## Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher: Courier Corporation
ISBN: 0486134776
Category: Mathematics
Page: 448
View: 4525

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: 8997

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.

## Number Systems and the Foundations of Analysis

Author: Elliott Mendelson
Publisher: Courier Corporation
ISBN: 0486457923
Category: Mathematics
Page: 358
View: 4257

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: 8404

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.

## Foundations of Stochastic Analysis

Author: M. M. Rao
Publisher: Courier Corporation
ISBN: 0486296539
Category: Mathematics
Page: 320
View: 2466

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.

## Precalculus

Fundamentals of Mathematical Analysis
Author: Edgar R. Lorch
Publisher: N.A
ISBN: 9780486818481
Category:
Page: 400
View: 960

Intended to provide undergraduate students with the background necessary for the study of calculus, this text by a distinguished mathematician offers a balanced treatment of theory and applications. Considerably more concise than most books in the field, it focuses on the structures of natural numbers, integers, and rational numbers. Each chapter features illustrative examples and notes. More than 1,000 exercises enrich the text, many with solutions.

## Foundations of Analysis

Author: David French Belding,Kevin J. Mitchell
Publisher: Courier Corporation
ISBN: 048646296X
Category: Mathematics
Page: 427
View: 4559

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.

## Foundations of Mathematical Analysis

Author: Saminathan Ponnusamy
Publisher: Springer Science & Business Media
ISBN: 0817682910
Category: Mathematics
Page: 570
View: 1822

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 Potential Theory

Author: Oliver Dimon Kellogg
Publisher: Courier Corporation
ISBN: 9780486601441
Category: Science
Page: 384
View: 7791

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: 4591

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.

## The Continuum

A Critical Examination of the Foundation of Analysis
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 0486679829
Category: Mathematics
Page: 130
View: 5680

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.

## Introduction to Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Category: Mathematics
Page: 272
View: 6109

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.

## Introductory Real Analysis

Author: A. N. Kolmogorov,S. V. Fomin
Publisher: Courier Corporation
ISBN: 0486134741
Category: Mathematics
Page: 416
View: 2567

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.

## An Introduction to Combinatorial Analysis

Author: John Riordan
Publisher: Princeton University Press
ISBN: 1400854334
Category: Mathematics
Page: 258
View: 4631

This book introduces combinatorial analysis to the beginning student. The author begins with the theory of permutation and combinations and their applications to generating functions. In subsequent chapters, he presents Bell polynomials; the principle of inclusion and exclusion; the enumeration of permutations in cyclic representation; the theory of distributions; partitions, compositions, trees and linear graphs; and the enumeration of restricted permutations. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

## Foundations of Analysis

Author: Edmund Landau
Publisher: American Mathematical Soc.
ISBN: 082182693X
Category: Mathematics
Page: 136
View: 7008

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 Elasticity

Author: Jerrold E. Marsden,Thomas J. R. Hughes
Publisher: Courier Corporation
ISBN: 0486142272
Category: Technology & Engineering
Page: 576
View: 1398

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.

## Concepts of Modern Mathematics

Author: Ian Stewart
Publisher: Courier Corporation
ISBN: 0486134954
Category: Mathematics
Page: 368
View: 4016

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.

## Foundations and Fundamental Concepts of Mathematics

Author: Howard Whitley Eves
Publisher: Courier Corporation
ISBN: 9780486696096
Category: Mathematics
Page: 344
View: 8195

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.

## Foundations of Mathematical Logic

Author: Haskell B. Curry
Publisher: Courier Corporation
ISBN: 0486153053
Category: Mathematics
Page: 416
View: 4974

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.

## Mathematical Foundations of Information Theory

Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 0486604349
Category: Mathematics
Page: 120
View: 9916

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.