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Author: Shaun Ault
Publisher: Springer Nature
ISBN: 3030266966
Category : Mathematics
Languages : en
Pages : 142
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Book Description
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.
Author: Shaun Ault
Publisher: Springer Nature
ISBN: 3030266966
Category : Mathematics
Languages : en
Pages : 142
Get Book Here
Book Description
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.
Author: Chunwei Song
Publisher: CRC Press
ISBN: 1040123414
Category : Mathematics
Languages : en
Pages : 120
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Book Description
This book endeavors to deepen our understanding of lattice path combinatorics, explore key types of special sequences, elucidate their interconnections, and concurrently champion the author's interpretation of the “combinatorial spirit”. The author intends to give an up-to-date introduction to the theory of lattice path combinatorics, its relation to those special counting sequences important in modern combinatorial studies, such as the Catalan, Schröder, Motzkin, Delannoy numbers, and their generalized versions. Brief discussions of applications of lattice path combinatorics to symmetric functions and connections to the theory of tableaux are also included. Meanwhile, the author also presents an interpretation of the "combinatorial spirit" (i.e., "counting without counting", bijective proofs, and understanding combinatorics from combinatorial structures internally, and more), hoping to shape the development of contemporary combinatorics. Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective will appeal to graduate students and advanced undergraduates studying combinatorics, discrete mathematics, or computer science.
Author: William Holderbaum
Publisher: Springer Nature
ISBN: 303091352X
Category : Technology & Engineering
Languages : en
Pages : 179
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Book Description
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.
Author: University of Michigan. College of Engineering
Publisher: UM Libraries
ISBN:
Category : Engineering schools
Languages : en
Pages : 422
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 810
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Book Description
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 46
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Book Description
Author:
Publisher:
ISBN:
Category : Automatic control
Languages : en
Pages :
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Book Description
Author: George Gasper
Publisher:
ISBN: 0511889186
Category : Mathematics
Languages : en
Pages : 456
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Book Description
Significant revision of classic reference in special functions.
Author: University of Michigan. College of Engineering
Publisher:
ISBN:
Category : Catalogs, College
Languages : en
Pages : 412
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Book Description
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.
