Title: Concrete mathematics : a foundation for computer science /
Authors: Graham, Ronald L., 1935-2020; Knuth, Donald Ervin, 1938-; Patashnik, Oren
Publisher: Addison-Wesley,
Year: 1994
Subjects: Mathematics; Computer science Mathematics; Wiskundige methoden.; Software.; Mathématiques; Informatique Mathématiques; Analysis.; Zahlentheorie.
Abstract: "This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline."--from Amazon.com.
Contents: 1. Recurrent problems : The Tower of Hanoi ; Lines in the plane ; The Josephus problem -- 2. Sums : Notation ; Sums and recurrences ; Manipulation of sums ; General methods ; Finite and infinite calculus ; Infinite sums -- 3. Integer functions : Floors and ceilings ; Floor/ceiling applications ; Floor/ceiling recurrences ; 'mod': the binary operation ; Floor/ceiling sums -- 4. Number theory : Divisibility ; Primes ; Prime examples ; Factorial factors ; Relative primality ; 'mod': the congruence relation ; Independent residues ; Additional applications ; Phi and mu -- 5. Binomial coefficients : Basic identities ; Basic practice ; Tricks of the trade ; Generating functions ; Hypergeometric functions ; Hypergeometric transformations ; Partial hypergeometric sums ; Mechanical summation -- 6. Special numbers : Stirling numbers ; Eulerian numbers ; Harmonic numbers ; Harmonic summation ; Bernoulli numbers ; Fibonacci numbers ; Continuants -- 7. Generating functions : Domino theory and change ; Basic maneuvers ; Solving recurrence ; Special generating functions ; Convolutions ; Exponential generating functions ; Dirichlet generating functions -- 8. Discrete probability : Definitions ; Mean and variance ; Probability generating functions ; Flipping coins ; Hashing -- 9. Asymptotics : A hierarchy ; O notation ; O manipulation ; Two asymptotic tricks ; Euler's summation formula ; Final summations.