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.

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.

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 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.

Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

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.

To the Western world, Ibuse Masuji is known primarily as the author of Black Rain, a document of the atomic holocaust and perhaps modern Japanese literature's most important contribution to the world of letters. In Japan, where is career has spanned six decades of revolutionary historical and social change, his popular novels, stories, essays and poems have won that nations' highest literary awards. John Whittier Treat's illuminating study of Ibuse is "an inquiry into the life and writings of a man brave enough to attempt a story that, in the view of more than one Hiroshima survivor, was "beyond words." Treat's analysis is the first comprehensive critical work on Ibuse outside of Japan. He provides a key to Ibuse's extraordinary writings, making his Japanese subject accessible to a Western audience. Moving beyond conventional distinctions between Ibuse's earlier and later works, Treat synthesizes a framework in which to read and understand Ibuse as a whole. He begins with a question: why and how did this author come to write Japan's most acclaimed novel of the Hiroshima bombing? His answer is organized chronologically and thematically, incorporating elements of both biography and literary criticism. He translates extensively from Ibuse's works and from interviews with the author. Pervasive themes, motifs, and images are developed and interrelated throughout the short stories, essays and early novels of the 1920s and 1930s, wartime journals, and the historical fiction based on the accounts of castaways in Edo period Japan. Ibuse's quintessential humor and irony culminate in the powerful realism of Black Rain and his postwar writing. Ibuse's voice emerges clearly. His message is human; his subject is man as a survivor. Treat's book reveals an author whose complex themes "explore what binds man to his world--not, as is so often the case with modern fiction, what separates him." To this end, says Treat, Ibuse's work is about the work of literature, about coming to terms "with the power of words to prescribe as well as describe how we see ourselves complete in a fractured world."

The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.

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”.