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Finitely Presented Groups
This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
Discrete, Finite and Lie Groups
In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.
Applications of Complex Variables
The subject of applied complex variables is so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the more specialized topics that are less commonplace. The book represents a one-stop reference for complex variables in engineering analysis. The applications of conformal mapping in this book are significantly more extensive than in other AEM textbooks. The treatments of complex integral transforms enable a much larger class of functions that can be transformed, resulting in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotics of complex integrals enables the analysis of models with irregular singular points. The book, which has more than 300 illustrations, is generous with realistic example problems.
Nonstandard Analysis
Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard an...
Commutative Algebra
The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner...
Organized Collapse: An Introduction to Discrete Morse Theory
Applied topology is a modern subject which emerged in recent years at a crossroads of many methods, all of them topological in nature, which were used in a wide variety of applications in classical mathematics and beyond. Within applied topology, discrete Morse theory came into light as one of the main tools to understand cell complexes arising in different contexts, as well as to reduce the complexity of homology calculations. The present book provides a gentle introduction into this beautiful theory. Using a combinatorial approach—the author emphasizes acyclic matchings as the central object of study. The first two parts of the book can be used as a stand-alone introduction to homology, ...
Numerical Methods with Python
Introduces students to appropriate use of computer programming within the scientific disciplines using Python. Discusses several common applications of programming and implementation using real world examples and hands on programming exercises. Students learn how to model situations such as image recognition, medical diagnosis, spread of disease, and others. The text could be used by students and lecturers for courses in Python, Numerical Methods, or as a first course in Data Science.
Languages and Automata
This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.
Gauss Hypergeometric Function
This book presents a novel journey of the Gauss hypergeometric function and contains the different versions of the Gaussian hypergeometric function, including its classical version. In particular, the $q$-Gauss or basic Gauss hypergeometric function, Gauss hypergeometric function with matrix arguments, Gauss hypergeometric function with matrix parameters, the matrix-valued Gauss hypergeometric function, the finite field version, the extended Gauss hypergeometric function, the $(p, q)$- Gauss hypergeometric function, the incomplete Gauss hypergeometric function and the discrete analogue of Gauss hypergeometric function. All these forms of the Gauss hypergeometric function and their properties are presented in such a way that the reader can understand the working algorithm and apply the same for other special functions. This book is useful for UG and PG students, researchers and faculty members working in the field of special functions and related areas.
