Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solvin...

Welcome to the Essential Science Fiction Novels book series, where you will find a selection of endless tales about the incredible technologies of the future, time travel and its consequences, adventures in interstellar spaceships, strange post-apocalyptic worlds, dangerous alien invasions and everything else the authors dreamed of or feared for the future of humanity.For this book, the literary critic August Nemo has chosen the 5 novels by authors who created memorable stories that shaped...

What historical, political, and ecclesial realities drove the canonization of the New Testament? How are the doctrines of Early Christianity related to the formation of the New Testament? Should the New Testament differ in authority from other early Christian texts? As these questions demonstrate, the enduring influence of the New Testament does not lessen the dispute over the events and factors leading to its adoption. Five Views on the New Testament Canon presents five distinct ways of u...

This volume addresses itself to the ways in which the so-called 'new sciences of complexity' can deepen and broaden neurobiological and psychological theories of mind. Complexity theory has gained increasing attention over the past 20 years across diverse areas of inquiry, including mathematics, physics, economics, biology, and the social sciences. Complexity theory concerns itself with how nonlinear dynamical systems evolve and change over time and draws on research arising from chaos the...

This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are...

Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational appro...

Jesus teaches that regardless of one's profession, if one does not demonstrate a changed life produced by God, one will not enter into heaven. Such a judgment will be made when Jesus returns and judges every person according to his or her "works." While this may seem contradictory to some more well-known passages ruling out the role of works in salvation (e.g., Rom 3:21–4:25; Gal 2:16–21; Eph 2:8–9), there is every good reason to understand that Jesus' teachings complement such passages. T...

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematica...

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as ...

Once you come to know Jesus Christ as your Savior and Lord, what is the next step? If you have been a believer for a while and want to grow further, what is the next step? If you have grown in your faith and want to learn how to help other believers grow in theirs, what is the next step? This book will begin to answer these important questions. In Peter's second letter to scattered believers, he challenges us to add seven character qualities to our faith that will help us grow to be more l...

The letters to the Philippian and Galatian congregations illustrate well the passion and intensity of Paul's writing. Together these letters provide a compelling portrait of a complex original thinker who probably was the most significant missionary of his day, a theologian and social critic of rare power and insight whose legacy continues today to spark heated debate. Yet if we can catch even a little of Paul's vision, we are likely to be transformed. We may find ourselves called, like Pa...

This commentary for preaching Matthew, a companion to WJK's successful Preaching the Gospel of Luke, Preaching the Gospel of John, and Preaching the Gospel of Mark, works through every passage of Matthew's Gospel with exegetical insight and a keen sensitivity to the demands of preaching. Stanley P. Saunders' commentary follows the biblical text, divided into passages. After each passage, a number of possibilities are presented for how to preach that text. He incl...