analysis modular mathematics series

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Analysis

Author : P. E. Kopp
ISBN : 9780340645963
Genre : Mathematics
File Size : 60. 30 MB
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This book builds on the material covered in Numbers, Sequences and Series, and provides students with a thorough understanding of the subject as it is covered on first year courses.

Numbers Sequences And Series

Author : Keith E. Hirst
ISBN : 9780340610435
Genre : Mathematics
File Size : 52. 49 MB
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Concerned with the logical foundations of number systems from integers to complex numbers.

Modular Functions And Dirichlet Series In Number Theory

Author : Tom M. Apostol
ISBN : 9781461209997
Genre : Mathematics
File Size : 53. 91 MB
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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Groups

Author : Camilla R. Jordan
ISBN : 9780340610459
Genre : Mathematics
File Size : 49. 83 MB
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Introduction to mathematical groups

Linear Algebra

Author : Reg Allenby
ISBN : 9780080571799
Genre : Mathematics
File Size : 71. 3 MB
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As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.

A Second Course In Complex Analysis

Author : William A. Veech
ISBN : 9780486151939
Genre : Mathematics
File Size : 60. 51 MB
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Geared toward upper-level undergraduates and graduate students, this clear, self-contained treatment of important areas in complex analysis is chiefly classical in content and emphasizes geometry of complex mappings. 1967 edition.

Partitions Q Series And Modular Forms

Author : Krishnaswami Alladi
ISBN : 9781461400288
Genre : Mathematics
File Size : 31. 44 MB
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Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Fourier Analysis On Number Fields

Author : Dinakar Ramakrishnan
ISBN : 9781475730852
Genre : Mathematics
File Size : 54. 61 MB
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A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.

Elementary Analysis

Author : Kenneth A. Ross
ISBN : 9781461462712
Genre : Mathematics
File Size : 49. 21 MB
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For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Ordinary Differential Equations

Author : William A. Adkins
ISBN : 9781461436188
Genre : Mathematics
File Size : 53. 50 MB
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Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations. Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.

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