The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. These methods often give very elegant solutions to problems that seem intractable without them. The origin of the field goes back to Minkowski, but the first comprehensive book on the subject was J. In the prologue of his book, Cassels gives several of the concepts and results that he considers at the core of this area of mathematics, including the following question: Let f x 1 ,…,x n be a real-valued function of real variables x i.

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Cassels known to his friends by the Gaelic form "Ian" of his first name was born of mixed English-Scottish parentage on 11 July in the picturesque cathedral city of Durham. With a first degree from Edinburgh, he commenced research in Cambridge in under L. Mordell, who had just succeeded G. Hardy in the Sadleirian Chair of Pure Mathematics. He obtained his doctorate and was elected a Fellow of Trinity College in After a year in Manchester, he returned to Cambridge and in became Sadleirian Professor.

Cassels has contributed to several areas of number theory and written a number of other expository books: - An introduction to diophantine approximations - Rational quadratic forms - Economics for mathematicians - Local fields - Lectures on elliptic curves - Prolegomena to a middlebrow arithmetic of curves of genus 2 with E.

An Introduction to the Geometry of Numbers. From the reviews: "The work is carefully written. It is well motivated, and interesting to read, even if it is not always easy Among the topi are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references. Representation of integers by quadratic forms. The quotient space. Successive minima. Inhomogeneous problems.

An Introduction to the Geometry of Numbers J. Cassels J.

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## An introduction to the geometry of numbers

Cassels known to his friends by the Gaelic form "Ian" of his first name was born of mixed English-Scottish parentage on 11 July in the picturesque cathedral city of Durham. With a first degree from Edinburgh, he commenced research in Cambridge in under L. Mordell, who had just succeeded G. Hardy in the Sadleirian Chair of Pure Mathematics. He obtained his doctorate and was elected a Fellow of Trinity College in After a year in Manchester, he returned to Cambridge and in became Sadleirian Professor. Cassels has contributed to several areas of number theory and written a number of other expository books: - An introduction to diophantine approximations - Rational quadratic forms - Economics for mathematicians - Local fields - Lectures on elliptic curves - Prolegomena to a middlebrow arithmetic of curves of genus 2 with E.

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## Geometry of numbers

It seems that you're in Germany. We have a dedicated site for Germany. It is well motivated, and interesting to read, even if it is not always easy Among the topics are lattices, reduction, Minkowski's Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references. Cassels known to his friends by the Gaelic form "Ian" of his first name was born of mixed English-Scottish parentage on 11 July in the picturesque cathedral city of Durham.

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## An Introduction to the Geometry of Numbers

Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation , the problem of finding rational numbers that approximate an irrational quantity. Minkowski's theorem on successive minima , sometimes called Minkowski's second theorem , is a strengthening of his first theorem and states that [3]. In research on the geometry of numbers was conducted by many number theorists including Louis Mordell , Harold Davenport and Carl Ludwig Siegel. In recent years, Lenstra, Brion, and Barvinok have developed combinatorial theories that enumerate the lattice points in some convex bodies.

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