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Linear Algebra with Applications

by Roger Baker & Kenneth Kuttler

This book gives a self- contained treatment of linear algebra with many of its most important applications. It is very unusual if not unique in being an elementary book which does not neglect arbitrary fields...

The Theory of Multiple Zeta Values with Applications in Combinatorics


This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics,...

Mathematical Conversations: Multicolor Problems, Problems in the Theory of Numbers, and Random Walks

by E. B. Dynkin & V. A. Uspenskii

Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability...

History of the Theory of Numbers, Volume II: Diophantine Analysis

by Leonard Eugene Dickson

Written by a distinguished University of Chicago professor, this 2nd volume in the series History of the Theory of Numbers presents material related to Diophantine Analysis. 1919 edition.

The Theory of Algebraic Numbers

by Harry Pollard & Harold G. Diamond

Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields;...

Essays on the Theory of Numbers

by Richard Dedekind

Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties...

Topics in Number Theory, Volumes I and II

by William J. LeVeque

Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956...

Number Theory and Its Applications

by Fuhuo Li, Nianliang Wang & Shigeru Kanemitsu

This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics before...

Analytic Number Theory: An Introductory Course(Reprinted 2009)

by Paul T Bateman & HAROLD G DIAMOND

This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative...

Analytic Number Theory for Undergraduates

by Heng Huat Chan

This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes...

Algebraic Number Theory

by Edwin Weiss

Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global,...

The Theory of Remainders

by Andrea Rothbart

An imaginative introduction to number theory and abstract algebra, this unique approach employs a pair of fictional characters whose dialogues explain theories and demonstrate applications in terms of football...

Elementary Number Theory: An Algebraic Approach

by Ethan D. Bolker

This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more....

An Adventurer's Guide to Number Theory

by Richard Friedberg

This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.

Topological Methods in Galois Representation Theory

by Victor P. Snaith

This advanced monograph on Galois representation theory by a renowned algebraist covers abelian and nonabelian cohomology of groups, characteristic classes of forms and algebras, explicit Brauer induction theory,...

Theory and Application of Infinite Series

by Konrad Knopp

Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic...

Introductory Complex Analysis

by Richard A. Silverman

Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers....

Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger

by Pierre Samuel

This text covers the basics of algebraic number theory, including divisibility theory in principal ideal domains, the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition....

Diophantine Approximations

by Ivan Niven

This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of complex numbers, and product of complex linear forms....

Mathematics: The Man-Made Universe

by Sherman K. Stein

Highly readable volume covers number theory, topology, set theory, geometry, algebra, and analysis, plus the primes, fundamental theory of arithmetic, probability, and more. Solutions manual available upon request....