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Steps into Analytic Number Theory
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 valu...
Not Always Buried Deep
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 Conversational Introduction to Algebraic Number Theory
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 mo...
An Introduction to Sociology
This second edition of the bestselling An Introduction to Sociology: Feminist Perspectives confirms the centrality of feminist perspectives and research to the sociological enterprise and introduces students and the general reader to the wide range of feminist contributions to key areas of sociological concern. This completely revised edition includes material on new feminist theories and post-modern feminism, as well as incorporating the findings of recent empirical research. Written by two experienced teachers and examiners, it gives students of sociology and women's studies an accessible overview of the feminist contribution to all the key areas of sociological concern.
Analytic Number Theory for Beginners
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this seco...
Mind as Machine
The development of cognitive science is one of the most remarkable and fascinating intellectual achievements of the modern era. It brings together psychology, neuroscience, artificial intelligence, computing, philosophy, linguistics, and anthropology in the project of understanding the mind by modelling its workings. Oxford University Press now presents a masterful history of cognitive science, told by one of its most eminent practitioners.
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The weekly source of African American political and entertainment news.
Early Childhood Services
This book explores the relationships between theory, policy and practice in early childhood services. Although primarily focused on the UK, it draws on contributions from Europe and further afield to explore the strengths and limitations of present practices and suggests ways in which new initiatives might be developed.
Pilgrims’ Passage
Why does Pilgrims’ Passage matter? Why can greed and deceit still manipulate us? Why do people choose power over family? Working to address these questions and more, Pilgrims Passage: Rebuilding the Past is a journey brimming with adventures through turbulent times during the transition into the twenty-first century. For Paul Bardeck and Claudia Weiss, discovering a thousand-year-old monk’s journal fuels their quest to rebuild a mysterious ancient monastery perched upon the foothills in the Slovakian High Tatras, with the promise of releasing boundless energy stored within ancient ruins, as well as the Book of ONE. Concurrently, Karl Vloda’s seemingly unquenchable thirst for wealth and power, fueled by the Black Star Pact’s dark energy, seems to make the quest for ancient truths a sideshow. As the pilgrims’ paths entangle, will the promise of timely truths finally come to light? Does standing against the powers of darkness really matter today?
