A series of rhymes about artists and their works introduces counting and grouping numbers, as well as such artistic styles as cubism, pointillism, and surrealism.
By means of the Zermelo-Fraenkel system, Suppes provides best treatment of axiomatic set theory on upper undergraduate and graduate levels. Topics include relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, more
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it ...
From the Reviews: "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive ...
This book is intended to provide an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then ...
The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of paradoxes that have led many scholars to doubt the soundness of its foundations. The ...
With every click of her camera, Tana Hoban zooms in on a new discovery. Where are there more? Or fewer? Or where is there less? The questions and answers depend on what (and how) one sees.'
If you want top grades and thorough understanding of set theory and related topics, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 530 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed ...
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.
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many ...
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a manner that would to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the Sun by breaking something so small as a pea into a finite number of pieces and putting it ...
In "Infinity and the Mind", Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past ...
How can the infinite, a subject so remote from our finite experience, be an everyday working tool for the working mathematician? Blending history, philosophy, mathematics and logic, Shaughan Lavine answers this question with clarity. An account of the origins of the modern mathematical theory of the infinite, his book is also a defense against the ...
Designed for undergraduate students of set theory, "Classic Set Theory" presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes: The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers; Defining natural numbers in terms of ...
"A Concise Introduction to Pure Mathematics, Second Edition" provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ...
This classic in the field is a compact introduction to some of the basic topics of mathematical logic. Major changes in this edition include a new section on semantic trees; an expanded chapter on Axiomatic Set Theory; and full coverage of effective computability, where Turing computability is now the central notion and diagrams (flow-charts) are ...
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book ...
This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems and special attention is given to the results needed in the theory of functions.
This text is designed as a "transition" textbook to introduce undergraduates to the writing of vigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. It serves as a bridge between computational courses, e.g. calculus, and more theoretical, proofs-oriented courses such as linear ...
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout ...
This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the centre of his exposition resulting in ...
Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from finite sets to cardinal numbers, infinite cardinals, and ordinals. Exercises appear throughout the text, with answers ...
This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a ...
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