Eulerian Numbers

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Eulerian Numbers

Author : T. Kyle Petersen
Publisher : Birkhäuser
ISBN 13 : 1493930915
Total Pages : 463 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Eulerian Numbers by : T. Kyle Petersen

Download or read book Eulerian Numbers written by T. Kyle Petersen and published by Birkhäuser. This book was released on 2015-10-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.

Handbook of Number Theory II

Author : J. Sándor
Publisher : Springer Science & Business Media
ISBN 13 : 1402025467
Total Pages : 637 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Number Theory II by : J. Sándor

Download or read book Handbook of Number Theory II written by J. Sándor and published by Springer Science & Business Media. This book was released on 2004 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.

Euler's Pioneering Equation

Author : Robin Wilson
Publisher : Oxford University Press
ISBN 13 : 0192514067
Total Pages : 200 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Euler's Pioneering Equation by : Robin Wilson

Download or read book Euler's Pioneering Equation written by Robin Wilson and published by Oxford University Press. This book was released on 2018-02-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Proceedings of the London Mathematical Society

Author : London Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 530 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis Proceedings of the London Mathematical Society by : London Mathematical Society

Download or read book Proceedings of the London Mathematical Society written by London Mathematical Society and published by . This book was released on 1900 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Papers presented to J.E. Littlewood on his 80th birthday" issued as 3d ser., v. 14 A, 1965.

Proceedings

Author :
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Proceedings by :

Download or read book Proceedings written by and published by . This book was released on 1988 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Discrete Mathematics

Author : Sriram Pemmaraju
Publisher : Cambridge University Press
ISBN 13 : 9780521806862
Total Pages : 508 pages
Book Rating : 4.8/5 (68 download)

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Book Synopsis Computational Discrete Mathematics by : Sriram Pemmaraju

Download or read book Computational Discrete Mathematics written by Sriram Pemmaraju and published by Cambridge University Press. This book was released on 2003-12-08 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This definitive reference on Combinatorica contains examples of all 450 functions plus tutorial text.

Cyclic Homology

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662217392
Total Pages : 467 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Cyclic Homology by : Jean-Louis Loday

Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Figurate Numbers

Author : Elena Deza
Publisher : World Scientific
ISBN 13 : 9814355488
Total Pages : 475 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Figurate Numbers by : Elena Deza

Download or read book Figurate Numbers written by Elena Deza and published by World Scientific. This book was released on 2012 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plane figurate numbers -- Space figurate numbers -- Multidimensional figurate members -- Areas of number theory including figurate numbers -- Fermat's polygonal number theorem.

Enumerative Combinatorics

Author : Charalambos A. Charalambides
Publisher : CRC Press
ISBN 13 : 9781584882909
Total Pages : 630 pages
Book Rating : 4.8/5 (829 download)

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Book Synopsis Enumerative Combinatorics by : Charalambos A. Charalambides

Download or read book Enumerative Combinatorics written by Charalambos A. Charalambides and published by CRC Press. This book was released on 2002-05-29 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

The Genius of Euler: Reflections on his Life and Work

Author : William Dunham
Publisher : American Mathematical Soc.
ISBN 13 : 147045744X
Total Pages : 326 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Genius of Euler: Reflections on his Life and Work by : William Dunham

Download or read book The Genius of Euler: Reflections on his Life and Work written by William Dunham and published by American Mathematical Soc.. This book was released on 2020-08-03 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Legacy of Leonhard Euler

Author : Lokenath Debnath
Publisher : World Scientific
ISBN 13 : 1848165269
Total Pages : 420 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis The Legacy of Leonhard Euler by : Lokenath Debnath

Download or read book The Legacy of Leonhard Euler written by Lokenath Debnath and published by World Scientific. This book was released on 2010 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler''s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler''s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author''s historically motivated method of teaching, special attention is given to demonstrate that Euler''s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler''s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. Erratum. Sample Chapter(s). Chapter 1: Mathematics Before Leonhard Euler (434 KB). Contents: Mathematics Before Leonhard Euler; Brief Biographical Sketch and Career of Leonhard Euler; Euler''s Contributions to Number Theory and Algebra; Euler''s Contributions to Geometry and Spherical Trigonometry; Euler''s Formula for Polyhedra, Topology and Graph Theory; Euler''s Contributions to Calculus and Analysis; Euler''s Contributions to the Infinite Series and the Zeta Function; Euler''s Beta and Gamma Functions and Infinite Products; Euler and Differential Equations; The Euler Equations of Motion in Fluid Mechanics; Euler''s Contributions to Mechanics and Elasticity; Euler''s Work on the Probability Theory; Euler''s Contributions to Ballistics; Euler and His Work on Astronomy and Physics. Readership: Undergraduate and graduate students of mathematics, mathematics education, physics, engineering and science. As well as professionals and prospective mathematical scientists.

Euler

Author : William Dunham
Publisher : American Mathematical Society
ISBN 13 : 147046618X
Total Pages : 185 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Euler by : William Dunham

Download or read book Euler written by William Dunham and published by American Mathematical Society. This book was released on 2022-01-13 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

7 Algorithm Design Paradigms

Author : Sung-Hyuk Cha
Publisher : Cha Academy llc
ISBN 13 : 1735168009
Total Pages : 798 pages
Book Rating : 4.7/5 (351 download)

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Book Synopsis 7 Algorithm Design Paradigms by : Sung-Hyuk Cha

Download or read book 7 Algorithm Design Paradigms written by Sung-Hyuk Cha and published by Cha Academy llc. This book was released on 2020-06-01 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intended readership includes both undergraduate and graduate students majoring in computer science as well as researchers in the computer science area. The book is suitable either as a textbook or as a supplementary book in algorithm courses. Over 400 computational problems are covered with various algorithms to tackle them. Rather than providing students simply with the best known algorithm for a problem, this book presents various algorithms for readers to master various algorithm design paradigms. Beginners in computer science can train their algorithm design skills via trivial algorithms on elementary problem examples. Graduate students can test their abilities to apply the algorithm design paradigms to devise an efficient algorithm for intermediate-level or challenging problems. Key Features: Dictionary of computational problems: A table of over 400 computational problems with more than 1500 algorithms is provided. Indices and Hyperlinks: Algorithms, computational problems, equations, figures, lemmas, properties, tables, and theorems are indexed with unique identification numbers and page numbers in the printed book and hyperlinked in the e-book version. Extensive Figures: Over 435 figures illustrate the algorithms and describe computational problems. Comprehensive exercises: More than 352 exercises help students to improve their algorithm design and analysis skills. The answers for most questions are available in the accompanying solution manual.

How Euler Did Even More

Author : C. Edward Sandifer
Publisher : The Mathematical Association of America
ISBN 13 : 0883855844
Total Pages : 254 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis How Euler Did Even More by : C. Edward Sandifer

Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

The Quarterly Journal of Pure and Applied Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.:/5 ( download)

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Book Synopsis The Quarterly Journal of Pure and Applied Mathematics by :

Download or read book The Quarterly Journal of Pure and Applied Mathematics written by and published by . This book was released on 1916 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Revue Semestrielle Des Publications Mathématiques

Author :
Publisher :
ISBN 13 :
Total Pages : 370 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Revue Semestrielle Des Publications Mathématiques by :

Download or read book Revue Semestrielle Des Publications Mathématiques written by and published by . This book was released on 1914 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Messenger of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 530 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis The Messenger of Mathematics by :

Download or read book The Messenger of Mathematics written by and published by . This book was released on 1897 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: