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Mathematics
Number Theory


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Triangular Arrays with Applications
Triangular Arrays with Applications
by Thomas Koshy
Publisher Comments
Triangular arrays are a unifying thread throughout various areas of discrete mathematics such as number theory and combinatorics. They can be used to sharpen a variety of mathematical skills and tools, such as pattern recognition, conjecturing, proof... (read more)

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Single Digits: In Praise of Small Numbers
Single Digits: In Praise of Small Numbers
by Marc Chamberland
Publisher Comments
"A veritable potpourri of mathematical factoids, Single Digits will provide you with conversational ammunition for all manner of nerdy gatherings."--Henry Reich, creator of MinutePhysics and MinuteEarth "Dispensing incisive, brief expositions of... (read more)

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Introduction To the Theory of Numbers (5TH 91 Edition)
Introduction To the Theory of Numbers (5TH 91 Edition)
by Ivan Niven
Book News Annotation
Certainly the quality of any text entering its 5th edition will in general terms be well known to potential users well in advance of any review. The 1st edition of this classic appeared in 1960, and the 4th in 1980. To the present edition (beyond the... (read more)

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Elementary Number Theory (Springer Undergraduate Mathematics Series)
Elementary Number Theory (Springer Undergraduate Mathematics Series)
by Gareth A. Jones
Review
From the reviews: BULLETIN OF MATHEMATICS BOOKS "?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."   G.A. Jones and J.M. Jones Elementary Number Theory "A welcome addition . . . a carefully and... (read more)

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Encyclopedia of Mathematics and Its Applications #150: Lattice Sums Then and Now
Encyclopedia of Mathematics and Its Applications #150: Lattice Sums Then and Now
by Jonathan Borwein
Publisher Comments
"The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built... (read more)

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Algebraic Number Theory and Fermat's Last Theorem
Algebraic Number Theory and Fermat's Last Theorem
by Ian Stewart
Publisher Comments
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two... (read more)

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Number theory IV :transcendental numbers
Number theory IV :transcendental numbers
by I. R. Shafarevich
Publisher Comments
This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also... (read more)

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Vorlesungen Uber Zahlentheorie (Cambridge Library Collection - Mathematics)
Vorlesungen Uber Zahlentheorie (Cambridge Library Collection - Mathematics)
by Peter Gustav Lejeune Dirichlet
Publisher Comments
Peter Gustav Lejeune Dirichlet (1805 59) may be considered the father of modern number theory. He studied in Paris, coming under the influence of mathematicians like Fourier and Legendre, and then taught at Berlin and G ttingen universities, where he was... (read more)

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Contributions in Mathematical and Computational Sciences #2: The Arithmetic of Fundamental Groups: Pia 2010
Contributions in Mathematical and Computational Sciences #2: The Arithmetic of Fundamental Groups: Pia 2010
by Jakob (edt) Stix
Publisher Comments
In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its... (read more)

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Developments in Mathematics #23: Partitions, Q-Series, and Modular Forms
Developments in Mathematics #23: Partitions, Q-Series, and Modular Forms
by Krishnaswami Alladi
Publisher Comments
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... (read more)

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de Gruyter Studies in Mathematics #41: Algebraic Graph Theory: Morphisms, Monoids and Matrices
de Gruyter Studies in Mathematics #41: Algebraic Graph Theory: Morphisms, Monoids and Matrices
by Ulrich Knauer
Book News Annotation
Knauer presents lectures he has delivered for graduate students of mathematics, though other majors and advanced undergraduates might find them useful as well. Homomorphisms, especially endomorphisms, form a common thread, he says, as well as the... (read more)

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Number Theory and Its History (Dover Classics of Science & Mathematics)
Number Theory and Its History (Dover Classics of Science & Mathematics)
by Oystein Ore
Publisher Comments
"A very valuable addition to any mathematical library." — School Science and Math This book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most other books on number theory in two important... (read more)

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Multiscale Potential Theory (Applied and Numerical Harmonic Analysis)
Multiscale Potential Theory (Applied and Numerical Harmonic Analysis)
by Willi Freeden
Publisher Comments
This self-contained book provides a basic foundation for students, practitioners, and researchers interested in some of the diverse new areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential... (read more)

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Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a #43: Sieves in Number Theory
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a #43: Sieves in Number Theory
by George Greaves
Publisher Comments
This book surveys the current state of the "small" sieve methods developed by Brun, Selberg and later workers. The book is suitable for university graduates making their first acquaintance with the subject, leading them towards the frontiers of modern... (read more)

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P-Adic Methods and Their Applications (Oxford Science Publications)
P-Adic Methods and Their Applications (Oxford Science Publications)
by Andrew J. Baker
Book News Annotation
A collection of ten intermediate articles for graduate students of mathematics just beginning their own research. Surveys the application of p-acidic numbers and analysis in such fields as number theory, algebraic geometry and topology, group... (read more)

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Algebraic Patching (Springer Monographs in Mathematics)
Algebraic Patching (Springer Monographs in Mathematics)
by Moshe Jarden
Publisher Comments
Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of... (read more)

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Graduate Texts in Mathematics #138: A Course in Computational Algebraic Number Theory
Graduate Texts in Mathematics #138: A Course in Computational Algebraic Number Theory
by Henri Cohen
Publisher Comments
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of... (read more)

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Publications of the Mathematical Society of Japan #11: Introduction to Arithmetic Theory of Automorphic Functions
Publications of the Mathematical Society of Japan #11: Introduction to Arithmetic Theory of Automorphic Functions
by Goro Shimura
Publisher Comments
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular... (read more)

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Developments in Mathematics #10: Number Theory and Modular Forms: Papers in Memory of Robert A. Rankin
Developments in Mathematics #10: Number Theory and Modular Forms: Papers in Memory of Robert A. Rankin
by Bruce C. Berndt
Publisher Comments
Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of... (read more)

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Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics)
Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics)
by William Stein
Publisher Comments
The systematic study of number theory was initiated around 300B.C. when Euclid proved that there are infinitely many prime numbers. At the same time, he also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive... (read more)

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