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Bieske T: Elementary Real Analysis

Elementary Real Analysis

A Practical Introduction

Reliability, Maintenance, and Safety Engineering

Nearly all our safety data collection and reporting systems are backward-looking: incident reports; dashboards; compliance monitoring systems, and so on. This book shows how we can use safety data in a forward-looking, predictive sense. It contains real use cases where organizations have reduced incidents by employing predictive analytics.

Reducing Risk through Modeling and Machine Learning

Predictive Safety Analytics

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

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications.

Summability, Fixed Point Theory and Generalized integrals 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.

A Very Short Introduction

Mathematical Biology

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

Numerical Methods Using MATLAB®, Fifth Edition continues to provide a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors’ approach is to integrate MATLAB with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB. MATLAB graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature. The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB to help researchers analyze a particular outcome. By using MATLAB it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics.

Using MATLAB

Numerical Methods

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

This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.

The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.

This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.

Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Non-Newtonian Sequence Spaces with Applications presents an alternative to the usual calculus based on multiplication instead of addition.

Non-Newtonian Sequence Spaces with 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

Convex Analysis in Polynomial Spaces with Applications

Elementary Real Analysis

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