## Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher: Courier Corporation
ISBN: 0486134776
Category: Mathematics
Page: 448
View: 8936

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

## Foundations of Modern Analysis

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category: Mathematics
Page: 250
View: 5905

Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

## Foundations of Analysis

Author: David French Belding,Kevin J. Mitchell
Publisher: Courier Corporation
ISBN: 048646296X
Category: Mathematics
Page: 427
View: 1598

This treatment develops the real number system and the theory of calculus on the real line, extending the theory to real and complex planes. Designed for students with one year of calculus, it features extended discussions of key ideas and detailed proofs of difficult theorems. 1991 edition.

## Number Systems and the Foundations of Analysis

Author: Elliott Mendelson
Publisher: Courier Corporation
ISBN: 0486457923
Category: Mathematics
Page: 358
View: 9945

Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.

## An Introduction to Mathematical Analysis

International Series of Monographs on Pure and Applied Mathematics
Author: Robert A. Rankin
Publisher: Elsevier
ISBN: 1483137309
Category: Mathematics
Page: 624
View: 7211

An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products. This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity. This monograph is intended for mathematics students.

## Introductory Real Analysis

Author: A. N. Kolmogorov,S. V. Fomin
Publisher: Courier Corporation
ISBN: 0486134741
Category: Mathematics
Page: 416
View: 8546

Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

## The Continuum

A Critical Examination of the Foundation of Analysis
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 0486679829
Category: Mathematics
Page: 130
View: 8388

Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.

## Foundations of Potential Theory

Author: Oliver Dimon Kellogg
Publisher: Courier Corporation
ISBN: 9780486601441
Category: Science
Page: 384
View: 4367

Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.

## Foundations of Probability

Author: Alfred Renyi
Publisher: Courier Corporation
ISBN: 0486462617
Category: Mathematics
Page: 366
View: 8815

Introducing many innovations in content and methods, this book involves the foundations, basic concepts, and fundamental results of probability theory. Geared toward readers seeking a firm basis for study of mathematical statistics or information theory, it also covers the mathematical notions of experiments and independence. 1970 edition.

## Introduction to Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Category: Mathematics
Page: 272
View: 2641

Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

## Foundations of Mathematical Analysis

Author: Saminathan Ponnusamy
Publisher: Springer Science & Business Media
ISBN: 0817682910
Category: Mathematics
Page: 570
View: 872

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

## Foundations of Analysis

Author: Edmund Landau
Publisher: American Mathematical Soc.
ISBN: 082182693X
Category: Mathematics
Page: 136
View: 8499

Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius. --American Mathematical Monthly Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, what are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege, and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis answers these important questions.

## Mathematical Foundations of Quantum Mechanics

Author: George W. Mackey
Publisher: Courier Corporation
ISBN: 0486154475
Category: Mathematics
Page: 160
View: 8828

This graduate-level text introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.

## Introduction to Real Analysis

Author: Michael J. Schramm
Publisher: Courier Corporation
ISBN: 0486131920
Category: Mathematics
Page: 384
View: 361

This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

## Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden,Thomas J. R. Hughes
Publisher: Courier Corporation
ISBN: 0486142272
Category: Technology & Engineering
Page: 576
View: 8366

Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.

## Foundations of Mathematical Logic

Publisher: Courier Corporation
ISBN: 0486153053
Category: Mathematics
Page: 416
View: 6794

Comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods: algorithms and epitheory, brief treatment of Markov's approach to algorithms, elementary facts about lattices, logical connectives, and more. 1963 edition.

## Foundations and Fundamental Concepts of Mathematics

Author: Howard Whitley Eves
Publisher: Courier Corporation
ISBN: 9780486696096
Category: Mathematics
Page: 344
View: 7066

This third edition of a popular, well-received text offers undergraduates an opportunity to obtain an overview of the historical roots and the evolution of several areas of mathematics. The selection of topics conveys not only their role in this historical development of mathematics but also their value as bases for understanding the changing nature of mathematics. Among the topics covered in this wide-ranging text are: mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, the real numbers system, sets, logic and philosophy and more. The emphasis on axiomatic procedures provides important background for studying and applying more advanced topics, while the inclusion of the historical roots of both algebra and geometry provides essential information for prospective teachers of school mathematics. The readable style and sets of challenging exercises from the popular earlier editions have been continued and extended in the present edition, making this a very welcome and useful version of a classic treatment of the foundations of mathematics. "A truly satisfying book." — Dr. Bruce E. Meserve, Professor Emeritus, University of Vermont.

## Concepts of Modern Mathematics

Author: Ian Stewart
Publisher: Courier Corporation
ISBN: 0486134954
Category: Mathematics
Page: 368
View: 5140

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

## Mathematical Foundations of Information Theory

Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 0486604349
Category: Mathematics
Page: 120
View: 7447

First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

## Foundations of the Theory of Probability

Second English Edition
Author: A.N. Kolmogorov
Publisher: Courier Dover Publications
ISBN: 0486829790
Category: Mathematics
Page: 96
View: 9343

This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.