Students progressing to advanced calculus are frequently confounded by the dramatic shift from mechanical to theoretical and from concrete to abstract. This text bridges the gap, offering a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition. Reprint of the John Wiley & Sons, Inc., New York, 1963 edition.
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Analysis in Euclidean Space by Kenneth Hoffman Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition.
Introduction to Analysis by Maxwell Rosenlicht Unusually clear, accessible coverage of set theory, real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, more. Wide range of problems. Written for junior and senior undergraduates. Bibliography.
The Continuum: A Critical Examination of the Foundation of Analysis by Hermann Weyl 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.
Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Intermediate Mathematical Analysis by Anthony E. Labarre, Jr. Focusing on concepts rather than techniques, this text deals primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition.
Real Analysis by Gabriel Klambauer Concise in treatment and comprehensive in scope, this text for graduate students introduces contemporary real analysis with a particular emphasis on integration theory. Includes exercises. 1973 edition.
Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin 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. Features 350 problems.
Introduction to Real Analysis by Michael J. Schramm 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.
Real Analysis by Norman B. Haaser, Joseph A. Sullivan Clear, accessible text for 1st course in abstract analysis. Explores sets and relations, real number system and linear spaces, normed spaces, Lebesgue integral, approximation theory, Banach fixed-point theorem, Stieltjes integrals, more. Includes numerous problems.
Introduction to the Theory of Sets by Joseph Breuer, Howard F. Fehr This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.
Concepts of Modern Mathematics by Ian Stewart 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.
Sequences, Combinations, Limits by S. I. Gelfand, M. L. Gerver, A. A. Kirillov, N. N. Konstantinov Focusing on theory more than computations, this text covers sequences, definitions, and methods of induction; combinations; and limits, with introductory problems, definition-related problems, and problems related to computation limits. 1969 edition.
Infinite Sequences and Series by Konrad Knopp Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
Combinatorial Enumeration by Ian P. Goulden, David M. Jackson Graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems, from elementary to research level, for discrete structures and their substructures. Full solutions to 350 exercises.
Basic Set Theory by Azriel Levy The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.
An Outline of Set Theory by James M. Henle An innovative introduction to set theory, this volume is for undergraduate courses in which students work in groups and present their solutions to the class. Complete solutions. 1986 edition.
Set Theory and Logic by Robert R. Stoll Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
