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Triesch E: Diskrete Mathematik

Diskrete Mathematik

Theorie und Werkzeuge zur Lösung von Abzähl- und Existenzproblemen

Professional Practice in Governance and Public Organizations

From Administrative Sources to Public Value

Data-Driven Learning in the EU

Universitext

The theory of elliptic functions and modular forms is rich and storied, though it has a reputation for difficulty. In this textbook, the authors successfully bridge foundational concepts and advanced material. Following Weierstrass’s approach to elliptic functions, they also cover elliptic curves and complex multiplication. The sections on modular forms, which can be read independently, include discussions of Hecke operators and Dirichlet series. Special emphasis is placed on theta series, with some advanced results included. With detailed proofs and numerous exercises, this book is well-suited for self-study or use as a reference. A companion website provides videos and a discussion forum on the topic.

Elliptic Functions and Modular Forms

Lecture Notes in Networks and Systems

This book reports on cutting-edge theories and methods for analyzing complex systems, such as transportation and communication networks and discusses multi-disciplinary approaches to dependability problems encountered when dealing with complex systems in practice. It presents the most relevant findings discussed at the 24th International Multidisciplinary Conference on Reliability and Statistics in Transportation and Communication (RelStat 2024), which took place as a hybrid event on September 25-28, 2024,&nbsp;in/from Riga, Latvia. The chapters span a broad spectrum of advanced theories and methods, with a special emphasis on smart technologies and algorithms for enhancing sustainability and resilience of transport systems in various sectors.

Selected Papers from the 24th International Multidisciplinary Conference on Reliability and Statistics in Transportation and Communication, RelStat-2024, Riga, Latvia, September 25-28, 2024

Reliability and Statistics in Transportation and Communication: Human Sustainability and Resilience in the Digital Age

Mathematical Methods, Econometrics, and Data Science

Discrete Choice Models

Elements in the Philosophy of Mathematics

Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are equal. The second argument is called 'the Mapping Argument' and relies on the assumption that if one thing is mapped/ superposed upon another thing and neither exceeds the other, the two things are equal to each other. Although these arguments were initially proposed in the context of discussions against the possibility of infinities, they have played pivotal roles in the historical evolution of the notion of INFINITIES OF DIFFERENT SIZES.

This Element explores medieval arguments for the impossibility of infinity, focusing on the early stages of the development of the notion of 'infinities of different sizes'. The Equality Argument and Mapping Argument, initially proposed in opposition to infinity, have played significant roles in the historical evolution of this concept.

Medieval Finitism

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fields This book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

Mathematics in Cybersecurity

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence empowers qualitative and mixed methods researchers in the data science movement by offering no-code, cost-free software access so that they can apply cutting-edge and innovative methods to synthetize qualitative data. The book builds on the idea that qualitative and mixed methods researchers should not have to learn to code to benefit from rigorous open-source, cost-free software that uses artificial intelligence, machine learning, and data visualization tools-just as people do not need to know C++ or TypeScript to benefit from Microsoft Word. The real barrier is the hundreds of R code lines required to apply these concepts to their databases. By removing the coding proficiency hurdle, this book will empower their research endeavors and help them become active members of and contributors to the applied data science community. The book offers a comprehensive explanation of data science and machine learning methodologies, along with access to software application tools to implement these techniques without any coding proficiency. The book addresses the need for innovative tools that enable researchers to tap into the insights that come out of cutting-edge data science tools with absolutely no computer language literacy requirements.

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence

Compendium of Essential Formulas

Statistics for Business and Economics

Compact Textbooks in Mathematics

This textbook offers a comprehensive introduction to quasi-Monte Carlo methods and several of their applications. Throughout, the authors use modern concepts and notations to provide an overview of how the theory behind quasi-Monte Carlo methods developed. While the main focus of this text is on the theory, it also explores several applications with a particular emphasis on financial problems.
This second edition contains substantial revisions and additions, including several new sections that more thoroughly cover weighted problems. New sections include coverage of the weighted Koksma-Hlawka inequality, weighted discrepancy of lattice point sets and tractability properties, polynomial lattice point sets, and more. In addition, the authors have corrected minor errors from the first edition and updated the bibliography and "Further reading" sections.
Introduction to Quasi-Monte Carlo Integration and Applications&nbsp;is suitable for advanced undergraduate students in mathematics and computer science. Readers should possess a basic knowledge of algebra, calculus, linear algebra, and probability theory. It may also be used for self-study or as a reference for researchers interested in the area.

Introduction to Quasi-Monte Carlo Integration and Applications

Computer Science Foundations and Applied Logic

Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources.&nbsp; Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction.&nbsp; This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises.&nbsp; Among topics addressed:&nbsp;•	In which order may actions may be generated and scheduled?&nbsp;•	What states and configurations may be reached in a concurrent system?&nbsp;•	Which interesting classes of systems can be analysed relatively efficiently?&nbsp;•	Is it possible to synthesise a system of some class from its behaviour?&nbsp;•	How can systems be represented algebraically, compositionally, and concisely?&nbsp; &nbsp;This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical—as well as in practical—aspects of Petri nets and related system models.&nbsp; Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources.&nbsp;Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction.&nbsp; This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises.&nbsp; Among topics addressed:&nbsp;• In which order may actions may be generated and scheduled?&nbsp;• What states and configurations may be reached in a concurrent system?&nbsp;• Which interesting classes of systems can be analysed relatively efficiently?&nbsp;• Is it possible to synthesise a system of some class from its behaviour?&nbsp;• How can systems be represented algebraically, compositionally, and concisely?&nbsp; This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical—as well as in practical—aspects of Petri nets and related system models.&nbsp; Eike Best&nbsp;has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany.&nbsp;Raymond Devillers&nbsp;has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

A Compendium on the Core Model, Analysis, and Synthesis

Petri Net Primer

Mathematical Sciences Research Institute Publications

This edited volume surveys Richman bidding combinatorial games, classical subtraction games and absolute additive theory. The recurring list of open problems, updated and annotated, will interest all practitioners of CGT and related fields including algebra, computer science, combinatorics, number theory and classical game theory.

Games of No Chance 6

Diskrete Mathematik

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