CRC Concise Encyclopedia of Mathematics

Author: Eric W. Weisstein

Publisher: CRC Press

ISBN: 1420035223

Category: Mathematics

Page: 3252

View: 7736

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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
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Automated Theory Formation in Pure Mathematics

Author: Simon Colton

Publisher: Springer Science & Business Media

ISBN: 1447101472

Category: Mathematics

Page: 380

View: 6227

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In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.
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The Art of Proving Binomial Identities

Author: Michael Z. Spivey

Publisher: CRC Press

ISBN: 1351215817

Category: Mathematics

Page: 368

View: 558

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The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.
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Sequences of Numbers Involved in Unsolved Problems

Author: Florentin Smarandache

Publisher: Infinite Study

ISBN: 1599730065

Category: Sequences (Mathematics)

Page: 139

View: 9367

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Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. The book contains definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost primes, mobile periodicals, functions, tables, prime/square/factorial bases, generalized factorials, generalized palindromes, etc. ).
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Discrete Mathematics with Ducks

Author: sarah-marie belcastro

Publisher: CRC Press

ISBN: 1351683691

Category: Mathematics

Page: 658

View: 6879

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Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study
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Twelfth Conference on Innovative Applications of Artificial Intelligence

Author: American Association for Artificial Intelligence

Publisher: Aaai Press

ISBN: 9780262511124

Category: Computers

Page: 1190

View: 3199

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AAAI proceedings describe innovative concepts, techniques, perspectives, and observations that present promising research directions in artificial intelligence. The annual AAAI National Conference provides a forum for information exchange and interaction among researchers from all disciplines of AI. Contributions include theoretical, experimental, and empirical results. Topics cover principles of cognition, perception, and action; the design, application, and evaluation of AI algorithms and systems; architectures and frameworks for classes of AI systems; and analyses of tasks and domains in which intelligent systems perform. Distributed for AAAI Press.
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The Math Encyclopedia of Smarandache type Notions

Vol. I. Number Theory

Author: Marius Coman

Publisher: Infinite Study

ISBN: 1599732521

Category:

Page: N.A

View: 3078

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About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.
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IAAI-2000

Twelfth Conference on Innovative Applications of Artificial Intelligence

Author: N.A

Publisher: Aaai Press

ISBN: 9780262511124

Category: Computers

Page: 1190

View: 7460

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AAAI proceedings describe innovative concepts, techniques, perspectives, and observations that present promising research directions in artificial intelligence.
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The Best Writing on Mathematics 2019

Author: Mircea Pitici

Publisher: Princeton University Press

ISBN: 0691198357

Category: Crafts & Hobbies

Page: 304

View: 396

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An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.
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