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Lecture Notes on Diophantine Analysis
These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Number Theory and Polynomials
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Introduction to Algebraic Independence Theory
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
Number Theory in Progress
Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.
Digital Phase Modulation
The last ten years have seen a great flowering of the theory of digital data modulation. This book is a treatise on digital modulation theory, with an emphasis on these more recent innovations. It has its origins in a collabor ation among the authors that began in 1977. At that time it seemed odd to us that the subjects of error-correcting codes and data modulation were so separated; it seemed also that not enough understanding underlay the mostly ad hoc approaches to data transmission. A great many others were intrigued, too, and the result was a large body of new work that makes up most of this book. Now the older disciplines of detection theory and coding theory have been generalized and ...
Experiential Consciousness and the Nature of Human Identity
Consciousness is hard to bring to the laboratory as it confronts us with a classic dilemma: can a mind observe itself? However, who, then, is observing the observer? Without experiential awareness, culture, the arts, science, and philosophy would not make sense. Would it make sense if refrigerators were to produce a “refrigerator culture” without the experience of freezing food? Virtually all human culture is destined to provide conscious experiences. This volume provides a rich array of views on human nature and the way it shows up in the strange land of human identity.
Handbook of Infertility & Ultrasound for Practicing Gynecologists
This handbook is a guide to infertility and ultrasound for gynaecologists and infertility specialists. The second edition has been fully revised and includes many new topics, providing the latest information in the field. Divided into two sections, the first half of the book covers infertility. Beginning with discussion on assessment of an infertile couple, the following chapters examine different hormone treatments, sperm preparation, and ovulation induction, including in patients with polycystic ovary syndrome. The remaining chapters cover male infertility, recurrent pregnancy loss, and practical tips for infertility management. The second part of the book covers ultrasound. Beginning with...
Donald School Textbook of Human Reproductive & Gynecological Endocrinology
Part of the renowned Donald School series, this book is a comprehensive guide to the diagnosis and management of reproductive and gynaecological endocrinology disorders. The book begins with an overview of ovulation and investigation and causes of female infertility including anovulation, tubal block, endometriosis and congenital uterine anomalies. The following chapters discuss ovarian stimulation and assisted reproductive techniques. The second half of the book covers causes and management of male infertility, and concludes with chapters on recurrent miscarriage, gamete banking, and assessment of early pregnancy. Authored by recognised experts in the field, the text is further enhanced by clinical photographs, illustrations, tables and flowcharts. Key points Comprehensive guide to diagnosis and management of reproductive and gynaecological endocrinology disorders Part of renowned Donald School series Covers investigation, causes and management of both female and male infertility Authored by recognised experts in the field
Diophantine Approximation on Linear Algebraic Groups
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
