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Meaning and Existence in Mathematics

Posted By: AvaxGenius
Meaning and Existence in Mathematics

Meaning and Existence in Mathematics by Charles Castonguay
English | PDF | 1972 | 168 Pages | ISBN : 3709171156 | 24.2 MB

The take-over of the philosophy of mathematics by mathematical logic is not complete. The central problems examined in this book lie in the fringe area between the two, and by their very nature will no doubt continue to fall partly within the philosophical re­ mainder. In seeking to treat these problems with a properly sober mixture of rhyme and reason, I have tried to keep philosophical jargon to a minimum and to avoid excessive mathematical compli­ cation. The reader with a philosophical background should be familiar with the formal syntactico-semantical explications of proof and truth, especially if he wishes to linger on Chapter 1, after which it is easier philosophical sailing; while the mathematician need only know that to "explicate" a concept consists in clarifying a heretofore vague notion by proposing a clearer (sometimes formal) definition or formulation for it. More seriously, the interested mathematician will find occasional recourse to EDWARD'S Encyclopedia of Philos­ ophy (cf. bibliography) highly rewarding. Sections 2. 5 and 2. 7 are of interest mainly to philosophers.

Mastering Calculus through Practice: A Study Guide with over 300 Solved Exercises

Posted By: AvaxGenius
Mastering Calculus through Practice: A Study Guide with over 300 Solved Exercises

Mastering Calculus through Practice: A Study Guide with over 300 Solved Exercises by Bárbara de Holanda Maia Teixeira, Edmundo Capelas de Oliveira
English | PDF,EPUB | 2021 | 353 Pages | ISBN : 3030833399 | 21.9 MB

This textbook covers key topics of Elementary Calculus through selected exercises, in a sequence that facilitates development of problem-solving abilities and techniques. It opens with an introduction to fundamental facts of mathematical logic, set theory, and pre-calculus, extending toward functions, limits, derivatives, and integrals. Over 300 solved problems are approached with a simple, direct style, ordered in a way that positively challenges students and helps them build self-confidence as they progress. A special final chapter adds five carefully crafted problems for a comprehensive recap of the work.

Propositional and Predicate Calculus: A Model of Argument

Posted By: AvaxGenius
Propositional and Predicate Calculus: A Model of Argument

Propositional and Predicate Calculus: A Model of Argument by Derek Goldrei
English | PDF(True) | 2005 | 321 Pages | ISBN : 1852339217 | 4.4 MB

At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:
- the representation of mathematical statements by formulas in a formal language;

The Mathematical Experience, Study Edition

Posted By: AvaxGenius
The Mathematical Experience, Study Edition

The Mathematical Experience, Study Edition by Philip J. Davis
English | PDF | 2012 | 522 Pages | ISBN : 0817682945 | 102.8 MB

Winner of the 1983 National Book Award, The Mathematical Experience presented a highly insightful overview of mathematics that effectively conveyed its power and beauty to a large audience of mathematicians and non-mathematicians alike. The study edition of the work followed about a decade later, supplementing the original material of the book with exercises to provide a self-contained treatment usable for the classroom.

New Computational Paradigms: Changing Conceptions of What is Computable

Posted By: AvaxGenius
New Computational Paradigms: Changing Conceptions of What is Computable

New Computational Paradigms: Changing Conceptions of What is Computable by S. Barry Cooper
English | PDF | 2008 | 555 Pages | ISBN : 0387360336 | 5.2 MB

In recent years, classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics. The deep interconnection between "computation" and "proof" has originated much of the most significant work in constructive mathematics and mathematical logic of the last 70 years. Moreover, the increasingly compelling necessity to deal with computability in the real world (such as computing on continuous data, biological computing, and physical models) has brought focus to new paradigms of computation that are based on biological and physical models. These models address questions of efficiency in a radically new way and even threaten to move the so-called Turing barrier, i.e. the line between the decidable and the un-decidable.

Sparse Estimation with Math and Python: 100 Exercises for Building Logic

Posted By: AvaxGenius
Sparse Estimation with Math and Python: 100 Exercises for Building Logic

Sparse Estimation with Math and Python: 100 Exercises for Building Logic by Joe Suzuki
English | PDF,EPUB | 2021 | 254 Pages | ISBN : 9811614377 | 85.5 MB

The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of sparse estimation by considering math problems and building Python programs.

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof

Posted By: AvaxGenius
An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof by Peter B. Andrews
English | PDF | 2002 | 404 Pages | ISBN : 1402007639 | 29.6 MB

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability.

Introduction to Mathematical Logic: Set Theory Computable Functions Model Theory

Posted By: AvaxGenius
Introduction to Mathematical Logic: Set Theory Computable Functions Model Theory

Introduction to Mathematical Logic: Set Theory Computable Functions Model Theory by Jerome Malitz
English | PDF | 1979 | 209 Pages | ISBN : 0387903461 | 16.5 MB

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere­ quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III.

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

Posted By: AvaxGenius
Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by Igor Lavrov
English | PDF | 2003 | 288 Pages | ISBN : 0306477122 | 16.9 MB

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

Cognitive Reasoning: A Formal Approach

Posted By: AvaxGenius
Cognitive Reasoning: A Formal Approach

Cognitive Reasoning: A Formal Approach by Tamás Gergely
English | PDF | 2010 | 424 Pages | ISBN : 354043058X | 4 MB

Dealing with uncertainty, moving from ignorance to knowledge, is the focus of cognitive processes. Understanding these processes and modelling, designing, and building artificial cognitive systems have long been challenging research problems.

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
English | PDF | 2020 | 234 Pages | ISBN : 3030522784 | 3.33 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.

From Peirce to Skolem, Volume 4: A Neglected Chapter in the History of Logic

Posted By: arundhati
From Peirce to Skolem, Volume 4: A Neglected Chapter in the History of Logic

Geraldine Brady, "From Peirce to Skolem, Volume 4: A Neglected Chapter in the History of Logic "
English | ISBN: 044450334X | 2000 | 480 pages | PDF | 20 MB