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Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.

Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.

THE HIGHLY ANTICIPATED SECOND NOVEL FROM THE WRITER EMILY ST. JOHN MANDEL (STATION ELEVEN) CALLS “SHARP, WITTY, AND IMMENSELY ENTERTAINING” Is a new life possible? Because Shira Greene’s life hasn’t quite turned out as planned. She’s a single mom living with her daughter and her gay friend, Ahmad. Her PhD on Dante’s Vita Nuova hasn’t gotten her a job, and her career as a translator hasn’t exactly taken off either. But then she gets a call from a Nobel Prize-winning Italian poet who insists she’s the only one who can translate his newest book. Stunned, Shira realizes that—just like that— her life can change. She sees a new beginning beckoning: academic glory, demand for her translations, and even love (her good luck has made her feel more open to the entreaties of a neighborhood indie bookstore owner). There’s only one problem: It all hinges on the translation, and as Shira starts working on the exquisitely intricate passages of the poet’s book, she realizes that it may in fact be, well ... impossible to translate. A deft, funny, and big-hearted novel about second chances, Good on Paper is a grand novel of family, friendship, and possibility.

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Sing to the Lord: Music in Divine Worship provides basic guidelines for understanding the role and ministry of music in the liturgy. An excellent resource for priests, deacons, and music ministers!

In this useful guide, Paul Cantor provides a clearly structured introduction to Shakespeare's most famous tragedy. Cantor examines Hamlet's status as tragic hero and the central enigma of the delayed revenge in the light of the play's Renaissance context. He offers students a lucid discussion of the dramatic and poetic techniques used in the play. In the final chapter he deals with the uniquely varied reception of Hamlet on the stage and in literature generally from the seventeenth century to the present day.

An Amazon Best of the Month Selection for May 2018 A slyly funny coming-of-age novel about a young woman fumbling her way into the mysteries of loss and the travails of adulthood as she tries to make sense of a vanished mother's legacy. When 22-year-old Olivia learned that her mother had only months to live, she pulled up roots, leaving Vassar and her career plans far behind to be with her mother for her last days. And yet, just four months after her mother's death, everyone in Olivia's family already seems ready to move on. Her brothers are settled comfortably in careers and families of their own; her father has already started to date again, inviting a woman named June on a family trip. Still reeling from the loss, Olivia looks for a new start of her own, throwing herself headlong into Manhattan's fast-moving media world, where she is alternately demeaned by bosses and pursued by men. But as Olivia tries to piece together an adulthood without her mother to guide her, she makes a shocking discovery: a secret romantic correspondence her mother had with a man who only signed each letter “F.” As she tries to untangle the mystery of F, Olivia will journey halfway across the world, to an ashram in rural India, on a quest that will reconfigure everything Olivia thought she knew about her family and her own place in an increasingly complex world. A profoundly moving and keenly observed contemplation of the debts we owe to the past and the ways we discover our futures, Alternative Remedies for Loss is the rare sort of book that can break and mend your heart in a single and unforgettable read.

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.