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The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.
Invigorate your reading life with 25 unique challenges and reward yourself with 25 bookish surprises! This delightful collection of 25 challenges and rewards inspires bookworms to engage with their reading life in a fresh new way. Each pocket inside this portfolio challenges readers to a bookish challenge. Once the reader completes a challenge, they can open the pocket to claim their prize. This one-size-fits-all gift is appropriate for readers of all ages, genres, and abilities. Bibliophiles are encouraged to: Read personally Re-read a book you loved as a child. Ask a family member what book has made a lasting impression on them. Find and read that book. Read compassionately Read a book that features an indigenous person. Read a book about a person with a disability. Read broadly Visit your local bookstore and ask a bookseller to recommend a book based on your recent favorites. Read in a place you’ve never read before. Engage creatively Make (or order) a snack or meal described in a book you’ve read. Write a letter to someone who has influenced your reading life. Prizes are all thoughtfully curated to supplement the reading life and include: A laser-engraved wooden bookmark Bookish greeting cards Coffee cup sleeve Book darts A mini notebook And much more!
In Fatherhood, beloved NBA player, poet, children’s advocate, and devoted dad Etan Thomas speaks from his heart on what matters most in his life: being there for his children. As a leading participant in President Obama’s Fatherhood Initiative, Etan has reached out to young men (often young fathers) in the juvenile detention system and in local communities. He knows firsthand the difference having a father in your life every day can make. Now he brings together a chorus of voices to weigh in on the importance of being a father in our nation today and to share what they’ve learned from being a father, having a father, or in some cases not having a father around. With Original Essays and Poems from Taye Diggs • Kareem Abdul-Jabbar • Malcolm-Jamal Warner • Ice Cube • Howard Dean • Tony Hawk • Isaiah Washington • Yao Ming • Al Sharpton • John King • Lamman Rucker • Derek Fisher • Kevin Durant • Russ Parr • Michael Moore • Chuck D • Malcolm Shabazz • Talem Acey • Will Downing • Chris Paul • Allan Houston • Talib Kweli • Black Ice • Cornel West • Elijah Cummings • Mumia Abu-Jamal • Grant Hill • Coach John Thompson • Roland Martin • Joakim Noah • Arn Tellum • Damian Marley • Abiodune Oyewole • Styles P • Baron Davis • David Aldridge • Stuart Scott • Dave Zirin • Kevin Powell • John Carlos • Derrick Coleman • J. Ivy • Joe Johnson • Al Horford • Pastor John Jenkins • Julian Thomas • Ed Gordon Jr. • Tito Puente Jr. • Billy Hunter • 13 of Nazareth • Messiah Ramkissoon Through these inspiring personal experiences, Etan and the men he’s gathered together hope to share the message that by standing up and taking an active role as fathers, men not only find their own lives more joyful and fulfilling—they pass on to the next generation an unshakable legacy of love, wisdom, responsibility, and strength.
The Ultimate Challenge: Coping with Death, dying and Bereavement, presents the topic as seen through a Canadian perspective, including Canadian demographics and examples specifically taken from events within Canada. There is a balance of theoretical, empirical and practical material, making The Ultimate Challenge: Coping with Death, Dying and Bereavement appropriate for students who want a basic knowledge of the area and for students who are training in mental health or medical areas in which such knowledge will have immediate applications. The area of death, dying and bereavement is multi-disciplinary, and this book draws on material from the different disciplines: psychology, sociology, anthropology, economics, history, political science, literature and the arts. Issues and concepts are illustrated with newspaper items and case studies, increasing the immediate relevance of the material presented.
AIDS "None of us is so unique as to be exempt from the human condition." As the numbers of reported AIDS cases continue to climb, and the disease continues to take more and more lives, those who have to deal with the complexities of this problem continue to ask: "How do we care for these terminally ill?" Using letters from patients, questions and answers between patient and doctor, and other compassionate tools, Dr. Elisabeth Kübler-Ross, the world's foremost expert on death and dying, shows us how to comfort the seriously ill and help AIDS patients through the critical "stages of dying" She addresses the stigma surrounding AIDS as a "gay disease" and makes a special plea for prisoners with AIDS, for women and children with AIDS, and for babies with AIDS. This remarkable book is warm and informative on one of the most important subjects of our time.
Join Ryan of the hit YouTube channel Ryan’s World and Ryan’s Mystery Playdate on Nickelodeon in this interactive, sports-themed 8x8 storybook that comes with a sheet of reusable stickers! Ryan dribbles, tumbles, and scores on his athletic playdate! Readers will use the stickers to help Ryan complete the challenges and meet his three playdates: Olympic gold-medal gymnast Laurie Hernandez, former Olympic gold-medal soccer player Brandi Chastain, and WNBA star Karlie Samuelson. Coated interior pages and reusable stickers allow readers to reread and play again and again! TM & © 2021 PocketWatch, Inc. & Hour Hand Productions, LLC. All Rights Reserved.
If you consider yourself a trivia expert, Uncle John has created the perfect book for you. Who knows more about trivia than the folks at the Bathroom Readers’ Institute? Nobody, that’s who! With more than 300 pages of fascinating facts arranged in a fun quiz format, Trivia Quiz will test your knowledge on a variety of subjects, and then you can stump your friends! Some sample questions: * What are pato, shinty, and hapkido? * What are the two moons of Mars called? * Where would you find a fetlock? * In what country would you find the world’s smallest mammal? Want the answers? Buy the book! Just kidding. Here they are: sports; Phobos and Deimos; just above a horse’s hoof; and Thailand, where you’ll find the tiny bumblebee bat. You’ll find thousands more fun questions (and answers) in Uncle John’s Trivia Quiz!
