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Number Theory In The Spirit Of Liouville

Author: Kenneth S. Williams
Publisher: Cambridge University Press
ISBN: 1107002532
Size: 33.92 MB
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A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.

Introduction To Compact Riemann Surfaces And Dessins D Enfants

Author: Ernesto Girondo
Publisher: Cambridge University Press
ISBN: 1139504185
Size: 53.63 MB
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Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this 2011 book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.

Ramanujan S Theta Functions

Author: Shaun Cooper
Publisher: Springer
ISBN: 3319561723
Size: 56.28 MB
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Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.

Number Theory Fourier Analysis And Geometric Discrepancy

Author: Giancarlo Travaglini
Publisher: Cambridge University Press
ISBN: 1107044030
Size: 23.62 MB
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"The first part of this book is dedicated to the first goal. The reader will find some topics typically presented in introductory books on Number Theory: factorization, arithmetic functions and integer points, congruences and cryptography, quadratic reciprocity, and sums of two and four squares. Starting from the first few pages we introduce some simple and captivating findings, such as Chebyshev's theorem and the elementary results for the Gauss circle problem and for the Dirichlet divisor problem, which may lead the reader to a deeper study of Number Theory, particularly students who are interested in Calculus and Analysis"--

The Block Theory Of Finite Group Algebras

Author: Markus Linckelmann
Publisher: Cambridge University Press
ISBN: 1108425917
Size: 70.90 MB
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A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Set Theory

Author: A. Hajnal
Publisher:
ISBN: 9781107362550
Size: 19.62 MB
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This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

The Red Book Of Mathematical Problems

Author: Kenneth S. Williams
Publisher: Courier Corporation
ISBN: 0486151824
Size: 31.15 MB
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DIVHandy compilation of 100 practice problems, hints and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Preface to the First Edition. Sources. 1988 edition. /div

Complex Algebraic Curves

Author: Frances Clare Kirwan
Publisher: Cambridge University Press
ISBN: 9780521423533
Size: 61.60 MB
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This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Transcendental Number Theory

Author: Alan Baker
Publisher: Cambridge University Press
ISBN: 9780521397919
Size: 22.64 MB
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An update of the classic book giving a systematic account of transcendental number theory.

The Geometry Of Heisenberg Groups

Author: Ernst Binz
Publisher: American Mathematical Soc.
ISBN: 0821844954
Size: 60.69 MB
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The three-dimensional Heisenberg group, being the simplest non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as well as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered. With no prerequisites beyond the standard mathematical curriculum, this book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics.