Download or read book Lectures on Transcendental Numbers written by K. Mahler and published by Springer. This book was released on 2006-11-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on the Theory of Algebraic Numbers written by E. T. Hecke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.

Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 1990-09-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.

Download or read book Analyses Concerning Passive and Active Synthesis written by Edmund Husserl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coming from what is arguably the most productive period of Husserl's life, this volume offers the reader a first translation into English of Husserl's renowned lectures on `passive synthesis', given between 1920 and 1926. These lectures are the first extensive application of Husserl's newly developed genetic phenomenology to perceptual experience and to the way in which it is connected to judgments and cognition. They include an historical reflection on the crisis of contemporary thought and human spirit, provide an archaeology of experience by questioning back into sedimented layers of meaning, and sketch the genealogy of judgment in `active synthesis'. Drawing upon everyday events and personal experiences, the Analyses are marked by a patient attention to the subtle emergence of sense in our lives. By advancing a phenomenology of association that treats such phenomena as bodily kinaesthesis, temporal genesis, habit, affection, attention, motivation, and the unconscious, Husserl explores the cognitive dimensions of the body in its affectively significant surroundings. An elaboration of these diverse modes of evidence and their modalizations (transcendental aesthetic), allows Husserl to trace the origin of truth up to judicative achievements (transcendental logic). Joined by several of Husserl's essays on static and genetic method, the Analyses afford a richness of description unequalled by the majority of Husserl's works available to English readers. Students of phenomenology and of Husserl's thought will find this an indispensable work.

Download or read book Pillars of Transcendental Number Theory written by Saradha Natarajan and published by Springer Nature. This book was released on 2020-05-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite–Lindemann–Weierstrass theorem, Gelfond–Schneider theorem, Schmidt’s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker’s original results. This book presents Baker’s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of “Exercises” and interesting information presented as “Notes,” intended to spark readers’ curiosity.

Download or read book Irrationality and Transcendence in Number Theory written by David Angell and published by CRC Press. This book was released on 2021-12-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation. Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates. Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background.

Download or read book Contributions to the Theory of Transcendental Numbers written by Gregory Chudnovsky and published by American Mathematical Soc.. This book was released on 1984 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.

Download or read book An Invitation to Modern Number Theory written by Steven J. Miller and published by Princeton University Press. This book was released on 2020-07-21 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

Download or read book The Transcendental Universe written by C. G. Harrison and published by SteinerBooks. This book was released on 1993-04-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Our very 'I' consciousness is possible because the mineral earth--the first layer of the interior of the Earth--and the other chthonic regions exist. Our human nature is a reflection of the subearthly and supraearthly realms that comprise the macrocosm and the microcosm. 'The true meaning of the microcosm-macrocosm analogy is not that the human being is a little cosmos, but that the cosmos is a big human being.' From this perspective, it makes complete sense that the subterranean realms described by spiritual science live within the deepest realms of our human nature and subconscious life of darker feelings and will. Deep within the human being, they radiate into the shadows of thought. This region is more familiarly known as Hell, Hades, or the Abyss. The subterranean spheres, then, are the Earth's 'dark side'" (from Paul V. O'Leary's introduction). Throughout human history, ancient wisdom and traditional myths have placed human beings between the heavens and the underworld, describing the heavens as the light-filled realm of the gods and the source of goodness, and characterizing the underworld as a demon-filled realm of darkness and the source of evil. Modern science, however, denies the heavens and knows little of the Earth's interior -- even physically -- beyond the first few miles, after which it simply resorts to conjecture based on the extrapolation of existing sensory data. In other words, natural science fails to take into account that the Earth is a living, spiritual being and ignores the presence of its soul-spiritual qualities and influences. To remedy this, during the early twentieth century, Rudolf Steiner researched the psychic, spiritual, and cosmic nature of the Earth's interior. He described how the different layers of the inner Earth affect and interact with human beings living on Earth. More theologically and cosmically, he spoke of the layers of "Hell," through which Jesus Christ traveled in the period between the Crucifixion and the Resurrection, uniting and integrating himself with the Earth and with human destiny. The seven authors in The Inner Life of the Earth approach this difficult and little-discussed topic from different directions. They discuss how the forces emanating from the interior of the Earth affect the weather, our atmosphere, human beings, and how human behavior in turn affects them, showing that earthly and human evolution are a unity and should never be thought of as occurring separately. They also discuss the deep significance of Christ's incarnation, by which he united with the Earth to become the Spirit of the Earth. Without Christ's deed, the Mystery of Golgotha, which reunites cosmic and human evolution with the divine, human beings would be unable to work in freedom with Christ or with Sophia, divine feminine Wisdom, in her form as the Soul of the Earth, to overcome evil and help lift all creation toward goodness and greater human, cosmic, and divine fellowship.

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Download or read book Introduction to Transcendental Numbers written by Serge Lang and published by . This book was released on 1966 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on p adic Differential Equations written by Bernard Dwork and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U. L. P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subject-p-adic analysis-was founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction . . . . . . . . . . 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory . . . . 33 4. Analytic Dual Theory. . . . . 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f,h 92 7. Hasse Invariants . . . . . . 108 8. The a --+ a' Map . . . . . . . . . . . . 110 9. Normalized Solution Matrix. . . . . .. 113 10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities. . . . . . . . . . . . . 137 11. Second-Order Linear Differential Equations Modulo Powers ofp ..... .

Download or read book Algebraic Cycles and Hodge Theory written by Mark L. Green and published by Springer Science & Business Media. This book was released on 1994-12-16 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

Download or read book Lectures on Formal and Rigid Geometry written by Siegfried Bosch and published by Springer. This book was released on 2014-08-22 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-02-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Download or read book 13 Lectures on Fermat s Last Theorem written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.

Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d