Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss's theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: The reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.
An original novel based on Fox's new hit television series, inspired by real-life forensic anthropologist and novelist Kathy Reichs, creator of the Temperance Brennan series. Original.
Karol Truman provides a comprehensive and enlightening resource for getting in touch with unresolved feelings which, she explains, can distort not only happiness but also health and well-being. Leaving no emotion unnamed, and in fact listing around 750 labels for feelings, Truman helps identify problem areas, and offers a "script" to help process the feelings, replacing the negative feeling with a new, positive outlook. A chapter on the possible emotions below the surface in various physical ailments gives the reader plenty to work with on a deep healing level. FEELINGS BURIED ALIVE NEVER DIE combines a supportive, common-sense, results-oriented approach to a problem that is widespread and that can stop people from living fully.
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
NATIONAL BESTSELLER • From the winner of the Nobel Prize in Literature and author of Never Let Me Go and the Booker Prize–winning novel The Remains of the Day comes a luminous meditation on the act of forgetting and the power of memory. In post-Arthurian Britain, the wars that once raged between the Saxons and the Britons have finally ceased. Axl and Beatrice, an elderly British couple, set off to visit their son, whom they haven't seen in years. And, because a strange mist has caused mass amnesia throughout the land, they can scarcely remember anything about him. As they are joined on their journey by a Saxon warrior, his orphan charge, and an illustrious knight, Axl and Beatrice slowly begin to remember the dark and troubled past they all share. By turns savage, suspenseful, and intensely moving, The Buried Giant is a luminous meditation on the act of forgetting and the power of memory.
‘Compulsive and thoroughly captivating… I found myself unable to tear myself away and as a consequence read it all in a single tense sitting… bags of suspense and action wrapped up in a thrillingly plotted story’ Reader’s Retreat, ⭐⭐⭐⭐⭐ On the first day in her new job, Detective Megan Thomas is called to a murder. The body lies deep in an underground bunker, in the middle of beautiful countryside. The two women in the nearest house claim to have no idea who it could be or who could have put it there. So why are they so nervous? And why does Noah, the young child living there, talk about a visitor he’s meant to keep secret? Megan is determined to solve the case. She’s moved to Devon for a fresh start, after years spent undercover. But when she looks at the victim, it triggers a panic attack. As her heart races and her breathing stalls, she’s forced to ask whether she can return to life in a regular crime unit. Her memories are too powerful to be buried, maybe too powerful to let her do her job. But the need to find justice for the unnamed victim still drives her. When another body is found on the stretch of beach where she swims every day, Megan realises that she is up against a truly vicious killer. Then Noah goes missing, and Megan finds herself in a race against time to save an innocent life. She won’t rest until she finds answers – no matter what it might cost her. A completely gripping new series from bestselling author Susan Wilkins, introducing the tough and determined Detective Megan Thomas. For fans of Ann Cleeves, LJ Ross and Mari Hannah, this will keep you hooked from the first page to the last. What readers are saying about Buried Deep: ‘My favourite read of 2020… I was engaged from the very first chapter… Brilliant’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘Extremely compulsive… my attention didn’t waver for a second and I read it in one sitting… keeps the interest and tension going with timely reveals, unexpected developments and a clever plot’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘I loved the book and was gripped straight from the off. Susan’s a great writer, building up the tension nicely and giving a thumping action-packed ending that really delivers.’ Jessie Keane, author of The Knock ‘Addictive, gripping, twisty… how this story unfolds is just brilliant’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘Thrilling… will have you gripped and enthralled right from the beginning… an addictive read’ Once Upon A Time Book Blog ‘One of the best… compelling… I loved this book.’ Nigeladamsbookworm, ⭐⭐⭐⭐⭐ ‘I loved Buried Deep… a gripping plot that had me frantically flipping pages… If you haven't yet read this, you need to. An excellent start to a series that promises to be brilliant.’ Sandy’s Book A Day ‘Loved this… if you like Vera you will love this book. Brilliant’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘Brilliant… had me hooked from the beginning’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘Brilliant book in my opinion! I want to read more and dive into Megan's past… She fascinates me. 5 stars.’ B for Bookreview, ⭐⭐⭐⭐⭐ ‘A terrific start to what promises to be an excellent new police procedural series’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘Gripping… twists and turns and plenty of suspicious characters… Looking forward to reading more’ Goodreads Reviewer ‘A suspenseful fast paced thriller’ Goodreads Reviewer, ⭐⭐⭐⭐⭐ ‘Murders, intricate plot, red herrings and twisted reveals… I knew I had a winner in my hands’ Shalini’s Books & Reviews ‘Full of action and suspense… hard to put down. Couldn't wait to find out what happened… Amazing.’ Goodreads Reviewer, ⭐⭐⭐⭐⭐
Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work.
The #1 New York Times best-selling author Wayne Dyer has been inspiring people to change their lives for many years. Now three of his most fascinating books are collected in this single volume: • The Power of Intention details Wayne’s research on intention as a force in the universe that allows the act of creation to take place. He explains that it is not something we do, but rather an energy we’re a part of. This is the first book to look at intention as a field of energy that we can access to begin co-creating our lives. • Inspiration dissects feelings of emptiness, the idea that there must be something more, and trying to determine the meaning of life . . . all evidence of a yearning to reconnect with our soul space. This book explains how we’ve chosen to enter this world of particles and form, and each chapter is filled with specifics for living an inspired life. From a very personal viewpoint, Wayne offers a blueprint through the world of Spirit to inspiration, our ultimate calling. • Excuses Begone! reveals how to change the self-defeating thinking patterns that have prevented us from living at the highest levels of success, happiness, and health. Wayne presents many of the conscious and subconscious crutches most of us employ, along with ways to cast them aside once and for all. The old, habituated ways of thinking will melt away as the absurdity of hanging on to them is exposed, and we ultimately come to realize that there are no excuses worth defending—ever. The Essential Wayne Dyer Collection is a must-read for those wanting to explore the power and potential of the human mind, as well as anyone who is finally ready to live the best life possible!
The title of this book may be read in two ways. One is 'algebraic number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a proper coverage of either topic would require more space than is available, and demand more of the reader than we wish to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without ever defining an abstract vector space: nor is there anything to suggest that they suf fered thereby. This historical fact may indicate that abstrac tion is not always as necessary as one commonly imagines; on the other hand the axiomatization of mathematics has led to enormous organizational and conceptual gains.
