Sets, Logic and Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sets, Logic and Categories write by Peter J. Cameron. This book was released on 1999-01-22. Sets, Logic and Categories available in PDF, EPUB and Kindle. 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.
Sets, Logic and Categories
Sets, Logic and Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sets, Logic and Categories write by Peter J. Cameron. This book was released on 2012-12-06. Sets, Logic and Categories available in PDF, EPUB and Kindle. 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.
Set Theory and Logic
Set Theory and Logic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Set Theory and Logic write by Robert R. Stoll. This book was released on 2012-05-23. Set Theory and Logic available in PDF, EPUB and Kindle. 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.
An Introduction to the Language of Category Theory
An Introduction to the Language of Category Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to the Language of Category Theory write by Steven Roman. This book was released on 2017-01-05. An Introduction to the Language of Category Theory available in PDF, EPUB and Kindle. This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
Category Theory in Context
Category Theory in Context - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Category Theory in Context write by Emily Riehl. This book was released on 2017-03-09. Category Theory in Context available in PDF, EPUB and Kindle. Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
