Daniel Greene, Donald Knuth – Mathematics for the Analysis of Algorithms

This monograph collects some basic mathematical strategies which are required for the evaluation of algorithms. It builds on the fundamentals of combinatorial evaluation and complicated variable idea to current many of the main paradigms utilized in the exact evaluation of algorithms, emphasizing the tougher notions. The authors cowl recurrence relations, operator strategies, and asymptotic evaluation in a format that’s concise sufficient for simple reference but detailed sufficient for these with little background with the materials.

 

Review

“This is a short cookbook of methods for analyzing the run time of computer algorithms, aimed at computer scientists … . a very erudite book, full of interesting things for both mathematicians and computer scientists … .” (Allen Stenger, MAA Reviews, September, 2015)

 

“Mathematics for the Analysis of Algorithms covers a variety of topics in a relatively small amount of pages. Despite its briefness, most of the topics are clearly and fully explained using detailed examples for better understanding. As such, the book is suitable for use as study material, as well as a good reference guide…The reviewer recommends this book to anyone interested in advanced theory of algorithms and the mathematics behind it, either as an exposition to the topic or as reference material in future work.”   ―SIGACT NEWS

 

“This e-book collects some basic mathematical strategies that are required for the evaluation of algorithms… This e-book arose from handouts for a sophisticated course on the evaluation of algorithms at Standard University, and the appendices record lectures, homework assignments and issues for the midterm and the closing exams with their options. In abstract, this e-book is a really beneficial assortment of mathematical strategies for the evaluation of algorithms and accompanies, in addition to enhances, the second writer’s collection The Art of Computer Programming

 

.”   ―Mathematical Reviews

“The book covers the important mathematical tools used in computer science, especially in the exact analysis of algorithms. A wide range of topics are covered, from the binomial theorem to the saddle point method and Laplace’s techniques for asymptotic analysis…The book is very well written. The style and the mathematical exposition make the book pleasant to read…It covers many of the major paradigms used in the analysis of algorithms in its one hundred plus pages.”   ―SIAM Review

 

“The book presents a welcome selection and careful exposition of material that can be (and is) covered in a single course…In this reviewer’s opinion, this would be an interesting text to use with a group of advanced students well-grounded in undergraduate mathematics and computer science, and would produce a valuable course for the participating students.”   ― Computing Reviews

 

“The reader has most likely heard of the expression ‘good things come in small packages.’ The validity of that maxim isn’t any extra in proof than in the work below overview, which is nothing lower than a mathematical wellspring amongst the in any other case parched world of theoretical algorithm evaluation. In solely 76 pages (not counting the bibliography and wonderful appendices), the authors cowl 4 essential subjects in algorithm evaluation, all from a rudimentary, however extremely authentic,

 

level of view: Binomial Identities, Recurrence Relations, Operator Methods, and Asymptotic Analysis. Each of these subjects is crucial to understanding the fashionable evaluation of algorithms, primarily from the velocity of execution perspective… In abstract, the e-book below overview shouldn’t be underestimated in its highly effective use of arithmetic for the evaluation of algorithms arising from pc science issues.”   ―Timothy Hall, Process Quality Improvement Consulting

“The analysis of algorthms is possible on mathematical and on computer scientific ways. This [book] is a mathematical look at this topic. It is based on an advanced course in computer science at Stanford University… The Appendices contain further difficult problems for applying the methods of this outstanding, full-of-thoughts book.”   ―P.L. Erdos (Periodica Mathematica Hungarica)

 

From the Back Cover

A quantitative research of the effectivity of pc strategies requires an in-depth understanding of each arithmetic and pc science. This monograph, derived from a sophisticated pc science course at Stanford University, builds on the fundamentals of combinatorial evaluation and complicated variable idea to current many of the main paradigms utilized in the exact evaluation of algorithms, emphasizing the tougher notions. The authors cowl recurrence relations, operator strategies, and asymptotic evaluation in a format that’s terse sufficient for simple reference but detailed sufficient for these with little background. Approximately half the e-book is dedicated to authentic issues and options from examinations given at Stanford.

 

 

 

“…a very valuable collection of mathematical techniques for the analysis of algorithms…”   ― Mathematical Reviews

 

“The book covers the important mathematical tools used in computer science, especially in the exact analysis of algorithms. A wide range of topics are covered, from the binomial theorem to the saddle point method and Laplace’s techniques for asymptotic analysis…The book is very well written. The style and the mathematical exposition make the book pleasant to read…It covers many of the major paradigms used in the analysis of algorithms in its one hundred plus pages.”   ― SIAM Review

 

“The e-book presents a welcome choice a

 

nd cautious exposition of materials that may be (and is) lined in a single course…In this reviewer’s opinion, this may be an fascinating textual content to make use of with a bunch of superior college students well-grounded in undergraduate arithmetic and pc science, and would produce a beneficial course for the collaborating college students.”   ― Computing Reviews