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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...

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,...

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...

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.

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;...

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...

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...

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...

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...

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...

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,...

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...

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....

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.

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,...

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...

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....

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....

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....

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....