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The Forcing Method in Set Theory - Matteo Viale - Bog - Springer International Publishing AG - Plusbog.dk

The Forcing Method in Set Theory - Matteo Viale - Bog - Springer International Publishing AG - Plusbog.dk

The main aim of this book is to provide a compact self-contained presentation of the forcing technique devised by Cohen to establish the independence of the continuum hypothesis from the axioms of set theory. The book follows the approach to the forcing technique via Boolean valued semantics independently introduced by Vopenka and Scott/Solovay; it develops out of notes I prepared for several master courses on this and related topics and aims to provide an alternative (and more compact) account of this topic with respect to the available classical textbooks. The aim of the book is to take up a reader with familiarity with logic and set theory at the level of an undergraduate course on both topics (e.g., familiar with most of the content of introductory books on first-order logic and set theory) and bring her/him to page with the use of the forcing method to produce independence (or undecidability results) in mathematics. Familiarity of the reader with general topology would also be quite helpful; however, the book provides a compact account of all the needed results on this matter. Furthermore, the book is organized in such a way that many of its parts can also be read by scholars with almost no familiarity with first-order logic and/or set theory. The book presents the forcing method outlining, in many situations, the intersections of set theory and logic with other mathematical domains. My hope is that this book can be appreciated by scholars in set theory and by readers with a mindset oriented towards areas of mathematics other than logic and a keen interest in the foundations of mathematics.

DKK 426.00
1

An Introduction to Proofs with Set Theory - Colin Lee - Bog - Springer International Publishing AG - Plusbog.dk

An Introduction to Proofs with Set Theory - Colin Lee - Bog - Springer International Publishing AG - Plusbog.dk

This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid''s algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor''s Paradox, Russel''s Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel''s Incompleteness Theorems.

DKK 519.00
1

Level Set Methods for Fluid-Structure Interaction - Emmanuel Maitre - Bog - Springer International Publishing AG - Plusbog.dk

Level Set Methods for Fluid-Structure Interaction - Emmanuel Maitre - Bog - Springer International Publishing AG - Plusbog.dk

This monograph is devoted to Eulerian models for fluid-structure interaction by applying the original point of view of level set methods. In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction problems. One major advantage compared to more conventional methods such as ALE methods is that they allow the use of a single grid and a single discretization method for the different media. Level set methods in addition provide a general framework to follow the fluid-solid interfaces, to represent the elastic stresses of solids, and to model the contact forces between solids. This book offers a combination of mathematical modeling, aspects of numerical analysis, elementary codes and numerical illustrations, providing the reader with insights into ??the applications and performance of these models. Assuming background at the level of a Master’s degree, Level Set Methods for Fluid-Structure Interaction provides researchers in the fields of numerical analysis of PDEs, theoretical and computational mechanics with a basic reference on the topic. Its pedagogical style and organization make it particularly suitable for graduate students and young researchers.

DKK 816.00
1

Feedback Arc Set - Robert Kudelic - Bog - Springer International Publishing AG - Plusbog.dk

Feedback Arc Set - Robert Kudelic - Bog - Springer International Publishing AG - Plusbog.dk

The main aim of the book is to give a review of all relevant information regarding a well-known and important problem of Feedback Arc Set (FAS). This review naturally also includes a history of the problem, as well as specific algorithms. To this point such a work does not exist: There are sources where one can find incomplete and perhaps untrustworthy information. With this book, information about FAS can be found easily in one place: formulation, description, theoretical background, applications, algorithms etc. Such a compendium will be of help to people involved in research, but also to people that want to quickly acquaint themselves with the problem and need reliable information. Thus research, professional work and learning can proceed in a more streamlined and faster way.

DKK 434.00
1

Quick Hits for Pediatric Emergency Medicine - - Bog - Springer International Publishing AG - Plusbog.dk

Quick Hits for Pediatric Emergency Medicine - - Bog - Springer International Publishing AG - Plusbog.dk

This book covers essential information necessary in diagnosing and treating pediatric patients in the emergency room. A second edition to its successful predecessor, this book addresses that need by placing vital clinical management and algorithms into a quick and simple guidebook that can be accessed within moments from a scrub pocket or white coat. It includes updated chapters from the original table of contents, as well as new chapters that address important topics, such as approaches to domestic violence and child abuse. Though it includes new chapters, it is still an easy, quick access reference that can be used for those facts that are absolutely essential, but are often difficult to remember. Color images and flow charts allow doctors to grasp the essentials quickly, while more detailed explanations are included alongside for trainees. Quick Hits for Pediatric Emergency Medicine, second edition uses updated tips, caveats, drug dosing, and pearlsto assist the provider who may not be familiar with all of the unique nuances of the pediatric population. This is ideal for emergency department physicians, nurses, and trainees including students, residents, and fellows.

DKK 901.00
1

Is ‘Fuzzy Theory’ an Appropriate Tool for Large Size Problems? - Ranjit Biswas - Bog - Springer International Publishing AG - Plusbog.dk

Is ‘Fuzzy Theory’ an Appropriate Tool for Large Size Problems? - Ranjit Biswas - Bog - Springer International Publishing AG - Plusbog.dk

The work in this book is based on philosophical as well as logical views on the subject of decoding the ''progress'' of decision making process in the cognition system of a decision maker (be it a human or an animal or a bird or any living thing which has a brain) while evaluating the membership value µ(x) in a fuzzy set or in an intuitionistic fuzzy set or in any such soft computing set model or in a crisp set. A new theory is introduced called by "Theory of CIFS". The following two hypothesis are hidden facts in fuzzy computing or in any soft computing process :- Fact-1: A decision maker (intelligent agent) can never use or apply ''fuzzy theory'' or any soft-computing set theory without intuitionistic fuzzy system. Fact-2 : The Fact-1 does not necessarily require that a fuzzy decision maker (or a crisp ordinary decision maker or a decision maker with any other soft theory models or a decision maker like animal/bird which has brain, etc.) must be aware or knowledgeable about IFS Theory! The "Theory of CIFS" is developed with a careful analysis unearthing the correctness of these two facts. Two examples of ''decision making problems'' with complete solutions are presented out of which one example will show the dominance of the application potential of intuitionistic fuzzy set theory over fuzzy set theory, and the other will show the converse i.e. the dominance of the application potential of fuzzy set theory over intuitionistic fuzzy set theory in some cases. The "Theory of CIFS" may be viewed to belong to the subjects : Theory of Intuitionistic Fuzzy Sets, Soft Computing, Artificial Intelligence, etc.

DKK 426.00
1