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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its...

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 mathematical questions about the nature of infinity and the nature of proof, set against a background of...

Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its...

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

This book...

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 marriage to co-habitation as the social norm, and it considers the health and well-being for particular...

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 marriage to co-habitation as the social norm, and it considers the health and well-being for particular...