Lectures on Transcendental Numbers PDF Download
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Author: K. Mahler
Publisher: Springer
ISBN: 3540379819
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Author: K. Mahler
Publisher: Springer
ISBN: 3540379819
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
Author: E. T. Hecke
Publisher: Springer Science & Business Media
ISBN: 1475740921
Category : Mathematics
Languages : en
Pages : 251
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Book Description
. . . 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.
Author: Alan Baker
Publisher: Cambridge University Press
ISBN: 9780521397919
Category : Mathematics
Languages : en
Pages : 180
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Book Description
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.
Author: Gregory Chudnovsky
Publisher: American Mathematical Soc.
ISBN: 0821815008
Category : Mathematics
Languages : en
Pages : 464
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Book Description
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.
Author: David Angell
Publisher: CRC Press
ISBN: 100052373X
Category : Mathematics
Languages : en
Pages : 243
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Book Description
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.
Author: Saradha Natarajan
Publisher: Springer Nature
ISBN: 9811541558
Category : Mathematics
Languages : en
Pages : 184
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Book Description
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.
Author: Edmund Husserl
Publisher: Springer Science & Business Media
ISBN: 9401008469
Category : Philosophy
Languages : en
Pages : 725
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Book Description
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.
Author: M. Ram Murty
Publisher: Springer
ISBN: 1493908324
Category : Mathematics
Languages : en
Pages : 219
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Book Description
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262362651
Category : Mathematics
Languages : en
Pages : 350
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Book Description
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.
Author: C. G. Harrison
Publisher: SteinerBooks
ISBN: 1584204974
Category : Body, Mind & Spirit
Languages : en
Pages : 228
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Book Description
"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.
