Challenging Mathematical Problems With Elementary Solutions, Volume I
Part 1 of the Dover Books on Mathematics series
Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. The problems, most of which can be solved with elementary mathematics, range from relatively simple to extremely difficult. Suitable for students, teachers, and any lover of mathematics. Complete solutions.
The Foundations of Statistics
Part of the Dover Books on Mathematics series
Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.
Invitation to Dynamical Systems
Part of the Dover Books on Mathematics series
This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.
The Number System
Part of the Dover Books on Mathematics series
This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
Calculus of Variations
Part of the Dover Books on Mathematics series
This text offers an introduction to the fundamentals and standard methods of the calculus of variations, covering fixed and movable boundaries, plus solutions of variational problems. 1961 edition.
Geometric Integration Theory
Part of the Dover Books on Mathematics series
Geared toward upper-level undergraduates and graduate students, this treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. 1957 edition.
Graph Theory
Part of the Dover Books on Mathematics series
An introductory text in graph theory, this treatment covers primary techniques and includes both algorithmic and theoretical problems. Algorithms are presented with a minimum of advanced data structures and programming details. 1988 edition.
Fractional Graph Theory
A Rational Approach To The Theory Of Graphs
Part of the Dover Books on Mathematics series
This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.
Convex Surfaces
Part of the Dover Books on Mathematics series
This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.
Part of the Dover Books on Mathematics series
Rigorous and concise, this text examines the basis of the distribution theories devised by Schwartz and by Mikusinki and surveys both functional and algebraic theories of distribution. 1962 edition.
Topological Methods in Euclidean Spaces
Part of the Dover Books on Mathematics series
Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.
Differential Calculus and Its Applications
Part of the Dover Books on Mathematics series
Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.
Boolean Reasoning
The Logic Of Boolean Equations
Part of the Dover Books on Mathematics series
Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
Abstract Methods in Partial Differential Equations
Part of the Dover Books on Mathematics series
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Introduction to Matrices and Linear Transformations
Part of the Dover Books on Mathematics series
This versatile undergraduate-level text contains enough material for a one-year course and serves as a support text and reference. It combines formal theory and related computational techniques. Solutions to selected exercises. 1978 edition.
A New Look at Geometry
Part of the Dover Books on Mathematics series
Richly detailed survey of the evolution of geometrical ideas and development of concepts of modern geometry: projective, Euclidean, and non-Euclidean geometry; role of geometry in Newtonian physics, calculus, relativity. Over 100 exercises with answers. 1966 edition.
Mathematical Logic
Part of the Dover Books on Mathematics series
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
Linear Algebra and Matrix Theory
Part of the Dover Books on Mathematics series
One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition.
Introduction to the Foundations of Mathematics
Part of the Dover Books on Mathematics series
Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
Two-Person Game Theory
Part of the Dover Books on Mathematics series
Clear, accessible treatment of mathematical models for resolving conflicts in politics, economics, war, business, and social relationships. Topics include strategy, game tree and game matrix, and much more. Minimal math background required. 1970 edition.
Lambda-Matrices and Vibrating Systems
Part of the Dover Books on Mathematics series
Features aspects and solutions of problems of linear vibrating systems with a finite number of degrees of freedom. Starts with development of necessary tools in matrix theory, followed by numerical procedures for relevant matrix formulations.
Lectures on Elementary Mathematics
Part of the Dover Books on Mathematics series
One of the 18th century's greatest mathematicians delivered these lectures at a training school for teachers. An exemplar among elementary expositions, they combine original ideas and elegant expression. 1898 edition.
An Introduction to the Theory of Groups
Part of the Dover Books on Mathematics series
This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates. Includes a wealth of simple examples, primarily geometrical, and end-of-chapter exercises. 1959 edition.
Approximate Calculation of Integrals
Part of the Dover Books on Mathematics series
This introduction to approximate integration approaches its subject from the viewpoint of functional analysis. The 3-part treatment covers concepts and theorems from the theory of quadrature, calculation of definite integrals, and calculation of indefinite integrals. 1962 edition.
Linear Algebra and Group Theory
Part of the Dover Books on Mathematics series
This accessible text by a Soviet mathematician features material not otherwise available to English-language readers. Its three-part treatment covers determinants and systems of equations, matrix theory, and group theory. 1961 edition.
Linear Algebra and Projective Geometry
Part of the Dover Books on Mathematics series
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
Differential Equations
Part of the Dover Books on Mathematics series
Practical, concise text covers the existence and uniqueness theorem, characteristics of first-order equations, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. 1961 edition.
Invariant Subspaces
Part of the Dover Books on Mathematics series
Broad survey focuses on operators on separable Hilbert spaces. Topics include normal operators, analytic functions of operators, shift operators, invariant subspace lattices, compact operators, invariant and hyperinvariant subspaces, more. 1973 edition.
Introduction to Partial Differential Equations
Part of the Dover Books on Mathematics series
Rigorous presentation, designed for use in a 1-semester course, explores basics; Fourier series; 2nd-order partial differential equations; wave, potential, and heat equations; approximate solution of partial differential equations, more. Exercises. 1961 edition.
The Convolution Transform
by Isidore Isaac Hirschman
Part of the Dover Books on Mathematics series
The relation between differential operators and integral transforms is the theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, more.
Algebraic Geometry
Part of the Dover Books on Mathematics series
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Logic in Elementary Mathematics
Part of the Dover Books on Mathematics series
This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Numerous examples and exercises. 1959 edition.
Harmonic Analysis and the Theory of Probability
Part of the Dover Books on Mathematics series
Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.
Non-Riemannian Geometry
by Luther Pfahler Eisenhart
Part of the Dover Books on Mathematics series
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Introduction to Partial Differential Equations
From Fourier Series To Boundary-value Problems
Part of the Dover Books on Mathematics series
The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition.
Constructive Real Analysis
Part of the Dover Books on Mathematics series
This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. Topics include iterations and fixed points, metric spaces, nonlinear programming, applications to integral equations, and more. 1967 edition.
Fibonacci Numbers
by Nikolai Nikolaevich Vorob'ev
Part of the Dover Books on Mathematics series
An engaging treatment of an 800-year-old problem explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. Its entertaining style will appeal to recreational readers and students alike.
Complex Integration and Cauchy's Theorem
Part of the Dover Books on Mathematics series
Brief monograph by a distinguished mathematician offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Includes applications to the calculus of residues. 1914 edition.
Games, Theory and Applications
Part of the Dover Books on Mathematics series
Accessible and informative, this introduction to game theory explores 2-person zero-sum games, 2-person non-zero sum games, n-person games, and a variety of applications. Numerous exercises with full solutions. Includes 30 illustrations. 1986 edition.
Interpolation
Part of the Dover Books on Mathematics series
In the mathematical subfield of numerical analysis, interpolation is a procedure that assists in "reading between the lines." Topics include displacement symbols and differences, divided differences, formulas of interpolation, much more. 1950 edition.
A Concept of Limits
Part of the Dover Books on Mathematics series
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
The Method of Trigonometrical Sums in the Theory of Numbers
Part of the Dover Books on Mathematics series
This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.
Elements of the Theory of Markov Processes and Their Applications
Part of the Dover Books on Mathematics series
Graduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition.
Foundations of Stochastic Analysis
Part of the Dover Books on Mathematics series
This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods. No prior knowledge of probability is assumed. Numerous problems, most with hints. 1981 edition.
Calculus of Variations
Mechanics, Control And Other Applications
Part of the Dover Books on Mathematics series
First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
Nonlinear Potential Theory of Degenerate Elliptic Equations
Part of the Dover Books on Mathematics series
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Introduction to Modern Algebra and Matrix Theory
Part of the Dover Books on Mathematics series
This unique text provides students with a basic course in both calculus and analytic geometry. It promotes an intuitive approach to calculus and emphasizes algebraic concepts. Minimal prerequisites. Numerous exercises. 1951 edition.
Introduction to Differentiable Manifolds
Part of the Dover Books on Mathematics series
This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
