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Examines when a prime $p$ can be written in the form $x^{2} + ny^{2}$. The book begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms.

Offers a rigorous introduction on an elementary level to the theory of analytic functions of one complex variable. The book covers standard topics in an introductory complex analysis course. The presentation is slanted toward the geometric approach to complex analysis.

Presents various theorems of the theory of sets along with complete proofs. This book discusses strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.

Suitable for beginners and experienced mathematicians, this book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. It offers a discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way.

A translation of Landau's famous "Elementare Zahlentheorie" with added exercises.

Motivated by questions about which functions could be represented by Dirichlet series, Harald Bohr founded the theory of almost periodic functions in the 1920s. This book discusses almost periodic functions of a complex variable.

Contains papers including the one on the theory of the Syzygetic Relations of two Rational Integral Functions, comprising an application to the Theory of Sturm's Functions. This work also contains Sylvester's dialytic method of elimination, his Essay on Canonical Forms, and early investigations in the theory of Invariants.

Offers an easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering. This title includes individual chapters that have been kept as far as possible independent of each other.

Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honours-level undergraduates, this volume focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by students who possess a basic familiarity with abstract algebra.

Presents the foundations of a general theory of algebras. Often called "universal algebra", this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is filled with useful illustrations and exercises that solidify the reader's understanding.

This second edition includes exercises at the end of each chapter, revised bibliographies, references and an index.

The six-volume collection, Generalized Functions, written by I.M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.

The six-volume collection, Generalized Functions, published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions.

The six-volume collection, Generalized Functions, published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions.

The six-volume collection, Generalized Functions, published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1 is devoted to basics of the theory of generalized functions.

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has avoided any presumption that the reader has knowledge of mathematical concepts until they are presented in the book.

This famous work is a textbook that emphasises the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the "canonical" topics, and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorisation and on functions holomorphic in a half-plane.

Gives a presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. This title is suitable for a class or for self-study.

Dirichlet (1805-1859) is well known for his significant contributions to several branches of mathematics. In analysis, he is remembered for his work in potential theory, especially his study of harmonic functions with prescribed boundary values, now known as the Dirichlet problem. This work features two volumes of ""Dirichlet's Collected Works"".

This flexible text is organised into two parts: Part I treats the theory of measure and integration over abstract measure spaces; Part II is more specialised, and includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic representation of positive linear forms, and Haar measure on a locally compact group.

Covers quadratic and higher forms. This book presents methods of attacking whole classes of problems.

Surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. This book discusses basic results on the existence of matchings and on the matching structure of graphs, as well as the impact of matching theory.

Covers The Euler-MacLaurin sum formula.

Offers a presentation of algebraic aspects of global class field theory.