Counting Lattice Paths Using Fourier Methods

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Counting Lattice Paths Using Fourier Methods

Author : Shaun Ault
Publisher : Springer Nature
ISBN 13 : 3030266966
Total Pages : 136 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Counting Lattice Paths Using Fourier Methods by : Shaun Ault

Download or read book Counting Lattice Paths Using Fourier Methods written by Shaun Ault and published by Springer Nature. This book was released on 2019-08-30 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a previously unexplored connection between combinatorics and Fourier analysis, this method will allow readers to move to higher-dimensional lattice path problems with ease. The technique is carefully developed in the first three chapters using the algebraic properties of the DFT, moving from one-dimensional problems to higher dimensions. In the following chapter, the discussion turns to geometric properties of the DFT in order to study the corridor state space. Each chapter poses open-ended questions and exercises to prompt further practice and future research. Two appendices are also provided, which cover complex variables and non-rectangular lattices, thus ensuring the text will be self-contained and serve as a valued reference. Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics. Instructors will also find this a valuable resource for use in their seminars. Readers should have a firm understanding of calculus, including integration, sequences, and series, as well as a familiarity with proofs and elementary linear algebra.

2nd IMA Conference on Mathematics of Robotics

Author : William Holderbaum
Publisher : Springer Nature
ISBN 13 : 303091352X
Total Pages : 179 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis 2nd IMA Conference on Mathematics of Robotics by : William Holderbaum

Download or read book 2nd IMA Conference on Mathematics of Robotics written by William Holderbaum and published by Springer Nature. This book was released on 2021-11-20 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the mathematical depth and sophistication of techniques used in different areas of robotics. Each chapter is a peer-reviewed version of a paper presented during the 2021 IMA Conference on the Mathematics of Robotics, held online September 8–10, 2021. The conference gave a platform to researchers with fundamental contributions and for academic and to share new ideas. The book illustrates some of the current interest in advanced mathematics and robotics such as algebraic geometry, tropical geometry, monodromy and homotopy continuation methods applied to areas such as kinematics, path planning, swam robotics, dynamics and control. It is hoped that the conference and this publications will stimulate further related mathematical research in robotics.

Fourier Methods for Mathematicians, Scientists and Engineers

Author : Mark Cartwright
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Fourier Methods for Mathematicians, Scientists and Engineers by : Mark Cartwright

Download or read book Fourier Methods for Mathematicians, Scientists and Engineers written by Mark Cartwright and published by . This book was released on 1990 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux

Author : Christian Krattenthaler
Publisher :
ISBN 13 : 9781470401313
Total Pages : 109 pages
Book Rating : 4.4/5 (13 download)

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Book Synopsis The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux by : Christian Krattenthaler

Download or read book The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux written by Christian Krattenthaler and published by . This book was released on 1995 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:

College of Engineering

Author : University of Michigan. College of Engineering
Publisher : UM Libraries
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis College of Engineering by : University of Michigan. College of Engineering

Download or read book College of Engineering written by University of Michigan. College of Engineering and published by UM Libraries. This book was released on 1990 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Annales de l'Institut Fourier

Author :
Publisher :
ISBN 13 :
Total Pages : 498 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Annales de l'Institut Fourier by :

Download or read book Annales de l'Institut Fourier written by and published by . This book was released on 2005 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Current Index to Statistics, Applications, Methods and Theory

Author :
Publisher :
ISBN 13 :
Total Pages : 810 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :

Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1996 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Referativnyĭ zhurnal

Author :
Publisher :
ISBN 13 :
Total Pages : 632 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Referativnyĭ zhurnal by :

Download or read book Referativnyĭ zhurnal written by and published by . This book was released on 1987 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability Theory Subject Indexes from Mathematical Reviews

Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 492 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Probability Theory Subject Indexes from Mathematical Reviews by : American Mathematical Society

Download or read book Probability Theory Subject Indexes from Mathematical Reviews written by American Mathematical Society and published by . This book was released on 1987 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computer & Control Abstracts

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computer & Control Abstracts by :

Download or read book Computer & Control Abstracts written by and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Nature of Computation

Author : Cristopher Moore
Publisher : OUP Oxford
ISBN 13 : 0191552763
Total Pages : 1004 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Nature of Computation by : Cristopher Moore

Download or read book The Nature of Computation written by Cristopher Moore and published by OUP Oxford. This book was released on 2011-08-12 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

Basic Hypergeometric Series

Author : George Gasper
Publisher :
ISBN 13 : 0511889186
Total Pages : 456 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis Basic Hypergeometric Series by : George Gasper

Download or read book Basic Hypergeometric Series written by George Gasper and published by . This book was released on 2011-02-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant revision of classic reference in special functions.

Computing the Continuous Discretely

Author : Matthias Beck
Publisher : Springer
ISBN 13 : 1493929690
Total Pages : 295 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Computing the Continuous Discretely by : Matthias Beck

Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

Analytic Combinatorics in Several Variables

Author : Robin Pemantle
Publisher : Cambridge University Press
ISBN 13 : 1107031575
Total Pages : 395 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Analytic Combinatorics in Several Variables by : Robin Pemantle

Download or read book Analytic Combinatorics in Several Variables written by Robin Pemantle and published by Cambridge University Press. This book was released on 2013-05-31 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.

College of Engineering (University of Michigan) Publications

Author : University of Michigan. College of Engineering
Publisher :
ISBN 13 :
Total Pages : 412 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis College of Engineering (University of Michigan) Publications by : University of Michigan. College of Engineering

Download or read book College of Engineering (University of Michigan) Publications written by University of Michigan. College of Engineering and published by . This book was released on 1990 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Also contains brochures, directories, manuals, and programs from various College of Engineering student organizations such as the Society of Women Engineers and Tau Beta Pi.

Quantum Dissipative Systems

Author : Ulrich Weiss
Publisher : World Scientific
ISBN 13 : 9812791795
Total Pages : 527 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Quantum Dissipative Systems by : Ulrich Weiss

Download or read book Quantum Dissipative Systems written by Ulrich Weiss and published by World Scientific. This book was released on 2008 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book OCo originally published in 1990 and republished in 1999 as an enlarged second edition OCo delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments. In this third edition, 26 chapters from the second edition contain additional material and several chapters are completely rewritten. It deals with the phenomena and theory of decoherence, relaxation, and dissipation in quantum mechanics that arise from the interaction with the environment. In so doing, a general path integral description of equilibrium thermodynamics and nonequilibrium dynamics is developed. Sample Chapter(s). Introduction (262 KB). Contents: General Theory of Open Quantum Systems; Few Sample Applications; Quantum Statistical Decay; The Dissipative Two-State System; The Dissipative Multi-State System. Readership: Advanced undergraduate and graduate students as well as researchers in quantum-statistical and condensed matter physics, quantum/classical mechanics, quantum information and computation, and quantum optics."