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Fel'shtyn A: Dynamical Zeta Functions
Nielsen Theory & Reide

Dynamical Zeta Functions Nielsen Theory & Reide

This comprehensive compendium addresses a critical need in the AI and machine learning era by bridging foundational information theory (IT) concepts with practical applications in statistical learning. Unlike traditional IT textbooks, this volume emphasizes how IT principles, such as entropy and source coding, underpin modern machine learning techniques like cross-entropy, decision trees, and evidence-lower bounds.This unique book connects IT with probabilistic inference, illustrated through real-world applications, such as decoding LDPC codes for error correction. The inclusion of the Lea probabilistic programming package is particularly valuable for pedagogy, offering students a hands-on tool to solve numerical problems and reinforce theoretical concepts.The useful reference text benefits professionals, researchers, academics and students in the fields of calculus and probability, communications and information sciences.

Introduction To Information Theory And Probabilistic Inference, An

Cambridge Monographs on Applied and Computational Mathematics

Cubature rules are indispensable tools in scientific computing and applied sciences whenever evaluating or discretizing integrals is needed. This monograph is the first comprehensive resource devoted to cubature rules in English since Stroud's classic 1971 book, and the first book about minimal cubature rules. The book explores the subject's theoretical side, which intersects with many branches of mathematics. Minimal cubature rules are intimately connected with common zeros of orthogonal polynomials, which can be described via the polynomial ideals and varieties. Many prominent or practical cubature rules are invariant under a finite group, and some involve symmetric functions and the discrete Fourier transform. Based on state-of-the-art research, the book systematically studies Gauss and minimal cubature rules, and includes a chapter on the practical aspects of construction cubature rules on triangles and simplexes. This comprehensive guide is ideal for researchers and advanced graduate students across the computational and applied mathematics community.

Theory and Practice

Minimal Cubature Rules

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author's motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.Features<ul> <li>Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates</li> <li>Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof</li> <li>Draws attention to connections with other areas of mathematics</li> <li>Plenty of exercises for students, both straightforward problems and more in-depth investigations</li> <li>Introduces many concepts that are required in more advanced topics in mathematics</li> </ul>New to the second edition<ul> <li>Complete solutions to all exercises, and hints for the in-depth investigations</li> <li>Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory</li> <li>A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties</li> <li>A thorough correction of typos and errors across all chapters</li> <li>Updates to the bibliography</li> </ul>

A Path into Rigorous Mathematics

Number Systems

De Gruyter Series in Nonlinear Analysis and Applications

Wave, Parabolic and Elliptic Equations on Time Scales

Partial Dynamic Equations

Elements in the Philosophy of Mathematics

This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to Bertrand Russell and the orientation referred to as 'scientific philosophy' that was active between 1850 and 1930. To give a better sense of the field, the Element further contains two examples of topics studied, that of mathematical structuralism and visual thinking in mathematics. These are in part presented from a methodological point of view, focussing on mathematics as an activity and questions related to how mathematics develops. In addition, the Element contains several examples from mathematics, both historical and contemporary , to illustrate and support the philosophical points.

Introducing the Philosophy of Mathematical Practice

De Gruyter Textbook

Implications of Natural-Language Sentences and All Logical Paradoxes Solved

Information-Oriented Logic

Theory of Stochastic Integrals aims to provide an answer to the problem of phenomena that cannot be analyzed through the classical Itô theory by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales.

Theory of Stochastic Integrals

Textbooks in Mathematics

This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.

Measure Theory and Fine Properties of Functions

This edited volume from mathematical modelling experts employs a structured approach to showcase the latest research and provide a comprehensive guide to the principles, techniques, and practical applications of mathematical modelling in the fields of engineering and the physical sciences.

Practical Examples and Case Studies

Mathematical Modelling for Engineering and Physical Applications

Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula. Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

Generalized Quantum Calculus with Applications

Very Short Introductions

Mathematical biology develops models which are applied to processes in biology and medicine. Philip K. Maini describes the art of modelling, what it is, why we do it.

Dynamical Zeta Functions Nielsen Theory & Reide

Informations bibliographiques

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