Set Theory And Its Applications In Physics And Computing - 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 Its Applications In Physics And Computing write by Yair Shapira. This book was released on 2022-06-24. Set Theory And Its Applications In Physics And Computing available in PDF, EPUB and Kindle. Why learn set theory? This book provides the answer — it is interesting, and also useful! Taking a new approach and looking from a fresh perspective, the discussion flows in a friendly and transparent way, supplemented with a lot of examples and figures. This makes the theory easily comprehensible: the proofs get vivid and visual, enveloped with interesting applications for students in (applied) math, physics, and engineering. Given the theory and the applications, the book could serve as a textbook in four (undergraduate) math courses: Introduction to set theory and its application; Chaos theory and stability — a geometrical point of view; Functional analysis — Han-Banach theory; and Cryptography with quantum computing. It teaches set theory from the basics, including the axiom of choice, the well ordering theorem, and Zorn's lemma. Furthermore, it uses Cantor's set to introduce chaos theory from a geometrical point of view. Moreover, it introduces the binomial formula (and other related formulas), and uses them in quantum statistical mechanics. And finally, it uses Zorn's lemma in functional analysis, general relativity, and quantum mechanics. There are also practical applications in cryptography, error correction, quantum computing and programming.
Basic Category Theory for Computer Scientists
Basic Category Theory for Computer Scientists - 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 Basic Category Theory for Computer Scientists write by Benjamin C. Pierce. This book was released on 1991-08-07. Basic Category Theory for Computer Scientists available in PDF, EPUB and Kindle. Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Notes on Set Theory
Notes on Set 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 Notes on Set Theory write by Yiannis Moschovakis. This book was released on 2013-04-17. Notes on Set Theory available in PDF, EPUB and Kindle. What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Soft Sets
Soft Sets - 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 Soft Sets write by Sunil Jacob John. This book was released on 2020-10-01. Soft Sets available in PDF, EPUB and Kindle. This book offers a self-contained guide to the theory and main applications of soft sets. It introduces readers to the basic concepts, the algebraic and topological structures, as well as hybrid structures, such as fuzzy soft sets and intuitionistic fuzzy sets. The last part of the book explores a range of interesting applications in the fields of decision-making, pattern recognition, and data science. All in all, the book provides graduate students and researchers in mathematics and various applied science fields with a comprehensive and timely reference guide to soft sets.
Relational Mathematics
Relational Mathematics - 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 Relational Mathematics write by Gunther Schmidt. This book was released on 2011. Relational Mathematics available in PDF, EPUB and Kindle. Relational mathematics is to operations research and informatics what numerical mathematics is to engineering: it is intended to help modelling, reasoning, and computing. Its applications are therefore diverse, ranging from psychology, linguistics, decision aid, and ranking to machine learning and spatial reasoning. Although many developments have been made in recent years, they have rarely been shared amongst this broad community of researchers. This comprehensive 2010 overview begins with an easy introduction to the topic, assuming a minimum of prerequisites; but it is nevertheless theoretically sound and up to date. It is suitable for applied scientists, explaining all the necessary mathematics from scratch using a multitude of visualised examples, via matrices and graphs. It ends with tangible results on the research level. The author illustrates the theory and demonstrates practical tasks in operations research, social sciences and the humanities.
