Lectures on the Theory of Algebraic Numbers

Lectures on the Theory of Algebraic Numbers
Author: E. T. Hecke
Publisher: Springer Science & Business Media
Total Pages: 251
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475740921

. . . 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.

Transcendental Number Theory

Transcendental Number Theory
Author: Alan Baker
Publisher: Cambridge University Press
Total Pages: 180
Release: 1990-09-28
Genre: Mathematics
ISBN: 9780521397919

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.

Transcendental Numbers

Transcendental Numbers
Author: Andrei B. Shidlovskii
Publisher: Walter de Gruyter
Total Pages: 489
Release: 2011-06-01
Genre: Mathematics
ISBN: 3110889056

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Pillars of Transcendental Number Theory

Pillars of Transcendental Number Theory
Author: Saradha Natarajan
Publisher: Springer Nature
Total Pages: 184
Release: 2020-05-02
Genre: Mathematics
ISBN: 9811541558

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.

Analyses Concerning Passive and Active Synthesis

Analyses Concerning Passive and Active Synthesis
Author: Edmund Husserl
Publisher: Springer Science & Business Media
Total Pages: 725
Release: 2012-12-06
Genre: Philosophy
ISBN: 9401008469

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.

Contributions to the Theory of Transcendental Numbers

Contributions to the Theory of Transcendental Numbers
Author: Gregory Chudnovsky
Publisher: American Mathematical Soc.
Total Pages: 464
Release: 1984
Genre: Mathematics
ISBN: 0821815008

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.

Irrationality and Transcendence in Number Theory

Irrationality and Transcendence in Number Theory
Author: David Angell
Publisher: CRC Press
Total Pages: 243
Release: 2021-12-30
Genre: Mathematics
ISBN: 100052373X

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.

Lectures on the Geometry of Numbers

Lectures on the Geometry of Numbers
Author: Carl Ludwig Siegel
Publisher: Springer Science & Business Media
Total Pages: 168
Release: 2013-03-09
Genre: Mathematics
ISBN: 366208287X

Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's requirements of accuracy in detail, both in the text and in the illustrations, but involving no changes in the structure and style of the lectures as originally delivered. This book is an enticing introduction to Minkowski's great work. It also reveals the workings of a remarkable mind, such as Siegel's with its precision and power and aesthetic charm. It is of interest to the aspiring as well as the established mathematician, with its unique blend of arithmetic, algebra, geometry, and analysis, and its easy readability.

Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics
Author: Joel David Hamkins
Publisher: MIT Press
Total Pages: 350
Release: 2021-02-02
Genre: Mathematics
ISBN: 0262362651

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.