Copyright Year 2022
ISBN 9780367742294
ISBN 9780367740900 paperback
August 13, 2021 Forthcoming by Chapman and Hall/CRC
360 Pages 43 B/W Illustrations
Mathematics is the basis of casino games, which are the bedrock of a $100 billion/year industry. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette takes an in-depth look at the four biggest table games in casinos: blackjack, baccarat, craps, and roulette. It guides readers through the mathematical principles that underpin these games and their different variations, providing insights that will be of huge interest to gamblers, casino managers, researchers, and students of mathematics.
A valuable teaching resource, replete with exercises, for any course of gambling mathematics
Suitable for a wide audience of professionals, researchers and students
Many practical applications for the gambling industry.
Table of Contents
1. Essential Probability. 1.1. Elementary Ideas. 1.2. Addition and Multiplication Rules. 1.3. Combinatorics. 1.4. Random Variables and Expected Value. 2. Roulette 2.1 Roulette Basics. 2.2. History of Roulette. 2.3. New Wheels. 2.4. Electronic Roulette Games. 2.5. Roulette with Cards. 2.6. Side Bets. 2.7. Roulette Betting Systems. 2.8. Exercises. 3. Craps. 3.1. Craps Basics. 3.2. Hazard. 3.3. Street Craps. 3.4. Crooked Dice. 3.5. Controlled Shooting. 3.6. Variations. 3.7. Card Craps. 3.8. Side Bets. 3.9. Exercises. 4. Baccarat. 4.1. Baccarat Basics. 4.2. Card Counting in Baccarat. 4.3. Variations. 4.4. Side Bets. 4.5. Exercises. 5. Blackjack. 5.1. Blackjack Basics. 5.2. Basic Strategy. 5.3. Card Counting. 5.4. Variations. 5.5. California Games. 5.6. Side Bets. 5.7. Exercises. Answers to Selected Exercises. References.
Author(s)
Mark Bollman is Professor of Mathematics and chair of the Department of Mathematics & Computer Science at Albion College in Albion, Michigan, and has taught 116 different courses in his career. Among these courses is "Mathematics of the Gaming Industry," where mathematics majors carefully study the math behind games of chance and travel to Las Vegas, Nevada, in order to compare theory and practice. He has also taken those ideas into Albion's Honors Program in "Great Issues in Humanities: Perspectives on Gambling," which considers gambling from literary, philosophical, and historical points of view as well as mathematically. Mark has also authored Basic Gambling Mathematics: The Numbers behind The Neon, Mathematics of Keno and Lotteries, and Mathematics of Casino Carnival Games.
Copyright Year 2022
ISBN 9780367774660
August 30, 2021 Forthcoming by Chapman and Hall/CRC
472 Pages 31 B/W Illustrations
Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive self-contained book covering this vibrant new area of pure and applied mathematics in depth.
The book begins with a historic overview, followed by chapters on Clifford- and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists and engineers (signal- and color image processing, electric engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.).
Intuitive real geometric approach to higher-dimensional Fourier transformations
A comprehensive reference, suitable for graduate students and researchers
Includes detailed definitions, properties, and many full step-by-step proofs
Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information.
1. Introduction. 1.1. Brief Historical Notes. 1.2. Quaternion Fourier Transforms (QFT). 1.3. Clifford Fourier Transforms in Clifford’s Geometric Algebra. 1.4. Quaternion and Clifford Wavelets. 2. Clifford Algebra. 2.1. Axioms of Clifford Algebra. 2.2. Quadratic Forms in Clifford’s Geometric Algebra. 2.3. Clifford Product and Derived Products. 2.4. Determinants in Geometric Algebra. 2.5. Gram-Schmidt Orthogonalization in Geometric Algebra. 2.6. Important Clifford Geometric Algebras. 2.7. How Imaginary Numbers Become Real in Clifford Algebras. 2.8. Quaternions and Geometry of Rotations In 3, 4 Dim. 3. Geometric Calculus. 3.1. Introductory Notes on Vector Differential Calculus. 3.2. Brief Overview of Vector Differential Calculus. 3.3. Geometric Algebra for Differential Calculus. 3.4. Vector Differential Calculus. 3.5. Summary on Vector Differential Calculus. 4. Quaternion Fourier Transforms. 4.1. Fundamentals of Quaternion Fourier Transforms (QFT). 4.2. Properties of Quaternion Fourier Transform. 4.3. Special Quaternion Fourier Transforms. 4.4. From QFT To Volume-Time FT, Spacetime FT. 5. Clifford Fourier Transforms. 5.1. Overview of Clifford Fourier Transforms. 5.2. One-Sided Clifford Fourier Transforms. 5.3. Two-Sided Clifford Fourier Transforms. 5.4. Clifford Fourier Transform and Convolution. 5.5. Special Clifford Fourier Transforms. 6. Relating QFTs And CFTs. 6.1. Background. 6.2. General Geometric Fourier Transform. 6.3. CFT Due to Sommen And Bulow. 6.4. Color Image CFT. 6.5. Two-Sided CFT. 6.6. Quaternion Fourier Transform (QFT) 6.7. Quaternion Fourier Stieltjes Transform. 6.8. Quaternion Fourier Mellin Transform, Clifford Fourier Mellin Transform. 6.9. Volume-Time CFT and Spacetime CFT. 6.10. One-Sided CFTs. 6.11. Pseudoscalar Kernel CFTs. 6.12. Quaternion and Clifford Linear Canonical Transforms. 6.13. Summary Interrelationship Of QFTs, CFTs. Appendix A. Square Roots of ?1 MAPLE, Cauchy-Schwarz, Uncertainty Equality. References. Bibliography. Index.
Eckhard Hitzer has a PhD in theoretical physics from the University of
Konstanz (Germany). He has been living in Japan since 1996 (Kyoto University,
University of Fukui, and since 2012 as Senior Associate Professor at International
Christian University [ICU] in Mitaka, Tokyo). He teaches Physics and Mathematics
at ICU. He has published over 100 International Scientific journal papers
and book chapters, is member of the editorial boards of three journals,
author of one book, editor of two books and of 10 special journal issues
and conference proceedings, active member and organizer of many scientific
conference committees and prize committees. He edits the Email newsletter
for everyone interested in Clifford Algebra and Geometric Algebra (GA-Net)
since 2003, and the blog GA-Net Updates since 2012. He works on pure and
applied Clifford (geometric) algebras, with specialization on space group
symmetry in crystallography, neural network and artificial intelligence
applications, and Clifford algebra based integral transformations. He has
been co-organizing the session Quaternion and Clifford Fourier Transforms
and Wavelets at the tri-annual International Conferences on Clifford Algebras
and their Applications since past ten years, and the annual workshop Empowering
Novel Geometric Algebra for Graphics & Engineering (ENGAGE) at the
international conference Computer Graphics International (CGI) since past
five years.
Copyright Year 2022
ISBN 9780367702359
August 16, 2021 Forthcoming by Chapman and Hall/CRC
336 Pages 55 B/W Illustrations
The third edition of this widely popular textbook is authored by a master teacher. This book provides a mathematically rigorous introduction to analysis of real-valued functions of one variable. This intuitive, student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics.
The material is presented clearly and as intuitive as possible while maintaining mathematical integrity. The author supplies the ideas of the proof and leaves the write-up as an exercise. The text also states why a step in a proof is the reasonable thing to do and which techniques are recurrent.
Examples, while no substitute for a proof, are a valuable tool in helping to develop intuition and are an important feature of this text. Examples can also provide a vivid reminder that what one hopes might be true is not always true.
Begins with a discussion of the axioms of the real number system.
The limit is introduced via sequences.
Examples motivate what is to come, highlight the need for hypothesis in a theorem, and make abstract ideas more concrete.
A new section on the Cantor set and the Cantor function.
Additional material on connectedness.
Exercises range in difficulty from the routine "getting your feet wet" types of problems to the moderately challenging problems.
Topology of the real number system is developed to obtain the familiar properties of continuous functions.
Some exercises are devoted to the construction of counterexamples.
The author presents the material to make the subject understandable and perhaps exciting to those who are beginning their study of abstract mathematics.
Preface
Introduction
The Real Number System
Sequences of Real Numbers
Topology of the Real Numbers
Continuous Functions
Differentiation
Integration
Series of Real Numbers
Sequences and Series of Functions
Fourier Series
Bibliography
Hints and Answers to Selected Exercises
Index
James R. Kirkwood holds a Ph.D. from University of Virginia. He has authored fifteen, published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts, Elementary Linear Algebra, Linear Algebra, and Markov Processes, are also published by CRC Press.
Copyright Year 2022
ISBN 9780367720292
July 27, 2021 Forthcoming by Chapman and Hall/CRC
424 Pages 16 Color & 78 B/W Illustrations
Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to arti?cial intelligence and computer science in general.
Introduction to Lattice Theory: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in arti?cial intelligence with focus on pattern recognition, multispectral image analysis, and biomimetic arti?cial neural networks. The book is self-contained and ? depending on the student’s major ? can be used at a senior undergraduate level or a ?rst-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines.
Filled with instructive examples and exercises to help build understanding
Suitable for researchers, professionals and students, both in mathematics and computer science
Every chapter consists of exercises with solution provided online at www.Routledge.com/9780367720292
Table of Contents
1. Elements of Algebra. 1.1. Sets, Functions, and Notations. 1.2. Algebraic Structures. 2. Pertinent Properties of R. 2.2. Elementary Properties of Euclidean Spaces. 3. Lattice Theory. 3.1. Historical Background. 3.2. Partial Orders and Lattices. 3.3. Relations with other branches of Mathematics. 4. Lattice Algebra. 4.1. Lattice Semigroups and Lattice Groups. 4.2. Minimax Algebra. 4.3. Minimax Matrix Theory. 4.4. The Geometry of S(X). 5. Matrix-Based Lattice Associative Memories. 5.1. Historical Background. 5.2. Associative Memories. 6. Extreme Points of Data Sets. 6.1. Relevant Concepts of Convex Set Theory. 6.2. Affine Subsets of EXT(s(X)). 7. Image Unmixing and Segmentation. 7,1, Spectral Endmembers and Linear Unmixing. 7.2. Aviris Hyperspectral Image Examples. 7.3. Endmembers and Clustering Validation Indexes. 7.4. Color Image Segmentation. 8. Lattice-Based Biomimetic Neural Networks. 8.1. Biomimetics Artificial Neural Networks. 8.2. Lattice Biomimetic Neural Networks. 9. Learning in Biomimetic Neural Networks. 9.1 Learning in Single-Layer LBNNS. 9.2. Multi-Layer Lattice Biomimetic Neural Network. Epilogues. Bibliography.
Professor Ritter has written more than 140 research papers in subjects ranging from pure and applied mathematics to pattern recognition, computer vision, and artificial neural networks. He is the founding editor of the Journal of Mathematical Imaging and Vision, and founding member and first chair of the Society for Industrial and Applied Mathematics (SIAM) Activity Group on Imaging Science (SIAG-IS). He was a member of the Deputy Undersecretary of Defense for Research and Advanced Technology’s advanced technology research on emerging technologies panel (1988) and a member of the advanced sensors committee on key technologies for the 1990s, formed by the same undersecretary (1989). Among other U.S. government-requested briefings attended by Professor Ritter were the annual Automatic Target Recognition Working Group (ATRWG) meetings held across the U.S. (1984?1996 and 2003). For his contribution, he was awarded the General Ronald W. Yates Award for Excellence in Technology Transfer by the U.S. Air Force Research Laboratory (1998). Among honors outside the realm of the Department of Defense are the Silver Core Award of the International Federation for Information Processing (1989); the Best Session Award at the American Society for Engineering Education (ASEE) Conference for Industry and Education Collaboration in San Jose, CA (1996); and the Best Paper Presentation Award at the International Joint Conference on Neural Networks (IJCNN) sponsored by the Institute of Electrical and Electronics Engineers Neural Networks Council (IEEE/NNC) and the International Neural Network Society (INNS) in Washington, DC (1999).
Gonzalo Urcid received his Bachelor degree in Communications and Electronic Engineering (1982) and his Master degree in Computational and Information Systems (1985) both from the University of the Americas in Puebla (UDLAP), Mexico. He has a Ph.D. degree (1999) in Optical Sciences from the National Institute of Astrophysics, Optics, and Electronics (INAOE) in Tonantzintla, Mexico and made a postdoctoral residence, between 2001 and 2002, as invited faculty at the CISE Department, University of Florida. Also, from 2001 to 2020 was awarded the distinction of National Researcher from the Mexican National Council of Science and Technology (SNI-CONACYT). Currently is an Associate Professor in the Optics Department at INAOE. His research interests include digital image processing and analysis, artificial neural networks based on lattice algebra, and lattice computing applied to artificial intelligence and pattern recognition.
Copyright Year 2022
ISBN 9780367701109
ISBN 9780367701086(paperback)
August 11, 2021 Forthcoming by Chapman and Hall/CRC
100 Pages 32 B/W Illustrations
For almost every phenomenon in Physics, Chemistry, Biology, Medicine, Economics, and other sciences one can make a mathematical model that can be regarded as a dynamical system. One-Dimensional Dynamical Systems: An Example-Led Approach seeks to deep-dive into α standard maps as an example-driven way of explaining the modern theory of the subject in a way that will be engaging for students.
Example-driven approach
Suitable as supplementary reading for a graduate or advanced undergraduate course in dynamical systems.
Table of Contents
1. Introduction. 2. Rotation Numbers. 2.1. Arnold Tongues for Double Standard Maps. 2.2 Arnold Tongues for ?-Standard Maps. 3. Topological conjugacy. 4. Critical points. 5. Topological theory of Chaos. 5.1. Topological Entropy. 5.2. Schwarzian Derivative. 6. Symbolic Dynamics. 6.1. Kneading Sequences for Double Standard Maps. 6.2 Kneading Sequences for ?-Standard Maps. 7. Tongues. 7.1. Length of Tongues. 7.2. Boundary of The Tongues. 7.3. Tip of the Tongues. 7.4. Connectedness of Tongues. 7.5. Arnold Tongues of Higher Periods for ?-Standard Maps. Bibliography.
Ana Rodrigues is an Associate Professor at the Mathematics Department, University of Exeter. She earned her PhD in Mathematics in Dynamical Systems in 2007 from the University of Porto.
Before arriving at Exeter, she was a postdoc at IUPUI - Indiana University Purdue University at Indianapolis (USA) for two years and then held a Research Assistant position at KTH - Royal Institute of Technology and Uppsala University (Sweden) financed by the Swedish Research Council.
Her research interests are in Dynamical Systems (Low-dimensional dynamical systems, ergodic theory, limit cycles of differential equations and dynamical systems with symmetry).