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Basic Set Theory
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
Understanding the Infinite
An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common se...
Axiomatic Set Theory
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Combinatorial and Algorithmic Mathematics
Detailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids Supported by rigorous math and computer science foundations, Combinatorial and Algorithmic Mathematics: From Foundation to Optimization provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as ...
Theoretical Writings
This volume, assembled with the collaboration of the author, presents an outline of Badiou's ambitious system. Starting from the controversial assertion that ontology is mathematics, this volume sets out the theory of the emergence of truths from the singular relationship between a subject and an event. Ranging from startling re-readings of canonical figures (Spinoza, Kant and Hegel) to decisive engagements with poetry, psychoanalysis and radical politics, Theoretical Writings is an indispensable introduction to one of the great thinkers of our time.
Proofs and Fundamentals
“Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a var...
Mathematical Logic and Foundations of Set Theory, Proceedings of an International Colloquium Held Under the Auspices of The Israel Academy of Sciences and Humanities
Mathematical Logic and Foundations of Set Theory, Proceedings of an International Colloquium Held Under the Auspices of The Israel Academy of Sciences and Humanities
The Future of Creation Order
This work provides an overview of attempts to assess the current condition of the concept of creation order within reformational philosophy compared to other perspectives. Focusing on the natural and life sciences, and theology, this first volume of two examines the arguments for and against the beauty, coherence and order shown in the natural world being related to the will or nature of a Creator. It examines the decay of a Deist universe, and the idea of the pre-givenness of norms, laws and structures as challenged by evolutionary theory and social philosophy. It describes the different responses to the collapse of order: that given by Christian philosophy scholars who still argue for the ...
Entropy Demystified
In this unique book, Arieh Ben-Naim invites the reader to experience the joy of appreciating something which has eluded understanding for many years OCo entropy and the Second Law of Thermodynamics. The book has a two-pronged message: first, that the Second Law is not OC infinitely incomprehensibleOCO as commonly stated in textbooks of thermodynamics but can, in fact, be comprehended through sheer common sense; and second, that entropy is not a mysterious quantity that has OC resisted understandingOCO but a simple, familiar and easily comprehensible concept. Written in an accessible style, the book guides the reader through an abundance of dice games and examples from everyday life. The author paves the way for readers to discover for themselves what entropy is, how it changes, and most importantly, why it always changes in one direction in a spontaneous process."
