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High Quality Content by WIKIPEDIA articles! The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences, created and maintained by N. J. A. Sloane, a researcher at AT T Labs. In October 2009, the intellectual property and hosting of the OEIS were transferred to the OEIS Foundation. OEIS records information on integer sequences of interest to both professional mathematicians and amateurs, and is widely cited. As of 20 November 2011(2011 -11-20) it contains over 200,000 sequences, making it the largest database of its kind.
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.
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 dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.
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. ).
Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting. Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems. Elementary exercises at the end of each expository section prompt students to review the material Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. Sets of discovery problems and illustrative examples reinforce learning. Bonus sections can be used for take-home exams, projects, or further study Instructor Notes sections offer suggestions on how to use the material in each chapter Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 141. Chapters: Prime number, Factorial, Binomial coefficient, Perfect number, Carmichael number, Integer sequence, Mersenne prime, Bernoulli number, Euler numbers, Fermat number, Square-free integer, Amicable number, Stirling number, Partition, Lah number, Super-Poulet number, Arithmetic progression, Derangement, Composite number, On-Line Encyclopedia of Integer Sequences, Catalan number, Pell number, Power of two, Sylvester's sequence, Regular number, Polite number, M nage problem, Greedy algorithm for Egyptian fractions, Practical number, Bell number, Dedekind number, Hofstadter sequence, Beatty sequence, Hyperperfect number, Elliptic divisibility sequence, Powerful number, Zn m's problem, Eulerian number, Singly and doubly even, Highly composite number, Strict weak ordering, Calkin-Wilf tree, Lucas sequence, Padovan sequence, Triangular number, Squared triangular number, Figurate number, Cube, Square triangular number, Multiplicative partition, Perrin number, Smooth number, Ulam number, Primorial, Lambek-Moser theorem, Harmonic divisor number, Lucas number, Home prime, Meander, Primefree sequence, Lucas-Carmichael number, Semiprime, Lazy caterer's sequence, Friendly number, Small set, Cullen number, Abundant number, Perfect totient number, Juggler sequence, Antichain, Perfect power, Pronic number, Superabundant number, Woodall number, Double Mersenne number, Strictly non-palindromic number, Boustrophedon transform, Somos sequence, Lucky number, Highly abundant number, Primary pseudoperfect number, Leyland number, Complete sequence, Weird number, Jacobsthal number, Sociable number, Ban number, Factorion, Giuga number, Almost prime, Primitive permutation group, Superperfect number, Euclid-Mullin sequence, Motzkin number, Untouchable number, Refactorable number, Sphenic number, Thabit number, Carol number, Primorial prime, Blum i...
Written by two well-known scholars in the field,Combinatorial Reasoning: An Introduction to the Art ofCounting presents a clear and comprehensive introduction to theconcepts and methodology of beginning combinatorics. Focusing onmodern techniques and applications, the book develops a variety ofeffective approaches to solving counting problems. Balancing abstract ideas with specific topical coverage, thebook utilizes real world examples with problems ranging from basiccalculations that are designed to develop fundamental concepts tomore challenging exercises that allow for a deeper exploration ofcomplex combinatorial situations. Simple cases are treated firstbefore moving on to general and more advanced cases. Additionalfeatures of the book include: • Approximately 700 carefully structured problems designedfor readers at multiple levels, many with hints and/or shortanswers • Numerous examples that illustrate problem solving usingboth combinatorial reasoning and sophisticated algorithmicmethods • A novel approach to the study of recurrence sequences,which simplifies many proofs and calculations • Concrete examples and diagrams interspersed throughout tofurther aid comprehension of abstract concepts • A chapter-by-chapter review to clarify the most crucialconcepts covered Combinatorial Reasoning: An Introduction to the Art ofCounting is an excellent textbook for upper-undergraduate andbeginning graduate-level courses on introductory combinatorics anddiscrete mathematics.

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