Combinatorics, Modeling, Elementary Number Theory: From Basic To Advanced PDF Download
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Author: Ivan V Cherednik
Publisher: World Scientific
ISBN: 9811265410
Category : Mathematics
Languages : en
Pages : 392
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Book Description
This book is mostly based on the author's 25 years of teaching combinatorics to two distinct sets of students: first-year students and seniors from all backgrounds, not just limited to only those majoring in mathematics and physics. The prerequisites are kept to a minimum; essentially, only high school algebra is required. The design is to go from zero knowledge to advanced themes and various applications during a semester of three or three and a half months with quite a few topics intended for research projects and additional reading.This unique book features the key themes of classical introductory combinatorics, modeling (mainly linear), and elementary number theory with a constant focus on applications in statistics, physics, biology, economics, and computer science. These applications include dimers, random walks, binomial and Poisson distributions, games of chance (lottery, dice, poker, roulette), pricing options, population growth, tree growth, modeling epidemic spread, invasion ecology, fission reactors, and networks.A lot of material is provided in the form of relatively self-contained problems, about 135, and exercises, about 270, which are almost always with hints and answers. A systematic introduction to number theory (with complete justifications) is a significant part of the book, including finite fields, Pell's equations, continued fractions, quadratic reciprocity, the Frobenius coin problem, Pisano periods, applications to magic and Latin squares and elements of cryptography. The recurrence relations and modeling play a very significant role, including the usage of Bessel functions for motivated readers. The book contains a lot of history of mathematics and recreational mathematics.
Author: Ivan V Cherednik
Publisher: World Scientific
ISBN: 9811265410
Category : Mathematics
Languages : en
Pages : 392
Get Book Here
Book Description
This book is mostly based on the author's 25 years of teaching combinatorics to two distinct sets of students: first-year students and seniors from all backgrounds, not just limited to only those majoring in mathematics and physics. The prerequisites are kept to a minimum; essentially, only high school algebra is required. The design is to go from zero knowledge to advanced themes and various applications during a semester of three or three and a half months with quite a few topics intended for research projects and additional reading.This unique book features the key themes of classical introductory combinatorics, modeling (mainly linear), and elementary number theory with a constant focus on applications in statistics, physics, biology, economics, and computer science. These applications include dimers, random walks, binomial and Poisson distributions, games of chance (lottery, dice, poker, roulette), pricing options, population growth, tree growth, modeling epidemic spread, invasion ecology, fission reactors, and networks.A lot of material is provided in the form of relatively self-contained problems, about 135, and exercises, about 270, which are almost always with hints and answers. A systematic introduction to number theory (with complete justifications) is a significant part of the book, including finite fields, Pell's equations, continued fractions, quadratic reciprocity, the Frobenius coin problem, Pisano periods, applications to magic and Latin squares and elements of cryptography. The recurrence relations and modeling play a very significant role, including the usage of Bessel functions for motivated readers. The book contains a lot of history of mathematics and recreational mathematics.
Author: Ivan Cherednik
Publisher: World Scientific Publishing Company
ISBN: 9789811265396
Category : Combinatorial analysis
Languages : en
Pages : 0
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Book Description
"A unique textbook devoted to introductory combinatorics, modeling and elementary number theory It is relatively simple to use in the classroom: 1 Chapter is designed for 2 weeks, and the notes can be provided designed for remote teaching or to display in the classroom Some of the advanced topics are good for research projects; the most popular ones in the author's classes were dimers, modeling tree growth, Magic squares and Pisano periods via finite fields Elementary number theory is exposed systematically (with complete proofs and good ones) An impressive collection of about 135 problems and 270 exercises (mostly with hints and answers) It contains a lot of history of mathematics and the games of chance, and many topics traditional in recreational mathematics The book also serves motivated high-school students, teachers of mathematics, and specialists in neighboring fields interested in combinatorics and its applications"--
Author: Ömer Eğecioğlu
Publisher: Springer Nature
ISBN: 3030712508
Category : Mathematics
Languages : en
Pages : 479
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Book Description
This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.
Author: Firuz Kamalov
Publisher: Springer Nature
ISBN: 3031414209
Category : Computer science
Languages : en
Pages : 933
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Book Description
This volume collects the proceedings of the International Conference on Recent Developments in Mathematics (ICRDM), held at Canadian University Dubai, UAE, in August 2022. This is the second of two volumes, with this volume focusing on more applied topics, particularly mathematical modeling and scientific computing, and the first covering recent advances in algebra and analysis. Each chapter identifies existing research problems, the techniques needed to solve them, and a thorough analysis of the obtained results. Advances in Mathematical Modeling and Scientific Computing will appeal to a range of postgraduate students, researchers, and industry professionals interested in exploring recent advancements in applied mathematics.
Author: University of Michigan--Dearborn
Publisher:
ISBN:
Category :
Languages : en
Pages : 312
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Book Description
Author: Peter Jephson Cameron
Publisher: Cambridge University Press
ISBN: 9780521457613
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Author: Albert Edward Ingham
Publisher: Cambridge University Press
ISBN: 9780521397896
Category : Mathematics
Languages : en
Pages : 140
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Book Description
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 0817682228
Category : Mathematics
Languages : en
Pages : 125
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Book Description
"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.
Author: Anonymous
Publisher: BoD – Books on Demand
ISBN: 3385488699
Category :
Languages : en
Pages : 242
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Book Description
Author: William Stein
Publisher: Springer Science & Business Media
ISBN: 0387855254
Category : Mathematics
Languages : en
Pages : 173
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Book Description
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
