Number Theory [electronic resource] : An Introduction to Mathematics: Part B / by William A. Coppel.

By: Coppel, William A [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextPublisher: Boston, MA : Springer US, 2006Description: X, 360 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387298542Subject(s): Mathematics | Matrix theory | Algebra | Special functions | Number theory | Mathematics | Number Theory | Linear and Multilinear Algebras, Matrix Theory | Special FunctionsAdditional physical formats: Printed edition:: No titleDDC classification: 512.7 LOC classification: QA241-247.5Online resources: Click here to access online
Contents:
The arithmetic of quadratic forms -- The geometry of numbers -- The number of prime numbers -- A character study -- Uniform distribution and ergodic theory -- Elliptic functions -- Connections with number theory.
In: Springer eBooksSummary: Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjects—such as linear algebra or real analysis—with which it is considered that every student of mathematics should be acquainted. On the other hand are courses given by lecturers in their own areas of specialization, which are intended to serve as a preparation for research. But after taking courses of only these two types, students might not perceive the sometimes surprising interrelationships and analogies between different branches of mathematics, and students who do not go on to become professional mathematicians might never gain a clear understanding of the nature and extent of mathematics. The two-volume Number Theory: An Introduction to Mathematics attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A, which should be accessible to a first-year undergraduate, deals with elementary number theory. Part B is more advanced than the first and should give the reader some idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches, we may obtain a broad picture. Audience This book is intended for undergraduate students in mathematics and engineering.
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The arithmetic of quadratic forms -- The geometry of numbers -- The number of prime numbers -- A character study -- Uniform distribution and ergodic theory -- Elliptic functions -- Connections with number theory.

Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjects—such as linear algebra or real analysis—with which it is considered that every student of mathematics should be acquainted. On the other hand are courses given by lecturers in their own areas of specialization, which are intended to serve as a preparation for research. But after taking courses of only these two types, students might not perceive the sometimes surprising interrelationships and analogies between different branches of mathematics, and students who do not go on to become professional mathematicians might never gain a clear understanding of the nature and extent of mathematics. The two-volume Number Theory: An Introduction to Mathematics attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A, which should be accessible to a first-year undergraduate, deals with elementary number theory. Part B is more advanced than the first and should give the reader some idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches, we may obtain a broad picture. Audience This book is intended for undergraduate students in mathematics and engineering.

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