 97: spectra
 98: doubly infinite sums
 98: infinite sums\sub doubly
 98: sums\sub doubly infinite
 99: partitions
 99: phi ($\approx1.61803$)\sub in solutions to recurrences
 99: spectra
 99: spiral function
100: $\sqrt2$ ($\approx1.41421$)
100: Josephus\sub numbers
100: Josephus\sub problem
100: Knuth\sub numbers
100: doubly exponential recurrences
100: fractional parts\sub in polynomials
100: recurrences\sub doubly exponential
100: recurrences\sub unfolding
100: replicative function
100: square root\sub of $2$
100: unfolding a recurrence
101: Fibonacci\sub algorithm
101: algorithms\sub Fibonacci's
101: algorithms\sub greedy
101: doubly exponential recurrences
101: greedy algorithm
101: partitions
101: recurrences\sub doubly exponential
101: spectra
101: unit fractions
102--105: divisibility
102--152: number theory
102--152: theory of numbers
102: $\divides$: divides
102: Graham
102: Knuth
102: Patashnik
102: multiple of a number
103--104: Euclid\sub algorithm
103--104: greatest common divisor
103: algorithms\sub Euclid's
103: gcd
103: hcf
103: lcm
103: least common multiple
104--105: summation\sub over divisors
104: algorithms\sub self-certifying
104: certificate of correctness
104: self-certifying algorithms
105--111: prime numbers
105: Mathews
105: Seaver
105: composite numbers
105: double sums\sub over divisors
105: interchanging the order of summation
105: nonprime numbers
105: summation\sub interchanging the order of
106--107: Fundamental Theorem of Arithmetic
106--107: factorization into primes
106--107: unique factorization
106: $\prod$-notation
106: Mathews
106: Seaver
106: algebraic integers
106: empty product
106: prime algebraic integers
106: product notation
107--108: Euclid (= xxx)
107: duality\sub between gcd and lcm
107: greatest common divisor
107: least common multiple
107: number system
107: number system\sub prime-exponent
107: prime-exponent representation
108--109: Euclid\sub numbers
108: $\ldots\,$
108: closed form\sub not
108: ellipsis ($\cdots@$)\sub elimination of
108: relatively prime integers
108: three-dots ($\cdots@$) notation\sub elimination of
109--110: Mersenne, Marin
109--110: Mersenne\sub numbers
109--110: Mersenne\sub primes
109--110: prime numbers\sub Mersenne
109--110: prime numbers\sub largest known
109: Cray X-MP
109: Hanoi
109: Slowinski, David Allen
109: Tower of Hanoi
109: doubly exponential recurrences
109: personal computer
109: radix notation
109: recurrences\sub doubly exponential
110--111: asymptotics\sub of $n$th prime
110--111: pi function
110--111: prime numbers\sub size of $n$th
110: factorization into primes
110: primality testing
111--112: permutations
111--115: $!$: factorial
111--115: factorial function
111: Eratosthenes, sieve of
111: Hardy, Godfrey Harold
111: Kramp, Christian
111: Rosser, John Barkley
111: Schoenfeld, Lowell
111: Wright, Sir Edward Maitland
111: counting\sub permutations
111: distribution\sub of primes
111: empty product
111: sieve of Eratosthenes
112--114: $\epsilon_p(n)$: largest power of $p$ dividing~$n$
112--114: divides exactly\sub in factorials
112--114: exactly divides\sub in factorials
112: Gau{\ss} (= Gauss)\sub trick
112: Stirling\sub approximation
112: asymptotics\sub of factorials
113--114: binary notation (radix~$2$)
113--114: radix notation\sub related to prime factors
113: ruler function
114: geometric progression\sub floored
114: nu function: sum of digits\sub binary (radix $2$)
114: sideways addition
115--123: relatively prime integers
115: $\rp$: is relatively prime to
115: notation\sub need for new
115: prime to
116--123: Stern--Brocot tree
116--123: fractions
116: Brocot, Achille
116: Stern, Moriz Abraham
116: mediant
116: number system\sub prime-exponent
116: prime-exponent representation
117: ancestor
117: binary trees
117: invariant relation
117: trees\sub binary
118--119: Farey, John, series
118--119: Farey\sub consecutive elements of
119--123: Stern--Brocot number system
119: number system
121: binary search
122--123: Stern--Brocot number system\sub simplest rational approximations from
122--123: irrational numbers\sub Stern--Brocot representations
122--123: irrational numbers\sub rational approximations to
122: $e$ ($\approx2.71828$)\sub representations of
122: Euler
122: Stern--Brocot number system\sub representation of $e$
123--126: $\equiv$: is congruent to
123--126: congruences
123--126: mod: congruence relation
123--129: modular arithmetic
123: Euclid\sub algorithm
123: Gau{\ss} (= Gauss)
123: algorithms\sub Euclid's
124: Hacker's Dictionary
124: equivalence relation
124: transitive law
125: inverse modulo $m$
126--129: number system\sub residue
126--129: residue number system
126: Chinese Remainder Theorem
126: Sun Ts\u u [= S\=unz\u{\i}, Master Sun]
127: Mersenne\sub primes
127: multiple-precision numbers
127: prime numbers\sub Mersenne
128--129: roots of unity\sub modulo $m$
128--129: square root\sub of $1$ (mod $m$)
129: trivial, clarified
130--131: Fermat's Last Theorem
130: Dirichlet\sub box principle
130: Fermat, Pierre de
130: box principle
130: pigeonhole principle
131--132: Fermat\sub numbers
131--133: Fermat's theorem (= Fermat's Little Theorem)
131: Connection Machine
131: Elkies, Noam David
131: Euler\sub disproved conjecture
131: Fermat
131: Frye, Roger Edward
131: Mersenne
131: Wiles, Andrew John
132--133: Wilson, Sir John, theorem
132--134: Euler
132: Fermat's theorem (= Fermat's Little Theorem)\sub converse of
132: inverse modulo $m$
132: last but not least
133--135: phi function
133--135: totient function
133: Euler\sub theorem
133: Sylvester, James Joseph
133: efficiency
133: primality testing\sub impractical method
134--135: fractions\sub unreduced
134--136: multiplicative functions
134: Farey\sub enumeration of
134: basic fractions
134: fractions\sub basic
135--137: summation\sub over divisors
136--137: Dedekind, Julius Wilhelm Richard
136--137: Liouville, Joseph
136--138: recurrences\sub implicit
136--139: M\"obius\sub function
136--139: implicit recurrences
136--139: inversion formulas\sub for sums over divisors
136: M\"obius, August Ferdinand
136: interchanging the order of summation
136: summation\sub interchanging the order of
137--139: $\Phi$: sum of $\varphi$
137--139: Farey\sub enumeration of
137--139: Phi function: sum of $\phi$
137--144: totient function\sub summation of
138: M\"obius
138: algorithms, analysis of
138: analysis of algorithms
138: basic fractions
138: fractions\sub basic
139--140: cycles\sub of beads
139--141: counting\sub necklaces
139--141: necklaces
139: Mertens, Franz Carl Joseph
139: name and conquer
140: MacMahon, Maj.~Percy Alexander
141--143: Fermat's theorem (= Fermat's Little Theorem)
141: summation\sub over divisors
142: Euler\sub theorem
144: Josephus\sub problem
144: multiplicative functions
144: number system\sub residue
144: residue number system
145: Bertrand, Joseph Louis Fran\c{c}ois
145: Bertrand\sub postulate
145: Chebyshev
145: Euclid\sub numbers
145: Fermat\sub numbers
145: M\"obius\sub function
145: distributive law\sub for gcd and lcm
145: greatest common divisor
145: least common multiple
145: squarefree
146--148: radix notation\sub related to prime factors
146: $\edivides$: exactly divides
146: $\epsilon_p(n)$: largest power of $p$ dividing~$n$
146: $\pi$ ($\approx3.14159$)
146: Chinese Remainder Theorem
146: Hanoi
146: Stern--Brocot number system\sub representation of $\pi$
146: Stern--Brocot number system\sub simplest rational approximations from
146: Tower of Hanoi