Translations. Ser. 1, 2. Number theory and analysis

Translations. Ser. 1, 2. Number theory and analysis
Author :
Publisher : American Mathematical Soc.
Total Pages : 548
Release :
ISBN-10 : 0821816020
ISBN-13 : 9780821816028
Rating : 4/5 (20 Downloads)

Synopsis Translations. Ser. 1, 2. Number theory and analysis by : American Mathematical Society

Translations: Number theory and analysis

Translations: Number theory and analysis
Author :
Publisher :
Total Pages : 552
Release :
ISBN-10 : CORNELL:31924001536386
ISBN-13 :
Rating : 4/5 (86 Downloads)

Synopsis Translations: Number theory and analysis by : American Mathematical Society

Introduction to Analytic Number Theory

Introduction to Analytic Number Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 352
Release :
ISBN-10 : 9781475755794
ISBN-13 : 1475755791
Rating : 4/5 (94 Downloads)

Synopsis Introduction to Analytic Number Theory by : Tom M. Apostol

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS

Mathematics and Its History

Mathematics and Its History
Author :
Publisher : Springer Nature
Total Pages : 400
Release :
ISBN-10 : 9783030551933
ISBN-13 : 3030551938
Rating : 4/5 (33 Downloads)

Synopsis Mathematics and Its History by : John Stillwell

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

Vladimir I. Arnold - Collected Works

Vladimir I. Arnold - Collected Works
Author :
Publisher : Springer Science & Business Media
Total Pages : 500
Release :
ISBN-10 : 9783642017421
ISBN-13 : 3642017428
Rating : 4/5 (21 Downloads)

Synopsis Vladimir I. Arnold - Collected Works by : Vladimir I. Arnold

Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.

Wavelet Theory

Wavelet Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 522
Release :
ISBN-10 : 9780821849842
ISBN-13 : 0821849840
Rating : 4/5 (42 Downloads)

Synopsis Wavelet Theory by : Igor Iakovlevič Novikov (mathématicien).)

Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.

Explorations in Complex Functions

Explorations in Complex Functions
Author :
Publisher : Springer Nature
Total Pages : 353
Release :
ISBN-10 : 9783030545338
ISBN-13 : 3030545334
Rating : 4/5 (38 Downloads)

Synopsis Explorations in Complex Functions by : Richard Beals

This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.

Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications

Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications
Author :
Publisher : American Mathematical Soc.
Total Pages : 266
Release :
ISBN-10 : 9780821868966
ISBN-13 : 0821868969
Rating : 4/5 (66 Downloads)

Synopsis Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications by : Jorge Arvesœ

This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.

Foundations of the Classical Theory of Partial Differential Equations

Foundations of the Classical Theory of Partial Differential Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 264
Release :
ISBN-10 : 9783642580932
ISBN-13 : 3642580939
Rating : 4/5 (32 Downloads)

Synopsis Foundations of the Classical Theory of Partial Differential Equations by : Yu.V. Egorov

From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993