Practical Foundations of Mathematics PDF Download

Author: Paul Taylor
Publisher: Cambridge University Press
ISBN: 9780521631075
Category : Mathematics
Languages : en
Pages : 590

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Book Description
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.

Author: Robert Harper
Publisher: Cambridge University Press
ISBN: 1107150302
Category : Computers
Languages : en
Pages : 513

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Book Description
This book unifies a broad range of programming language concepts under the framework of type systems and structural operational semantics.

Author: Yves Nievergelt
Publisher: Springer Science & Business Media
ISBN: 146120125X
Category : Mathematics
Languages : en
Pages : 425

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Book Description
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.

Author: Matthias Baaz
Publisher: Cambridge University Press
ISBN: 1139498436
Category : Mathematics
Languages : en
Pages : 541

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Book Description
This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Author: C. K. Raju
Publisher: Pearson Education India
ISBN: 9788131708712
Category : Calculus
Languages : en
Pages : 536

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Book Description
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.

Author: Marcin Trepczyński
Publisher: BRILL
ISBN: 9004445951
Category : Philosophy
Languages : en
Pages : 316

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Book Description
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.

Author: Cathy Canavan-McGrath
Publisher:
ISBN: 9780176502706
Category : Algebra
Languages : en
Pages : 595

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Book Description
This educational resource has been developed by many writers and consultants to bring the very best of mathematics to you.

Author: Kenneth Kunen
Publisher:
ISBN: 9781904987147
Category : Mathematics
Languages : en
Pages : 251

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Book Description
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Author: Dana Center
Publisher: Pearson
ISBN: 9780134192499
Category :
Languages : en
Pages :

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Book Description
NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for Pearson's MyLab & Mastering products may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. "This course is ideal for accelerating students as an alternative to the traditional developmental math sequence and preparing them for a college-level statistics, liberal arts math, or STEM-prep course." "MyMathLab for Foundations for Mathematical Reasoning" is the first in a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways and a supporting student success course. "Foundations for Mathematical Reasoning" is the common starting point for all three mathematics pathways and is designed to build the mathematical skills and understanding necessaryfor success in a quantitative literacy, statistics, or algebra course. "

Author: Robert Harper
Publisher: Cambridge University Press
ISBN: 1316654338
Category : Computers
Languages : en
Pages : 513

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Book Description
This text develops a comprehensive theory of programming languages based on type systems and structural operational semantics. Language concepts are precisely defined by their static and dynamic semantics, presenting the essential tools both intuitively and rigorously while relying on only elementary mathematics. These tools are used to analyze and prove properties of languages and provide the framework for combining and comparing language features. The broad range of concepts includes fundamental data types such as sums and products, polymorphic and abstract types, dynamic typing, dynamic dispatch, subtyping and refinement types, symbols and dynamic classification, parallelism and cost semantics, and concurrency and distribution. The methods are directly applicable to language implementation, to the development of logics for reasoning about programs, and to the formal verification language properties such as type safety. This thoroughly revised second edition includes exercises at the end of nearly every chapter and a new chapter on type refinements.