Böcker av John Stillwell

This book unifies ideas from set theory and mathematical logic and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developm

How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proofΓÇöone of the most significant and defining features of mathematical thoughtΓÇöthrough critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge.Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as ΓÇ£infinitesimal algebra,ΓÇ¥ and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, G├╢del, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved.Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the fieldΓÇÖs power and progress.

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics.

This text plugs a gap in the standard curriculum by linking set theory with analysis. It features a distinctive, detailed treatment of the real numbers system, and combines an introduction to set theory with exposition of the essence of analysis.

Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics.

This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it's accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Addresses the technical and data-related side of studying population flows. With expert international contributors currently working in the field, this authoritative book allows readers to better understand interaction data and the ways knowledge of population flows can be put to use.

Offers a comprehensive introduction to the role of infinity in mathematics, from ancient to modern times. Suitable for general audience, this book explains the critical philosophical issues connected to the concept of infinity and their relevance for the foundations of mathematics.

In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates.