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The General Theory of Dirichlet's Series

by G. H. Hardy & Marcel Riesz

This classic work by two distinguished mathematicians explains theory and formulas behind Dirichlet's series and offers first systematic account of Riesz's theory of summation of series by typical means. 1915...


Mathematical Papers

by George Green & N. M. Ferrers

This compilation of Green's most significant works includes essays on theories of electricity and magnetism, laws of the equilibrium of fluids, the attractions of ellipsoids of variable densities, and more....


The Philosophy of Mathematics: Translated from Cours de Philosophie Positive by W. M. Gillespie

by Auguste Comte

Written by the nineteenth-century French philosophical founder of positivism, this comprehensive map of mathematical science assigns to each part of the complex whole its true position and value.


The Hindu-Arabic Numerals

by David Eugene Smith & Louis Charles Karpinski

Concise history of the origin and development of Hindu-Arabic numerals recounts international labors of scholars, assesses the historical testimony, and draws conclusions from the evidence. 1911 edition.


Lectures on Partial Differential Equations

by I. G. Petrovsky

Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from...


Elementary Concepts of Topology

by Paul Alexandroff

Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept...


Contributions to the Founding of the Theory of Transfinite Numbers

by Georg Cantor

The famous articles, 1895–7, that founded a new branch of mathematics. Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordinal types of simple...


Non-Euclidean Geometry

by Stefan Kulczycki

This accessible approach features stereometric and planimetric proofs, and elementary proofs employing only the simplest properties of the plane. A short history of geometry precedes the systematic exposition....


Abstract Sets and Finite Ordinals: An Introduction to the Study of Set Theory

by G. B. Keene

This text unites logical and philosophical aspects of set theory in a manner intelligible to mathematicians without training in formal logic and to logicians without a mathematical background. 1961 edition.


The Nature of Mathematics

by Philip E. B. Jourdain

Anyone interested in mathematics will appreciate this survey, which explores the distinction between the body of knowledge known as mathematics and the methods used in its discovery. 1913 edition.


Vector Analysis

by Homer E. Newell

This text combines the logical approach of a mathematical subject with the intuitive approach of engineering and physical topics. Applications include kinematics, mechanics, and electromagnetic theory. Includes...


Projective Geometry

by T. Ewan Faulkner

Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective...


Theory of Markov Processes

by E. B. Dynkin, D. E. Brown & T. Kovary

An investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. 1961 edition.


Infinite Series

by James M Hyslop

This concise text focuses on the convergence of real series. Topics include functions and limits, real sequences and series, series of non-negative terms, general series, series of functions, the multiplication...


General Investigations of Curved Surfaces: Edited with an Introduction and Notes by Peter Pesic

by Karl Friedrich Gauss, Adam Hiltebeitel & James Morehead

This influential work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. 1902...


The Early Mathematical Manuscripts of Leibniz

by G. W. Leibniz & J. M. Child

Leibniz's own accounts of his work, plus critical and historical notes and essays, include his "Historia et Origio Calculi Differentialis," manuscripts of the period 1673-77, and essays by C. I. Gerhardt.


Kernel Functions and Elliptic Differential Equations in Mathematical Physics

by Stefan Bergman & Menahem Schiffer

Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications....


Introductory Non-Euclidean Geometry

by Henry Parker Manning

This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry....


The Elements of Non-Euclidean Geometry

by D. M.Y. Sommerville

Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics....


Matrix Vector Analysis

by Richard L. Eisenman

This outstanding text and reference for upper-level undergraduates features extensive problems and solutions in its application of matrix ideas to vector methods for a synthesis of pure and applied mathematics....