sets logic and categories springer undergraduate mathematics series

Download Book Sets Logic And Categories Springer Undergraduate Mathematics Series in PDF format. You can Read Online Sets Logic And Categories Springer Undergraduate Mathematics Series here in PDF, EPUB, Mobi or Docx formats.

Sets Logic And Categories

Author : Peter J. Cameron
ISBN : 9781447105893
Genre : Mathematics
File Size : 87. 35 MB
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Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Elements Of Logic Via Numbers And Sets

Author : D.L. Johnson
ISBN : 3540761233
Genre : Mathematics
File Size : 28. 2 MB
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This is an elementary text, aimed at first-year undergraduates, which has been designed to bridge the gap between school and university mathematics and to emphasise the importance of proofs - both how to follow a proof and how to construct a proof. The book lays the foundation for most of the key subjects studied in an undergraduate degree program, and provides numerous exercises and a bibliography with suggestions for further and background reading.

A Course On Mathematical Logic

Author : Shashi Mohan Srivastava
ISBN : 9781461457466
Genre : Mathematics
File Size : 35. 56 MB
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This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

Naive Set Theory

Author : Paul R. Halmos
ISBN : 9780486814872
Genre : Mathematics
File Size : 58. 34 MB
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Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.

Linear Functional Analysis

Author : Bryan Rynne
ISBN : 1848000057
Genre : Mathematics
File Size : 27. 81 MB
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This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality.

Notes On Logic And Set Theory

Author : P. T. Johnstone
ISBN : 0521336929
Genre : Mathematics
File Size : 71. 92 MB
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A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.

Sets For Mathematics

Author : F. William Lawvere
ISBN : 0521010608
Genre : Mathematics
File Size : 23. 33 MB
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In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Introductory Mathematics Algebra And Analysis

Author : Geoffrey C. Smith
ISBN : 9781447106197
Genre : Mathematics
File Size : 87. 83 MB
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This text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a brief introduction to group theory. It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with continuity and functions. The book features numerous exercises of varying difficulty throughout the text.

Sets Logic And Maths For Computing

Author : David Makinson
ISBN : 9781447125006
Genre : Computers
File Size : 36. 90 MB
Format : PDF
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This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

Probability Models

Author : John Haigh
ISBN : 9781447153436
Genre : Mathematics
File Size : 85. 52 MB
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The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This textbook contains many worked examples and several chapters have been updated and expanded for the second edition. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.

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