While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory...

Why were most historically important mathematicians wealthy? Why were they often lawyers and many had pastors for fathers? Why were original results sometimes discovered by two mathematicians independently within a short time of each other? Why did the Italian Fibonacci, speak Arabic?It all began a couple of years ago, when one of the authors started to write short biographies of important historical mathematicians for the teaching journal Australian Primary Mathematics Classroom. ...

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of t...

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections ...

Yearning for the Impossible: The Surprising Truth of Mathematics, Second Edition explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress. The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. This new edition contains many...

Many parts of the world are experiencing rapid demographic restructuring, resulting in an ageing population with increasingly significant work and care pressures on cohorts less able or willing to provide support. This book examines some of the important trends that have underpinned reductions in fertility, including delayed child-bearing and increased childlessness. It demonstrates how relationships between partners have resulted in new living arrangements with changing attitudes from mar...

This book offers a selection of the best articles presented at the CUPUM (Computers in Urban Planning and Urban Management) Conference, held in the second week of July 2017 at the University of South Australia in Adelaide.It provides a state-of-the-art overview of the availability and application of planning support systems (PSS) in the context of smart cities, big data, and urban futures. Rapid advances in computing, information, communication and web-based technologies are reachi...

Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject.Ideas are shown to evolve from natural ma...

This book is a selection of the best and peer-reviewed articles presented at the CUPUM (Computers in Urban Planning and Urban Management) conference, held in the second week of July 2015 at MIT in Boston, USA. The contributions provide state-of the art overview of the availability and application of Planning Support Systems (PSS) in the framework of Smart Cities.

The collection of reliable and comprehensive data on the magnitude, composition and distribution of a country’s population is essential in order for governments to provide services, administer effectively and guide a country’s development. The primary source of basic demographic statistics is frequently a population census, which provides hugely important data sets for policy makers, practitioners and researchers working in a wide range of different socio-demographic contexts.The R...

Inequality is one of the major problems of the contemporary world. Significant geographical disparities exist within nations of the developed world, as well as between these countries and those referred to as the ‘South’ in the Bruntland Report. Issues of equity and deprivation must be addressed in view of sustainable development. However, before policymakers can remove the obstacles to a fairer world, it is essential to understand the nature of inequality, both in terms of its spatial and...