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...

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 ...

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...

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...

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 popular text introduces the reader to all aspects of psychometric assessment, including its history, the construction and administration of traditional tests, and the latest techniques for psychometric assessment online.Rust, Kosinski, and Stillwell begin with a comprehensive introduction to the increased sophistication in psychometric methods and regulation that took place during the 20th century, including the many benefits to governments, businesses, and customers. In this ...

Warriors of Freedom: 70 Memoirs of Union Soldiers is a remarkable anthology that delves into the harrowing experiences and profound reflections of Union soldiers during the American Civil War. This collection presents a wide range of literary styles, from detailed diary entries to eloquent memoirs, capturing the raw and unfiltered perspectives of those who fought on the front lines. Through these diverse narratives, the anthology explores themes of bravery, sacrifice, camaraderie, and the ...

Was it worth it? Why did they volunteer in the first place? What did they experience on the battlefield? Which comrades did they have to leave behind, in the midst of blood and mud? How did they survive? What are they most proud of? How do they view those harrowing experiences as time has gone by? Was the conviction worth the sacrifice? Learn the real truth from the veterans of the Brothers' War. This anthology is dedicated to the heroes of the Civil War, to every soldier who had to endure...

70 Civil War Memoirs of Union Soldiers is a compelling anthology that captures the diverse experiences and voices of those who served in the Union Army. The collection encapsulates a wide range of literary styles, from the stark and harrowing narratives of battlefield confrontations to deeply reflective accounts of the personal and collective struggles of war. Intimately tied to the historical context of the Civil War, the anthology provides a panoramic view of the conflict, underscoring t...

This anthology is dedicated to honor and preserve from oblivion the great courage, the sacrifices and the ultimate devotion of all Americans during the Civil War - the soldiers, the volunteers, the medical stuff and the civilians who supported the troops. In the hope this great divide and bloodthirsty hatred never emerges again in our nation, we honor the people who gave their lives or sacrificed everything they could offer in order to serve the greater good in which they believed. The edi...

'100+ Civil War Soldier Memoirs" includes memoirs and testimonies by Union and Confederate soldiers, voices from both trenches. Their struggle and sacrifice, their pride and devotion to their country - is something they all have in common. This anthology captures a broad spectrum of experiences, from the fierce battles and strategic maneuvers to the intimate reflections and everyday challenges of soldiers on both sides of the war. Showcasing a rich diversity of literary styles and personal...