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Practical Foundations of Mathematics by Paul Taylor Pdf
This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.
Foundations of Logic and Mathematics by Yves Nievergelt Pdf
This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Practical Foundations of Business System Specifications by Haim Kilov,Ken Baclavski Pdf
"In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. " Roger Bacon (1214?-1294?) "Mathematics-the art and science of effective reasoning. " E. W. Dijkstra, 1976 "A person who had studied at a good mathematical school can do anything. " Ye. Bunimovich, 2000 This is the third book published by Kluwer based on the very successful OOPSLA workshops on behavioral semantics (the first two books were published in 1996 [KH 1996] and 1999 [KRS 1999]). These workshops fostered precise and explicit specifications of business and system semantics, independently of any (possible) realization. Some progress has been made in these areas, both in academia and in industry. At the same time, in too many cases only lip service to elegant specifica tions of semantics has been provided, and as a result the systems we build or buy are all too often not what they are supposed to be. We used to live with that, and quite often users relied on human intermediaries to "sort the things out. " This approach worked perfectly well for a long time.
Philosophical Approaches to the Foundations of Logic and Mathematics by Marcin Trepczyński Pdf
Philosophical Approaches to the Foundations of Logic and Mathematics consists of eleven articles addressing various aspects of the "roots" of logic and mathematics, their basic concepts and the mechanisms that work in the practice of their use.
Cultural Foundations of Mathematics by C. K. Raju Pdf
The Volume Examines, In Depth, The Implications Of Indian History And Philosophy For Contemporary Mathematics And Science. The Conclusions Challenge Current Formal Mathematics And Its Basis In The Western Dogma That Deduction Is Infallible (Or That It Is Less Fallible Than Induction). The Development Of The Calculus In India, Over A Thousand Years, Is Exhaustively Documented In This Volume, Along With Novel Insights, And Is Related To The Key Sources Of Wealth-Monsoon-Dependent Agriculture And Navigation Required For Overseas Trade - And The Corresponding Requirement Of Timekeeping. Refecting The Usual Double Standard Of Evidence Used To Construct Eurocentric History, A Single, New Standard Of Evidence For Transmissions Is Proposed. Using This, It Is Pointed Out That Jesuits In Cochin, Following The Toledo Model Of Translation, Had Long-Term Opportunity To Transmit Indian Calculus Texts To Europe. The European Navigational Problem Of Determining Latitude, Longitude, And Loxodromes, And The 1582 Gregorian Calendar-Reform, Provided Ample Motivation. The Mathematics In These Earlier Indian Texts Suddenly Starts Appearing In European Works From The Mid-16Th Century Onwards, Providing Compelling Circumstantial Evidence. While The Calculus In India Had Valid Pramana, This Differed From Western Notions Of Proof, And The Indian (Algorismus) Notion Of Number Differed From The European (Abacus) Notion. Hence, Like Their Earlier Difficulties With The Algorismus, Europeans Had Difficulties In Understanding The Calculus, Which, Like Computer Technology, Enhanced The Ability To Calculate, Albeit In A Way Regarded As Epistemologically Insecure. Present-Day Difficulties In Learning Mathematics Are Related, Via Phylogeny Is Ontogeny , To These Historical Difficulties In Assimilating Imported Mathematics. An Appendix Takes Up Further Contemporary Implications Of The New Philosophy Of Mathematics For The Extension Of The Calculus, Which Is Needed To Handle The Infinities Arising In The Study Of Shock Waves And The Renormalization Problem Of Quantum Field Theory.
The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations by A. K. Aziz Pdf
The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.
Foundations of Mathematics by Carole Skinner,Judith Dancer Pdf
Foundations of Mathematics outlines seven strands of practice which underpin successful mathematical development inchildren aged 3-7. Early years mathematics specialists, Carole and Judith, draw on their experience of working with early years practitioners, including consultants and advisers, across the UK and internationally. The book is completely up-to-date and embeds the Revised Early Years Foundation Stage throughout the book. The book brims with multi-sensory ideas that will trigger children's curiosity, measuring using sand mousse, hunting for buried treasure and building secret dens outdoors. There are: - activities that involve playing and exploring,- games to make learning active, and- experiences to develop creative and critical thinking. Alongside these practical experiences and activities are clear explanations of the reasoning behind the ideas with clear guidance on the role of the practitioner and 'Home Challenges' to promote the engagement of families. The authors provide straightforward advice to support the development of a mathematically-enriched learning environment and ideas to help children transfer learning into their own child-initiated play, to build a genuine and solid foundation for mathematics.
Foundations of Mathematical Logic by Haskell Brooks Curry Pdf
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.
Foundations for the Future in Mathematics Education by Richard A. Lesh,Eric Hamilton,James J. Kaput Pdf
The central question addressed in Foundations for the Future in Mathematics Education is this: What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that are emphasized in mathematics classrooms and tests, and those that are needed for success beyond school in the 21st century? This is an urgent question. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem-solving activities has changed dramatically during the past twenty years, as powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields. For K-12 students and teachers, questions about the changing nature of mathematics (and mathematical thinking beyond school) might be rephrased to ask: If the goal is to create a mathematics curriculum that will be adequate to prepare students for informed citizenship—as well as preparing them for career opportunities in learning organizations, in knowledge economies, in an age of increasing globalization—how should traditional conceptions of the 3Rs be extended or reconceived? Overall, this book suggests that it is not enough to simply make incremental changes in the existing curriculum whose traditions developed out of the needs of industrial societies. The authors, beyond simply stating conclusions from their research, use results from it to describe promising directions for a research agenda related to this question. The volume is organized in three sections: *Part I focuses on naturalistic observations aimed at clarifying what kind of “mathematical thinking” people really do when they are engaged in “real life” problem solving or decision making situations beyond school. *Part II shifts attention toward changes that have occurred in kinds of elementary-but-powerful mathematical concepts, topics, and tools that have evolved recently—and that could replace past notions of “basics” by providing new foundations for the future. This section also initiates discussions about what it means to “understand” the preceding ideas and abilities. *Part III extends these discussions about meaning and understanding—and emphasizes teaching experiments aimed at investigating how instructional activities can be designed to facilitate the development of the preceding ideas and abilities. Foundations for the Future in Mathematics Education is an essential reference for researchers, curriculum developers, assessment experts, and teacher educators across the fields of mathematics and science education.
Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.