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    https://sophisticatedspectra.com/article/drosia-serenity-a-modern-oasis-in-the-heart-of-larnaca.2521391.html

    DROSIA SERENITY
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    Drosia Serenity is not only an architectural gem but also a highly attractive investment opportunity. Located in the desirable residential area of Drosia, Larnaca, this modern development offers 5–7% annual rental yield, making it an ideal choice for investors seeking stable and lucrative returns in Cyprus' dynamic real estate market. Feel free to check the location on Google Maps.
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    Formal Concept Analysis: Foundations and Applications

    Posted By: AvaxGenius
    Formal Concept Analysis: Foundations and Applications

    Formal Concept Analysis: Foundations and Applications by Bernhard Ganter, Gerd Stumme, Rudolf Wille
    English | PDF (True) | 2005 | 359 Pages | ISBN : 3540278915 | 5.6 MB

    Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. It thereby allows us to mathematically represent, analyze, and construct conceptual structures. The formal concept analysis approach has been proven successful in a wide range of application fields.

    Unequal: The Maths of When Things Do and Don’t Add Up

    Posted By: First1
    Unequal: The Maths of When Things Do and Don’t Add Up

    Unequal: The Maths of When Things Do and Don’t Add Up by Eugenia Cheng
    English | June 5th, 2025 | ISBN: 1805223062 | 400 pages | True EPUB | 4.72 MB

    At first glance, the concept of equality in maths seems unambiguous. When we see the equality sign, we think of 'solving for x' or balancing two sides of an equation or maybe even the many famous equations that make use of this elegant, innocuous symbol.

    Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics

    Posted By: AvaxGenius
    Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics

    Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics by Lorenz Halbeisen , Regula Krapf
    English | PDF (True) | 2020 | 234 Pages | ISBN : 3030522814 | 3.3 MB

    This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers.

    From Boolean Logic to Switching Circuits and Automata: Towards Modern Information Technology (Repost)

    Posted By: AvaxGenius
    From Boolean Logic to Switching Circuits and Automata: Towards Modern Information Technology (Repost)

    From Boolean Logic to Switching Circuits and Automata: Towards Modern Information Technology by Radomir S. Stanković , Jaakko Astola
    English | PDF (True) | 2011 | 212 Pages | ISBN : 3642116817 | 105.6 MB

    Logic networks and automata are facets of digital systems. The change of the design of logic networks from skills and art into a scientific discipline was possible by the development of the underlying mathematical theory called the Switching Theory. The fundamentals of this theory come from the attempts towards an algebraic description of laws of thoughts presented in the works by George J. Boole and the works on logic by Augustus De Morgan.

    Rewriting, Computation and Proof

    Posted By: AvaxGenius
    Rewriting, Computation and Proof

    Rewriting, Computation and Proof: Essays Dedicated to Jean-Pierre Jouannaud on the Occasion of his 60th Birthday by Hubert Comon-Lundh, Claude Kirchner, Hélène Kirchner
    English | PDF (True) | 2007 | 287 Pages | ISBN : 3540731466 | 5.7 MB

    Jean-Pierre Jouannaud has deeply influenced, and is still influencing, research in Informatics, through the many important results he has produced in various research fields and through the generations of scholars he has educated. He has played a leading role in field of rewriting and its technology, advancing the research areas of unification, rewriting and completion modulo, conditional rewriting, termination proofs, modular properties, and automated proofs by induction in rewrite theories. Following his strong interest for algebraic specification languages and their efficient implementation, Jean-Pierre Jouannaud has contributed to the design, semantics and implementation of OBJ2 and has recently augmented the Maude rewriting logic system with an essential feature: membership equational logic. He was a member of the CNU (National University Council) and a member of the CNRS national committee. He is now heading with great success the computer science laboratory at the Ecole Polytechnique thus showing his exceptional qualities as a research team manager and supervisor of students.

    Proof Theory: History and Philosophical Significance

    Posted By: AvaxGenius
    Proof Theory: History and Philosophical Significance

    Proof Theory: History and Philosophical Significance by Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen
    English | PDF | 2000 | 261 Pages | ISBN : 0792365445 | 25.9 MB

    hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math­ ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se­ cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis­ tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.

    Model Theory and Algebraic Geometry

    Posted By: AvaxGenius
    Model Theory and Algebraic Geometry

    Model Theory and Algebraic Geometry by Elisabeth Bouscaren
    English | PDF | 1998 | 223 Pages | ISBN : 3540648631 | 12.1 MB

    Introduction Model theorists have often joked in recent years that the part of mathemat­ ical logic known as "pure model theory" (or stability theory), as opposed to the older and more traditional "model theory applied to algebra" , turns out to have more and more to do with other subjects ofmathematics and to yield gen­ uine applications to combinatorial geometry, differential algebra and algebraic geometry. We illustrate this by presenting the very striking application to diophantine geometry due to Ehud Hrushovski: using model theory, he has given the first proof valid in all characteristics of the "Mordell-Lang conjecture for function fields" (The Mordell-Lang conjecture for function fields, Journal AMS 9 (1996), 667-690). More recently he has also given a new (model theoretic) proof of the Manin-Mumford conjecture for semi-abelian varieties over a number field. His proofyields the first effective bound for the cardinality ofthe finite sets involved (The Manin-Mumford conjecture, preprint). There have been previous instances of applications of model theory to alge­ bra or number theory, but these appl~cations had in common the feature that their proofs used a lot of algebra (or number theory) but only very basic tools and results from the model theory side: compactness, first-order definability, elementary equivalence…

    Proof Theory: An Introduction

    Posted By: AvaxGenius
    Proof Theory: An Introduction

    Proof Theory: An Introduction by Wolfram Pohlers
    English | PDF | 1989 | 220 Pages | ISBN : 3540518428 | 9.4 MB

    Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

    Algebraic Complexity Theory

    Posted By: AvaxGenius
    Algebraic Complexity Theory

    Algebraic Complexity Theory by Peter Bürgisser , Michael Clausen , Mohammad Amin Shokrollahi
    English | PDF | 1997 | 630 Pages | ISBN : 3540605827 | 50.2 MB

    The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro­ posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under­ standing of the intrinsic computational difficulty of problems.

    Adapting Proofs-as-Programs: The Curry--Howard Protocol

    Posted By: AvaxGenius
    Adapting Proofs-as-Programs: The Curry--Howard Protocol

    Adapting Proofs-as-Programs: The Curry–Howard Protocol by Iman Hafiz Poernomo , Martin Wirsing , John Newsome Crossley
    English | PDF (True) | 2005 | 417 Pages | ISBN : 0387237593 | 2.6 MB

    This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was ?rst conceived. At that time, there was a belief that proofs-as-programs had the - tential for practical application to semi-automated software development. I- tial applications were mostly concerned with ?ne-grain, mathematical program synthesis. For various reasons, research interest in the area eventually tended toward more theoretic issues of constructive logic and type theory. However, in recent years, the situation has become more balanced, and there is increasingly active research in applying constructive techniques to industrial-scale, complex software engineering problems. Thismonographdetailsseveralimportantadvancesinthisdirectionofpr- tical proofs-as-programs. One of the central themes of the book is a general, abstract framework for developing new systems of program synthesis by adapting proofs-as-programs to new contexts.

    Problems and Proofs in Numbers and Algebra (Repost)

    Posted By: AvaxGenius
    Problems and Proofs in Numbers and Algebra (Repost)

    Problems and Proofs in Numbers and Algebra by Richard S. Millman , Peter J. Shiue , Eric Brendan Kahn
    English | PDF (True) | 2015 | 230 Pages | ISBN : 331914426X | 1.9 MB

    Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.

    Proofs and Fundamentals: A First Course in Abstract Mathematics

    Posted By: AvaxGenius
    Proofs and Fundamentals: A First Course in Abstract Mathematics

    Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan D. Bloch
    English | PDF (True) | 2011 | 378 Pages | ISBN : 1441971262 | 4.6 MB

    “Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences.

    Concurrency, Graphs and Models: Essays Dedicated to Ugo Montanari on the Occasion of His 65th Birthday

    Posted By: AvaxGenius
    Concurrency, Graphs and Models: Essays Dedicated to Ugo Montanari on the Occasion of His 65th Birthday

    Concurrency, Graphs and Models: Essays Dedicated to Ugo Montanari on the Occasion of His 65th Birthday by Pierpaolo Degano, Rocco Nicola, José Meseguer
    English | PDF (True) | 2008 | 823 Pages | ISBN : 3540686762 | 25.2 MB

    This Festschrift volume, pubished in honor of Ugo Montanari on the occasion of his 65th birthday, contains 43 papers, written by friends and colleagues, all leading scientists in their own right, who congregated at a celebratory symposium held on June 12, 2008, in Pisa. The volume consists of seven sections, six of which are dedicated to the main research areas to which Ugo Montanari has contributed: Graph Transformation; Constraint and Logic Programming; Software Engineering; Concurrency; Models of Computation; and Software Verification. Each of these six sections starts with an introductory paper giving an account of Ugo Montanari’s contribution to the area and describing the papers in the section. The final section consists of a number of papers giving a laudation of Ugo Montanari’s numerous achievements.

    Theory of Finite and Infinite Graphs

    Posted By: AvaxGenius
    Theory of Finite and Infinite Graphs

    Theory of Finite and Infinite Graphs by Dénes König
    English | PDF | 1990 | 430 Pages | ISBN : 1468489739 | 27.2 MB

    To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in 1936. "From Konigsberg to Konig's book" sings the poetess, "So runs the graphic tale . . . " [10]. There were earlier books that took note of graph theory. Veb­ len's Analysis Situs, published in 1931, is about general combinato­ rial topology. But its first two chapters, on "Linear graphs" and "Two-Dimensional Complexes", are almost exclusively concerned with the territory still explored by graph theorists. Rouse Ball's Mathematical Recreations and Essays told, usually without proofs, of the major graph-theoretical advances ofthe nineteenth century, of the Five Colour Theorem, of Petersen's Theorem on I-factors, and of Cayley's enumerations of trees. It was Rouse Ball's book that kindled my own graph-theoretical enthusiasm. The graph-theoretical papers of Hassler Whitney, published in 1931-1933, would have made an excellent textbook in English had they been collected and published as such. But the honour of presenting Graph Theory to the mathe­ matical world as a subject in its own right, with its own textbook, belongs to Denes Konig. Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amuse­ ment, how one mathematician scorned it as "The slums of Topol­ ogy".

    Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

    Posted By: AvaxGenius
    Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

    Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets by Stephen Ernest Rodabaugh, Erich Peter Klement
    English | PDF | 2003 | 468 Pages | ISBN : 1402015151 | 4.6 MB

    This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan­ dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish­ ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand­ book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand­ book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem­ inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti­ eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.