Pillars Of Transcendental Number Theory
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Pillars Of Transcendental Number Theory
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Author : Saradha Natarajan
language : en
Publisher: Springer Nature
Release Date : 2020-05-02
Pillars Of Transcendental Number Theory written by Saradha Natarajan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-02 with Mathematics categories.
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.
Abstract Algebra And Famous Impossibilities
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Author : Sidney A. Morris
language : en
Publisher: Springer Nature
Release Date : 2022-11-26
Abstract Algebra And Famous Impossibilities written by Sidney A. Morris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-26 with Mathematics categories.
This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction. Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach. Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.
Perfect Powers An Ode To Erd S
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Author : Saradha Natarajan
language : en
Publisher: Springer Nature
Release Date : 2025-04-26
Perfect Powers An Ode To Erd S written by Saradha Natarajan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-26 with Mathematics categories.
The book explores and investigates a long-standing mathematical question whether a product of two or more positive integers in an arithmetic progression can be a square or a higher power. It investigates, more broadly, if a product of two or more positive integers in an arithmetic progression can be a square or a higher power. This seemingly simple question encompasses a wealth of mathematical theory that has intrigued mathematicians for centuries. Notably, Fermat stated that four squares cannot be in arithmetic progression. Euler expanded on this by proving that the product of four terms in an arithmetic progression cannot be a square. In 1724, Goldbach demonstrated that the product of three consecutive positive integers is never square, and Oblath extended this result in 1933 to five consecutive positive integers. The book addresses a conjecture of Erdős involving the corresponding exponential Diophantine equation and discusses various number theory methods used to approach a partial solution to this conjecture. This book discusses diverse ideas and techniques developed to tackle this intriguing problem. It begins with a discussion of a 1939 result by Erdős and Rigge, who independently proved that the product of two or more consecutive positive integers is never a square. Despite extensive efforts by numerous mathematicians and the application of advanced techniques, Erdős' conjecture remains unsolved. This book compiles many methods and results, providing readers with a comprehensive resource to inspire future research and potential solutions. Beyond presenting proofs of significant theorems, the book illustrates the methodologies and their limitations, offering a deep understanding of the complexities involved in this mathematical challenge.
General Financial Awareness Vol 2 Topicwise Notes For All Banking Related Exams A Complete Preparation Book For All Your Banking Exams With Solved Mcqs Ibps Clerk Ibps Po Sbi Po Sbi Clerk Rbi And Other Banking Exams
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Author : EduGorilla Prep Experts
language : en
Publisher: EduGorilla Community Pvt. Ltd.
Release Date : 2023-04-29
General Financial Awareness Vol 2 Topicwise Notes For All Banking Related Exams A Complete Preparation Book For All Your Banking Exams With Solved Mcqs Ibps Clerk Ibps Po Sbi Po Sbi Clerk Rbi And Other Banking Exams written by EduGorilla Prep Experts and has been published by EduGorilla Community Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Education categories.
EduGorilla's General/Financial Awareness (Vol 2) Study Notes are the best-selling notes for General/Financial Awareness in the English edition. Their content for banking exams is well-researched and covers all topics related to General/Financial Awareness. The notes are designed to help students prepare thoroughly for their exams, with topic-wise notes that are comprehensive and easy to understand. The notes also include solved multiple-choice questions (MCQs) for self-evaluation, allowing students to gauge their progress and identify areas that require further improvement. These study notes are tailored to the latest syllabus of all banking-related exams, making them a valuable resource for exam preparation.
The Certainty
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Author : Mayukh Maitra
language : en
Publisher: Educreation Publishing
Release Date : 2016-11-16
The Certainty written by Mayukh Maitra and has been published by Educreation Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Education categories.
The book deals with the Information theory and explores the logical methods in determination of a measure in the field probability associated with the information processing for real time systems and models, such as to distinguish the certainty that is a power function, and identify the uncertainty which as an unknown variable is a complement of the function, in order to achieve accuracy of the intended results to precisely meet with the predictions.
Dirichlet
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Author : Uta C. Merzbach
language : en
Publisher: Springer
Release Date : 2018-12-29
Dirichlet written by Uta C. Merzbach and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-29 with Mathematics categories.
This is the first extensive biography of the influential German mathematician, Peter Gustav Lejeune Dirichlet (1805 – 1859). Dirichlet made major contributions to number theory in addition to clarifying concepts such as the representation of functions as series, the theory of convergence, and potential theory. His mathematical methodology was explicitly based on a thorough knowledge of the work of his predecessors and his belief in the underlying unity of the branches of mathematics. This unified approach is exemplified in a paper that effectively launched the field of analytic number theory. The same orientation pervaded his teaching, which had a profound influence on the work of many mathematicians of subsequent generations. Chapters dealing with his mathematical work alternate with biographical chapters that place Dirichlet’s life and those of some of his notable associates in the context of the political, social, and artistic culture of the period. This book will appeal not only to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.
Pools Of Water Pillars Of Cl
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Author :
language : en
Publisher: University of Washington Press
Release Date :
Pools Of Water Pillars Of Cl written by and has been published by University of Washington Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Theory Of Algebraic Number Fields
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Author : David Hilbert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Theory Of Algebraic Number Fields written by David Hilbert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.
Ways Of Being Bound Perspectives From Post Kantian Philosophy And Relational Sociology
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Author : Patricio A. Fernández
language : en
Publisher: Springer Nature
Release Date : 2022-11-01
Ways Of Being Bound Perspectives From Post Kantian Philosophy And Relational Sociology written by Patricio A. Fernández and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-01 with Philosophy categories.
This book addresses the topic of 'being bound' from a philosophical and a sociological perspective. It examines several ways in which we are bound. We are bound to acknowledge the truth and to follow laws; we are bound to others and to the world. Who we are is partly defined by those bonds, regardless of whether we live up to them – or even of whether we acknowledge them. Puzzling questions arise from the fact that we are bound, such as: How are those bonds binding? Wherein lies their normative character? A venerable philosophical tradition, particularly since Kant, has provided an account of normativity that crucially appeals to such notions as “self-legislation.” But can our normative bonds be properly understood in these essentially first-personal terms? Many argue that our social condition resists any account of those bonds that fails to acknowledge the perspectives of the second and the third person. The first part of the book explores these themes from a historical perspective in the tradition of transcendental philosophy (Kant, Fichte, Hegel, Husserl and Heidegger); it examines the phenomenon of “being bound”, i.e., why and how we are bound. The second part of the book offers a sociological analysis of social bonds that is both historical and systematic. Based on sociological approaches to “solidarity” and “reflexivity”, it explores the way in which the phenomenon of “being bound” manifests through the concept of a “social relation”.
Pillars In The History Of Biblical Interpretation Volume 1
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Author : Stanley E. Porter
language : en
Publisher: Wipf and Stock Publishers
Release Date : 2016-08-17
Pillars In The History Of Biblical Interpretation Volume 1 written by Stanley E. Porter and has been published by Wipf and Stock Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-17 with Religion categories.
This two-volume set is part of a growing body of literature concerned with the history of biblical interpretation. The ample introduction first sets key players into the story of the development of the major strands of biblical interpretation since the Enlightenment, identifying how different theoretical and methodological approaches are related to each other and describing the academic environment in which they emerged and developed. Volume 1 contains fourteen essays on twenty-two interpreters who were principally active before 1980, and volume 2 has nineteen essays on twenty-seven of those who were active primarily after this date. Each chapter provides a brief biography of one or more scholars, as well as a detailed description of their major contributions to the field. This is followed by an (often new) application of the scholar's theory. By focusing on the individual scholars and their work, the book recognizes that interpretive approaches arise out of certain circumstances, and that scholars are influenced by, and have influences upon, both other interpreters and the times in which they live. This set is ideal for any class on the history of biblical interpretation and for those who want a greater understanding of how the current field of biblical studies developed.