sets logic and categories springer undergraduate mathematics series

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Sets Logic And Categories

Author : Peter J. Cameron
ISBN : 9781447105893
Genre : Mathematics
File Size : 80. 85 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 : 40. 85 MB
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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.

Special Relativity

Author : Nicholas M.J. Woodhouse
ISBN : 9783540466765
Genre : Science
File Size : 51. 60 MB
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Categories And Modules With K Theory In View

Author : A. J. Berrick
ISBN : 0521632765
Genre : Mathematics
File Size : 26. 18 MB
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This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.

Handbook Of Mathematical Induction

Author : David S. Gunderson
ISBN : 9781420093650
Genre : Mathematics
File Size : 52. 33 MB
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Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.

Algebras And Representation Theory

Author : Karin Erdmann
ISBN : 9783319919980
Genre : Mathematics
File Size : 49. 99 MB
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This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

Internationale Mathematische Nachrichten

Author :
ISBN : CORNELL:31924074884572
Genre : Mathematics
File Size : 65. 98 MB
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Naive Mengenlehre

Author : Paul R. Halmos
ISBN : 3525405278
Genre : Arithmetic
File Size : 41. 7 MB
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Mathematical Reviews

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ISBN : UVA:X006089133
Genre : Mathematics
File Size : 64. 53 MB
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Mathematische Modellierung

Author : Christof Eck
ISBN : 9783662543351
Genre : Mathematics
File Size : 39. 66 MB
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Das Lehrbuch bietet eine lebendige und anschauliche Einführung in die mathematische Modellierung von Phänomenen aus den Natur- und Ingenieurwissenschaften. Leser lernen, mathematische Modelle zu verstehen und selbst herzuleiten und finden eine Fülle von Beispielen, u. a. aus den Bereichen chemische Reaktionskinetik, Populationsdynamik, Strömungsdynamik, Elastizitätstheorie und Kristallwachstum. Die Methoden der Linearen Algebra, der Analysis und der Theorie der gewöhnlichen und partiellen Differentialgleichungen werden sorgfältig eingeführt.

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