|You are here: Home / Shop / Product Detail Page|
Roads to Infinity: The Mathematics of Truth and Proof (Hardback)
"While many popular books have been written on the advances in our understanding of infinity, sparked by the set theory of Georg Cantor in the 1870s and incompleteness theorems of Kurt Gödel in the 1930s, such books generally dwell on a single aspect of either set theory or logic. The aim of this book is to explain the whole, in which set theory interacts with logic, and both begin to affect mainstream mathematics (the latter being quite a recent development, not yet given much space in popular accounts)." — From the dust jacket's inside front flap
Need More Info?Please contact us if you've got questions about this product.
LIKE NEW: This book and its dust jacket are in excellent, like-new condition.
Continued from the dust jacket: “In Roads to Infinity, award-winning author John Stillwill explores the consequences of accepting infinity, which are rich and surprising. The read needs very little background beyond high school mathematics, but should have a willingness to grapple with alien ideas. Stillwell’s style eases the reader into the technicalities of set theory and logic by tracing a single thread in each chapter, beginning with a natural mathematical question and following a sequence of historic responses to that question. Each response typically leads to new questions, and from them new concepts and theorems emerge. At the end of each chapter a section called ‘Historical Background’ situates the thread in a bigger picture of mathematics and its history.
“By following this path, key ideas are presented first, then revisited and reinforced by showing a wider view. Some readers, however, may be impatient to get to the core theorems and will skip the historical background sections, at least at first reading. Others, in search of a big picture from the beginning, may begin by reading the historical background and then come back to fill in details.”
- The Diagonal Argument
- Computability and Proof
- Natural Unprovable Sentences
- Axioms of Infinity
The book concludes with “Bibliography,” and “Index.”
- Stillwell, John
- A K Peters, Ltd.
- Publish Date:
- Hardback with Dust Jacket
- Weight (pounds):
- Dimensions (W”xL”xH”):
Products related to "Roads to Infinity: The Mathematics of Truth and Proof (Hardback)"
"Logic is the glue that binds together arguments and proofs in all domains. This text aims to teach the use of this fundamental and pervasive tool and exercise it thoroughly in applications that arise in computer science and mathematics." — From the back cover
"This QUICK STUDY® guide is an outline of the basic topics taught in introductory Logic courses. Due to its condensed format, use it as a study guide, but not as a replacement for assigned class work." — From "Note" on Page 4
"This classic text is as fresh and useful today as when first published. Noted for the economy of its presentation, it includes a wealth of basic and key results from all parts of mathematical logic." — Solomon Feferman, Stanford University
This book is a textbook for elementary college courses in logic and the methodology of deductive science. It is from a revised second edition of a classical work that was first published in Polish in 1936.
"This book is an introduction to modern logic, but it is quite different from other introductory books on the subject." — From the back cover
"The goal of The Reasoned Schemer is to help the functional programmer think logically and the logic programmer think functionally." — From the back cover
"Around 1930 the type free lambda calculus was introduced as a foundation for logic and mathematics. Due to the appearance of paradoxes, this aim was not fulfilled, however. Nevertheless a consistent part of the theory turned out to be quite successful as a theory of computations. It gave an imporatnt momentum to early recusion theory and more recently to computer science." — From the back cover
"...[The book] is a treasure, which deserves wide adoption as a text and much consultation by historians and mathematicians alike." — Physis Rivista Internazionale di Storia della Scienza
"This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory." — From the back cover
Graduate Texts in Mathematics: Classical Topology and Combinatorial Group Theory, Second Edition (Hardback)
"This is a well-balanced introduction to topology that stresses geometric aspects." — From the back cover
"Numbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields—algebra, analysis, and geometry—meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book." — From the back cover
"Geometry of Surfaces explores the interplay between geometry and topology in the simplest nontrivial case: the surfaces of constant curvature. As such, it provides a concise introduction to modern geometry for a wide audience." — From the back cover
"Despite its success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of mathematical and physical problems, tensor analysis has always had a rather restricted level of use, with an emphasis on notation and the manipulation of indices. This book is an attempt to broaden this point of view at the stage where the student first encounters the subject." — From the back cover
"This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically with minimal prerequisites and plenty of geometric intuition." — From the back cover