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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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.
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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.
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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.
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