A provocative look at the tools and history of real analysis This new edition of Real Analysis: A Historical Approach continues to serve as an interesting read for students of analysis. Combining historical coverage with a superb introductory treatment, this book helps readers easily make the transition from concrete to abstract ideas. The book begins with an exciting sampling of classic and famous problems first posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton, and Euler are each summoned in turn, illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, which introduce the various aspects of the completeness of the real number system as well as sequential continuity and differentiability and lead to the Intermediate and Mean Value Theorems. The Second Edition features: A chapter on the Riemann integral, including the subject of uniform continuity Explicit coverage of the epsilon-delta convergence A discussion of the modern preference for the viewpoint of sequences over that of series Throughout the book, numerous applications and examples reinforce concepts and demonstrate the validity of historical methods and results, while appended excerpts from original historical works shed light on the concerns of influential mathematicians in addition to the difficulties encountered in their work. Each chapter concludes with exercises ranging in level of complexity, and partial solutions are provided at the end of the book. Real Analysis: A Historical Approach, Second Edition is an ideal book for courses on real analysis and mathematical analysis at the undergraduate level. The book is also a valuable resource for secondary mathematics teachers and mathematicians.
Praise for the First Edition "Stahl offers the solvability of equations from the historicalpoint of view...one of the best books available to support aone-semester introduction to abstract algebra." —CHOICE Introductory Modern Algebra: A Historical Approach, SecondEdition presents the evolution of algebra and provides readerswith the opportunity to view modern algebra as a consistentmovement from concrete problems to abstract principles. With a fewpertinent excerpts from the writings of some of the greatestmathematicians, the Second Edition uniquely facilitates theunderstanding of pivotal algebraic ideas. The author provides a clear, precise, and accessibleintroduction to modern algebra and also helps to develop a moreimmediate and well-grounded understanding of how equations lead topermutation groups and what those groups can inform us about suchdiverse items as multivariate functions and the 15-puzzle.Featuring new sections on topics such as group homomorphisms, theRSA algorithm, complex conjugation, the factorization of realpolynomials, and the fundamental theorem of algebra, the SecondEdition also includes: An in-depth explanation of the principles and practices ofmodern algebra in terms of the historical development from theRenaissance solution of the cubic equation to Dedekind'sideals Historical discussions integrated with the development ofmodern and abstract algebra in addition to many new explicitstatements of theorems, definitions, and terminology A new appendix on logic and proofs, sets, functions, andequivalence relations Over 1,000 new examples and multi-level exercises at the end ofeach section and chapter as well as updated chapter summaries Introductory Modern Algebra: A Historical Approach, SecondEdition is an excellent textbook for upper-undergraduatecourses in modern and abstract algebra.
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.
The mathematical theory of games was first developed as a model for situations of conflict, whether actual or recreational. It gained widespread recognition when it was applied to the theoretical study of economics by von Neumann and Morgenstern in Theory of Games and Economic Behavior in the 1940s. The later bestowal in 1994 of the Nobel Prize in economics on Nash underscores the important role this theory has played in the intellectual life of the twentieth century. This volume is based on courses given by the author at the University of Kansas. The exposition is "gentle" because it requires only some knowledge of coordinate geometry; linear programming is not used. It is "mathematical" because it is more concerned with the mathematical solution of games than with their applications. Existing textbooks on the topic tend to focus either on the applications or on the mathematics at a level that makes the works inaccessible to most non-mathematicians. This book nicely fits in between these two alternatives. It discusses examples and completely solves them with tools that require no more than high school algebra. In this text, proofs are provided for both von Neumann's Minimax Theorem and the existence of the Nash Equilibrium in the $2 \times 2$ case. Readers will gain both a sense of the range of applications and a better understanding of the theoretical framework of these two deep mathematical concepts.
The Poincare Half-Planeprovides an elementary and constructive development of this geometry that brings the undergraduate major closer to current geometric research. At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing the students' understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor.
It's sweltering summer in New York City, and Asa Leventhal is alone. His co-workers ignore or condescend to him, his wife is away with her mother, and his estranged brother has run off, abandoning his wife and two sons. One night, Leventhal is confronted by a stranger--'one of those guys who want you to think they can see to the bottom of your soul'--who reveals himself to be a marginal figure from his distant past. Leventhal, accused of ruining the man's life, becomes shocked and dismissive, vehemently denying any part in the man's unhappy lot. But as time passes, he is increasingly unable to separate his own good fortune from the bad luck of this down-and-out stranger, who will not leave him be. A brief, haunting rumination on the vagaries of fate and responsibility, The Victim is, in the words of Norman Rush, Saul Bellow's "purest creation.
Stahl's Second Edition continues to provide students with the elementary and constructive development of modern geometry that brings them closer to current geometric research. At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing the students' understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor. This distinct approach makes these advanced geometry principles accessible to undergraduates and graduates alike.
Expecting to be inducted into the army, Joseph has given up his job and carefully prepared for his departure to the battlefront. When a series of mix-ups delays his induction, he finds himself facing a year of idleness. Dangling Man is his journal, a wonderful account of his restless wanderings through Chicago's streets, his musings on the past, his psychological reaction to his inactivity while war rages around him, and his uneasy insights into the nature of freedom and choice.
La breve y tragicómica historia de Tommy Wilhelm, un hombre agobiado por las deudas y la incertidumbre sobre su futuro. Con su encanto en horas bajas, Tommy Wilhelm ha llegado al terrible día de hacer recuento. Y tiene miedo. A sus cuarenta, todavía conserva es ímpetu infantil que le ha llevado al centro del caos: separado de su mujer e hijos, reñido con su padre, su carrera de actor fracasada (un agente de Hollywood lo ha calificado como «el tipo que siempre pierde a la chica»), y con problemas económicos. Tiene que revisar los errores del pasado y curar su espirítu, y para hacerlo, nadie mejor que un misterioso y filosófico timador, pretendido psicólogo, quien le garantizará ese glorioso e iluminador momento de la verdad que está buscando, ofreciéndole una última esperanza: Carpe diem. Vive el momento. Juégatelo todo a una sola carta... Reseña: «Sus libros forman parte de mi paisaje más cercano.» Antonio Muñoz Molina
This dazzling collection of shorter fiction describes a series of self-awakenings -- a suburban divorcee deciding among lovers, a celebrity drawn into his cousin's life of crime, a father remembering bygone Chicago, an artist, and an academic awaiting extradition for some unnamed offense.
Who is Mr. Sammler? A Jewish intellectual educated in Western philosophy, a one-eyed Holocaust survivor, the future author of the greatest biography ever written of H.G. Wells ... or merely the trusted confidant of countless eccentric New Yorkers, a "registrar of follies"? Through the chaotic streets of the Upper West Side old Artur Sammler paces, meditating on the human condition; attentive to everything and appalled by nothing; haunted by his past, present, and future. His world seems on the brink of apocalypse; both the recent moon landing and the death of his beloved benefactor have him furiously speculating on the end. With his inimitable tragicomic mastery Saul Bellow delves once again, and the reader with him, into a contemporary and chaotic universe in which the most profound reflections on the meaning of life mingle with the absurd, histrionic, endless minutiae of the every day.
A provocative look at the tools and history of real analysis This new edition of Real Analysis: A Historical Approach continues to serve as an interesting read for students of analysis. Combining historical coverage with a superb introductory treatment, this book helps readers easily make the transition from concrete to abstract ideas. The book begins with an exciting sampling of classic and famous problems first posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton, and Euler are each summoned in turn, illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, which introduce the various aspects of the completeness of the real number system as well as sequential continuity and differentiability and lead to the Intermediate and Mean Value Theorems. The Second Edition features: A chapter on the Riemann integral, including the subject of uniform continuity Explicit coverage of the epsilon-delta convergence A discussion of the modern preference for the viewpoint of sequences over that of series Throughout the book, numerous applications and examples reinforce concepts and demonstrate the validity of historical methods and results, while appended excerpts from original historical works shed light on the concerns of influential mathematicians in addition to the difficulties encountered in their work. Each chapter concludes with exercises ranging in level of complexity, and partial solutions are provided at the end of the book. Real Analysis: A Historical Approach, Second Edition is an ideal book for courses on real analysis and mathematical analysis at the undergraduate level. The book is also a valuable resource for secondary mathematics teachers and mathematicians.
Understanding Modern Mathematics is an exceptional collection of topics meant to better acquaint students with mathematics through an exposure to its applications and an analysis of its culture. The text provides an in-depth focus on such key topics as probability, statistics, voting systems, game theory, and linear programming. Two additional chapters on geometry and symmetry can be found on the text's web site, providing students the opportunity to see the 3-dimensional geometric figures in full color. The text provides students with an understanding of how these important mathematical topics are relevant in their everyday lives while emphasizing the history of mathematics . Understanding Modern Mathematics is the perfect complement to any Liberal Arts Mathematics course. Click Here to View Chapter 6 Click Here to View Chapter 7
Introductory treatment for undergraduates provides insightful expositions of specific applications of mathematics and elements of mathematical history and culture. Topics include probability, statistics, voting systems game theory, geometry, Egyptian arithmetic, and more. 2016 edition.
Encouraged by his friend, Chick, to write down his ideas about humankind, university professor Abe Ravelstein receives unexpected acclaim and bounty and invites Chick to join his his success, a situation that sparks a philosophical journey for both.
In this invigorating new assessment of Anna Karenina, Gary Saul Morson overturns traditional interpretations of the classic novel and shows why readers have misunderstood Tolstoy's characters and intentions. Morson argues that Tolstoy's ideas are far more radical than has been thought: his masterpiece challenges deeply held conceptions of romantic love, the process of social reform, modernization, and the nature of good and evil. By investigating the ethical, philosophical, and social issues with which Tolstoy grappled, Morson finds in Anna Karenina powerful connections with the concerns of today. He proposes that Tolstoy's effort to see the world more wisely can deeply inform our own search for wisdom in the present day. The book offers brilliant analyses of Anna, Karenin, Dolly, Levin, and other characters, with a particularly subtle portrait of Anna's extremism and self-deception. Morson probes Tolstoy's important insights (evil is often the result of negligence; goodness derives from small, everyday deeds) and completes the volume with an irresistible, original list of One Hundred and Sixty-Three Tolstoyan Conclusions.
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