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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.
Book Synopsis Not Always Buried Deep by : Paul Pollack
Download or read book Not Always Buried Deep written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2009-10-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bones by : Max Allan Collins
Download or read book Bones written by Max Allan Collins and published by Simon and Schuster. This book was released on 2006-03 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
‘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, ⭐⭐⭐⭐⭐
Book Synopsis Buried Deep by : Susan Wilkins
Download or read book Buried Deep written by Susan Wilkins and published by Bookouture. This book was released on 2020-04-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘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, ⭐⭐⭐⭐⭐
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.
Book Synopsis A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z by : Paul Pollack
Download or read book A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2017-08-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Buried Giant by : Kazuo Ishiguro
Download or read book The Buried Giant written by Kazuo Ishiguro and published by Vintage. This book was released on 2015-03-03 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Algebraic Number Theory by : Ian Stewart
Download or read book Algebraic Number Theory written by Ian Stewart and published by Springer. This book was released on 1979-05-31 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
A serial killer terrorizes a small California town in this gripping thriller from #1 New York Times bestselling author Tami Hoag. California, 1985—Four children and young teacher Anne Navarre make a gruesome discovery: a partially buried female body, her eyes and mouth glued shut. A serial killer is at large, and the very bonds that hold their idyllic town together are about to be tested to the breaking point. Tasked with finding the killer, FBI investigator Vince Leone employs a new and controversial FBI technique called “profiling,” which plunges him into the lives of the four children—and the young teacher whose need to uncover the truth is as intense as his own. But as new victims are found and pressure from the media grows, Vince and Anne find themselves circling the same small group of local suspects, unsure if those who suffer most are the victims themselves—or those close to the killer, blissfully unaware that someone very near to them is a murderous psychopath…
Book Synopsis Deeper Than the Dead by : Tami Hoag
Download or read book Deeper Than the Dead written by Tami Hoag and published by Penguin. This book was released on 2023-04-04 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A serial killer terrorizes a small California town in this gripping thriller from #1 New York Times bestselling author Tami Hoag. California, 1985—Four children and young teacher Anne Navarre make a gruesome discovery: a partially buried female body, her eyes and mouth glued shut. A serial killer is at large, and the very bonds that hold their idyllic town together are about to be tested to the breaking point. Tasked with finding the killer, FBI investigator Vince Leone employs a new and controversial FBI technique called “profiling,” which plunges him into the lives of the four children—and the young teacher whose need to uncover the truth is as intense as his own. But as new victims are found and pressure from the media grows, Vince and Anne find themselves circling the same small group of local suspects, unsure if those who suffer most are the victims themselves—or those close to the killer, blissfully unaware that someone very near to them is a murderous psychopath…
This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
Book Synopsis Steps into Analytic Number Theory by : Paul Pollack
Download or read book Steps into Analytic Number Theory written by Paul Pollack and published by Springer Nature. This book was released on 2021-02-08 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
Tim can't wait to go on holiday - especially as he gets to bring his friend Biscuits along. But their trip unexpectedly becomes truly, terribly adventurous when an encounter with two local bully-boys threatens to disrupt the fun. Narrated by Tim and interspersed with revealing, illustrated extracts from Tim and Biscuits's holiday diaries, this is a wondefully enjoyable story from one of the most popular writers around that both girls and boys will love.
Book Synopsis Buried Alive! by : Jacqueline Wilson
Download or read book Buried Alive! written by Jacqueline Wilson and published by Random House. This book was released on 2008-09-04 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim can't wait to go on holiday - especially as he gets to bring his friend Biscuits along. But their trip unexpectedly becomes truly, terribly adventurous when an encounter with two local bully-boys threatens to disrupt the fun. Narrated by Tim and interspersed with revealing, illustrated extracts from Tim and Biscuits's holiday diaries, this is a wondefully enjoyable story from one of the most popular writers around that both girls and boys will love.
Bestselling author Harvey Mackay reveals his techniques for the most essential tool in business--networking, the indispensable art of building contacts. Now in paperback, Dig Your Well Before You're Thirsty is Harvey Mackay's last word on how to get what you want from the world through networking. For everyone from the sales rep facing a career-making deal to the entrepreneur in search of capital, Dig Your Well explains how meeting these needs should be no more than a few calls away. This shrewdly practical book distills Mackay's wisdom gleaned from years of "swimming with sharks," including: What kinds of networks exist How to start a network, and how to wring the most from it The smart way to downsize your list--who to keep, who to dump How to keep track of favors done and favors owed--Is it my lunch or yours? What you can do if you are not good at small talk Dig Your Well Before You're Thirsty is a must for anyone who wants to get ahead by reaching out.
Book Synopsis Dig Your Well before You're Thirsty by : Harvey Mackay
Download or read book Dig Your Well before You're Thirsty written by Harvey Mackay and published by Crown Currency. This book was released on 1999-02-16 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bestselling author Harvey Mackay reveals his techniques for the most essential tool in business--networking, the indispensable art of building contacts. Now in paperback, Dig Your Well Before You're Thirsty is Harvey Mackay's last word on how to get what you want from the world through networking. For everyone from the sales rep facing a career-making deal to the entrepreneur in search of capital, Dig Your Well explains how meeting these needs should be no more than a few calls away. This shrewdly practical book distills Mackay's wisdom gleaned from years of "swimming with sharks," including: What kinds of networks exist How to start a network, and how to wring the most from it The smart way to downsize your list--who to keep, who to dump How to keep track of favors done and favors owed--Is it my lunch or yours? What you can do if you are not good at small talk Dig Your Well Before You're Thirsty is a must for anyone who wants to get ahead by reaching out.
