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Counterexamples in Analysis

Bernard R. Gelbaum

Counterexamples in Analysis

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These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as «real variables,» starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of...

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Bernard R. Gelbaum

An Introduction to the Theory of Li...

Georgi E. Shilov

An Introduction to the Theory of Linear Spaces

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This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers.

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Georgi E. Shilov

Advanced Calculus

Avner Friedman

Advanced Calculus

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This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable...

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Avner Friedman

Functional Analysis

Frigyes Riesz

Functional Analysis

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Classic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition.

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Frigyes Riesz

Mathematical Foundations of Quantum...

A. Y. Khinchin

Mathematical Foundations of Quantum Statistics

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A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.

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A. Y. Khinchin

The Logic of Chance

John Venn

The Logic of Chance

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No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used for teaching elementary mathematics. In The Logic of Chance, he employs the same directness that makes his diagrams so effective.The three-part treatment commences with an overview of the physical foundations of the science of...

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John Venn

The Gentle Art of Mathematics

Dan Pedoe

The Gentle Art of Mathematics

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This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more.

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Dan Pedoe

Intriguing Mathematical Problems

Oswald Jacoby

Intriguing Mathematical Problems

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Amusing and informative in its approach to solving mathematical bafflers, this treasury of theories, games, puzzles and oddities of all kinds, compiled by one of the world's best card players (Jacoby) and an expert in mathematical recreations (Benson) will delight and fascinate math enthusiasts.Although primarily intended to entertain, the wide variety of puzzles ― ranging from facile curiosities to very difficult intellectual exercises ― will challenge you to keep your...

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Oswald Jacoby

Pythagorean Triangles

Waclaw Sierpinski

Pythagorean Triangles

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The Pythagorean Theorem is one of the fundamental theorems of elementary geometry, and Pythagorean triangles — right triangles whose sides are natural numbers — have been studied by mathematicians since antiquity. In this classic text, a brilliant Polish mathematician explores the intriguing mathematical relationships in such triangles.Starting with «primitive» Pythagorean triangles, the text examines triangles with sides less than 100, triangles with two sides that are...

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Waclaw Sierpinski

Advanced Calculus

David V. Widder

Advanced Calculus

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This classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text in both applied mathematics and engineering.Believing that clarity of exposition depends largely on precision of statement, the author has taken pains...

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David V. Widder

Analysis in Euclidean Space

Kenneth Hoffman

Analysis in Euclidean Space

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Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory.Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power...

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Kenneth Hoffman

Concepts of Mathematical Modeling

Walter J. Meyer

Concepts of Mathematical Modeling

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Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions...

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Walter J. Meyer

Axiomatic Set Theory

Patrick Suppes

Axiomatic Set Theory

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One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: «Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?» Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics...

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Patrick Suppes

Applied Multivariate Analysis

S. James Press

Applied Multivariate Analysis

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Geared toward upper-level undergraduates and graduate students, this two-part treatment deals with the foundations of multivariate analysis as well as related models and applications. Starting with a look at practical elements of matrix theory, the text proceeds to discussions of continuous multivariate distributions, the normal distribution, and Bayesian inference; multivariate large sample distributions and approximations; the Wishart and other continuous multivariate distributions; and basic...

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S. James Press

A Concise History of Mathematics

Dirk J. Struik

A Concise History of Mathematics

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This compact, well-written history — first published in 1948, and now in its fourth revised edition — describes the main trends in the development of all fields of mathematics from the first available records to the middle of the 20th century. Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating.Beginning with the ancient Near East, the author traces the ideas and...

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Dirk J. Struik

Basic Algebra I

Nathan Jacobson

Basic Algebra I

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A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials,...

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Nathan Jacobson

Concepts of Modern Mathematics

Ian Stewart

Concepts of Modern Mathematics

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Some years ago, «new math» took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of «new math» have been eliminated and its positive elements...

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Ian Stewart

Basic Algebra II

Nathan Jacobson

Basic Algebra II

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A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for more than three decades. Nathan Jacobson's books possess a conceptual and theoretical orientation; in addition to their value as classroom texts, they serve as valuable references.Volume II comprises all of the subjects usually covered in a first-year graduate course in algebra. Topics include categories, universal algebra, modules, basic...

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Nathan Jacobson

Calculus

Morris Kline

Calculus

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Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition....

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Morris Kline

Complex Variables

Stephen D. Fisher

Complex Variables

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The most important topics in the theory and application of complex variables receive a thorough, coherent treatment in this introductory text. Intended for undergraduates or graduate students in science, mathematics, and engineering, this volume features hundreds of solved examples, exercises, and applications designed to foster a complete understanding of complex variables as well as an appreciation of their mathematical beauty and elegance. <BR>Prerequisites are minimal; a three-semester...

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Stephen D. Fisher

A History of Mathematical Notations

Cajori Florian

A History of Mathematical Notations

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This classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, its eventual decline or ultimate survival. The author’s coverage of obsolete notations — and what we can learn from them — is as comprehensive as those which have survived and still enjoy favor. Originally published in 1929 in a two-volume edition, this monumental work is...

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Cajori Florian

Mathematics for the Nonmathematicia...

Morris Kline

Mathematics for the Nonmathematician

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Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these—the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural...

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Morris Kline

The Fourth Dimension Simply Explain...

Henry P. Manning

The Fourth Dimension Simply Explained

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To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable — or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension.This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by Scientific American, these essays are so...

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Henry P. Manning

An Introduction to Linear Algebra

L. Mirsky

An Introduction to Linear Algebra

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"The straight-forward clarity of the writing is admirable." — American Mathematical Monthly.This work provides an elementary and easily readable account of linear algebra, in which the exposition is sufficiently simple to make it equally useful to readers whose principal interests lie in the fields of physics or technology. The account is self-contained, and the reader is not assumed to have any previous knowledge of linear algebra. Although its accessibility makes it suitable for...

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L. Mirsky

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