Guide To The Umbral Calculus, A Different Mathematical Language

Guide To The Umbral Calculus, A Different Mathematical Language
Author :
Publisher : World Scientific
Total Pages : 295
Release :
ISBN-10 : 9789811255342
ISBN-13 : 9811255342
Rating : 4/5 (42 Downloads)

Synopsis Guide To The Umbral Calculus, A Different Mathematical Language by : Silvia Licciardi

This book covers different aspects of umbral calculus and of its more recent developments. It discusses the technical details in depth, including its relevant applications. The book has therefore manyfold scopes to introduce a mathematical tool, not widespread known as it should be; to present a complete account of the relevant capabilities through the use of different examples of applications; to provide a formal bridge between different fields of research in pure and applied.

Algebraic Combinatorics and Computer Science

Algebraic Combinatorics and Computer Science
Author :
Publisher : Springer Science & Business Media
Total Pages : 542
Release :
ISBN-10 : 9788847021075
ISBN-13 : 8847021073
Rating : 4/5 (75 Downloads)

Synopsis Algebraic Combinatorics and Computer Science by : H. Crapo

This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Umbral Calculus

Umbral Calculus
Author :
Publisher : Courier Dover Publications
Total Pages : 209
Release :
ISBN-10 : 9780486834139
ISBN-13 : 0486834131
Rating : 4/5 (39 Downloads)

Synopsis Umbral Calculus by : Steven Roman

Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus.

A Comprehensive Treatment of q-Calculus

A Comprehensive Treatment of q-Calculus
Author :
Publisher : Springer Science & Business Media
Total Pages : 491
Release :
ISBN-10 : 9783034804301
ISBN-13 : 303480430X
Rating : 4/5 (01 Downloads)

Synopsis A Comprehensive Treatment of q-Calculus by : Thomas Ernst

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.​

The Cumulative Book Index

The Cumulative Book Index
Author :
Publisher :
Total Pages : 2236
Release :
ISBN-10 : UOM:39015058373575
ISBN-13 :
Rating : 4/5 (75 Downloads)

Synopsis The Cumulative Book Index by :

A world list of books in the English language.

Catalog of Copyright Entries. Third Series

Catalog of Copyright Entries. Third Series
Author :
Publisher : Copyright Office, Library of Congress
Total Pages : 1152
Release :
ISBN-10 : STANFORD:36105006280866
ISBN-13 :
Rating : 4/5 (66 Downloads)

Synopsis Catalog of Copyright Entries. Third Series by : Library of Congress. Copyright Office

Includes Part 1, Number 1: Books and Pamphlets, Including Serials and Contributions to Periodicals (January - June)

Paperbound Books in Print

Paperbound Books in Print
Author :
Publisher :
Total Pages : 1544
Release :
ISBN-10 : UOM:39015020648294
ISBN-13 :
Rating : 4/5 (94 Downloads)

Synopsis Paperbound Books in Print by :

Combinatorics: The Rota Way

Combinatorics: The Rota Way
Author :
Publisher : Cambridge University Press
Total Pages : 397
Release :
ISBN-10 : 9781139476768
ISBN-13 : 1139476769
Rating : 4/5 (68 Downloads)

Synopsis Combinatorics: The Rota Way by : Joseph P. S. Kung

Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

Algebra: Chapter 0

Algebra: Chapter 0
Author :
Publisher : American Mathematical Soc.
Total Pages : 713
Release :
ISBN-10 : 9781470465711
ISBN-13 : 147046571X
Rating : 4/5 (11 Downloads)

Synopsis Algebra: Chapter 0 by : Paolo Aluffi

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.