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The Prime Number Theorem

Author : G. J. O. Jameson
ISBN : 0521891108
Genre : Mathematics
File Size : 66.80 MB
Format : PDF
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The prime numbers appear to be distributed in a very irregular way amongst the integers, but the prime number theorem provides a simple formula that tells us (in an approximate but well-defined sense) how many primes we can expect to find that are less than any integer we might choose. This is indisputably one of the the great classical theorems of mathematics. Suitable for advanced undergraduates and beginning graduates, this textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.
Category: Mathematics

Number Theory In The Spirit Of Liouville

Author : Kenneth S. Williams
ISBN : 9781107002531
Genre : Mathematics
File Size : 65.68 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.
Category: Mathematics

Set Theory For The Working Mathematician

Author : Krzysztof Ciesielski
ISBN : 0521594650
Genre : Mathematics
File Size : 76.62 MB
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Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Category: Mathematics

Potential Theory In The Complex Plane

Author : Thomas Ransford
ISBN : 0521466547
Genre : Mathematics
File Size : 51.36 MB
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Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.
Category: Mathematics

Undergraduate Algebraic Geometry

Author : Miles Reid
ISBN : 0521356628
Genre : Mathematics
File Size : 75.61 MB
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.
Category: Mathematics

Local Fields

Author : John William Scott Cassels
ISBN : 0521315255
Genre : Mathematics
File Size : 80.20 MB
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This book provides a fairly elementary and self-contained introduction to local fields.
Category: Mathematics

Complex Algebraic Curves

Author : Frances Clare Kirwan
ISBN : 0521423538
Genre : Mathematics
File Size : 75.91 MB
Format : PDF, Kindle
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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.
Category: Mathematics

Number Theory Fourier Analysis And Geometric Discrepancy

Author : Giancarlo Travaglini
ISBN : 9781107044036
Genre : Mathematics
File Size : 76.27 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"--
Category: Mathematics

An Introduction To Twistor Theory

Author : S. A. Huggett
ISBN : 0521456894
Genre : Mathematics
File Size : 45.36 MB
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This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics.
Category: Mathematics