Elements Of Logic Via Numbers And Sets

Author : D.L. Johnson
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447106036

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Elements of Logic via Numbers and Sets by D.L. Johnson Pdf

In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Author : Roman Kossak
Publisher : Springer Nature
Page : 256 pages
File Size : 49,5 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9783031562150

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Mathematical Logic by Roman Kossak Pdf

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 44,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647

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Set Theory and Logic by Robert R. Stoll Pdf

Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Author : Gareth A. Jones,Josephine M. Jones
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447106135

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Elementary Number Theory by Gareth A. Jones,Josephine M. Jones Pdf

An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Author : Roman Kossak
Publisher : Springer
Page : 186 pages
File Size : 44,8 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319972985

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Mathematical Logic by Roman Kossak Pdf

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Author : Louis F. Roethel,Abraham Weinstein
Publisher : Unknown
Page : 293 pages
File Size : 40,6 Mb
Release : 1972
Category : Mathematics
ISBN : 0534000940

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Logic, Sets, and Numbers by Louis F. Roethel,Abraham Weinstein Pdf

Author : Bryan Rynne,M.A. Youngson
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 50,8 Mb
Release : 2007-12-29
Category : Mathematics
ISBN : 9781848000056

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Linear Functional Analysis by Bryan Rynne,M.A. Youngson Pdf

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.

Author : Zdzislaw Brzezniak,Tomasz Zastawniak
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 44,8 Mb
Release : 2000-07-26
Category : Mathematics
ISBN : 3540761756

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Basic Stochastic Processes by Zdzislaw Brzezniak,Tomasz Zastawniak Pdf

Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

Author : John M. Howie
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447103417

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Real Analysis by John M. Howie Pdf

Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.

Author : Martin D. Crossley
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 40,8 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 1852337826

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Essential Topology by Martin D. Crossley Pdf

This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

Author : Marek Capinski,Peter E. Kopp
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 50,8 Mb
Release : 2004
Category : Mathematics
ISBN : 1852337818

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Measure, Integral and Probability by Marek Capinski,Peter E. Kopp Pdf

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

Author : David F. Parker
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447100195

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Fields, Flows and Waves by David F. Parker Pdf

This book serves as an introduction to the use of mathematics in describing collective phenomena in physics and biology. Derived from a course of innovative lectures, the book shows students early in their studies how many of the topics they have encountered – partial differential equations, differential equations, Fourier series, and linear algebra – are useful in constructing, analysing and interpreting phenomena present in the real world. Throughout, ideas are developed using worked examples and exercises with solution. The text does not assume a strong background in physics.

Author : Geoff Smith,Olga Tabachnikova
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447104612

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Topics in Group Theory by Geoff Smith,Olga Tabachnikova Pdf

The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.

Author : Mícheál O'Searcoid
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 41,6 Mb
Release : 2006-12-26
Category : Mathematics
ISBN : 9781846286278

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Metric Spaces by Mícheál O'Searcoid Pdf

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

Author : Nicholas F. Britton
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447100492

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Essential Mathematical Biology by Nicholas F. Britton Pdf

This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.