Items related to Introduction to Real Analysis (Dover Books on Mathematics)
This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics.The four-part treatment begins with an introduction to basic logical structures and techniques of proof, including discussions of the cardinality concept and the algebraic and order structures of the real and rational number systems. Part Two presents in-depth examinations of the completeness of the real number system and its topological structure. Part Three reviews and extends the previous explorations of the real number system, and the final part features a selection of topics in real function theory. Numerous and varied exercises range from articulating the steps omitted from examples and observing mechanical results at work to the completion of partial proofs within the text.
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This beautifully written text starts with proofs and sets in the first 40 pages and continues in the rest of Parts I and II to maintain an ongoing emphasis on the construction of proofs, demonstrating proper skills through detailed examples using the "forward-backward" method.
From the Back Cover:
Key Topics: After introducing the materials of analysis—emphasizing the structure of the real number system—in Parts I and II, this text reviews and extends calculus in Part III. Readers use their newly acquired knowledge of the real nu mber system in their reexamination of calculus, then move on to Part IV's “testing laboratory”where they explore the strength and basic nature of materials.
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- PublisherDover Publications
- Publication date2008
- ISBN 10 0486469131
- ISBN 13 9780486469133
- BindingPaperback
- Number of pages384
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Book Description Paperback. Condition: new. Paperback. This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics.The four-part treatment begins with an introduction to basic logical structures and techniques of proof, including discussions of the cardinality concept and the algebraic and order structures of the real and rational number systems. Part Two presents in-depth examinations of the completeness of the real number system and its topological structure. Part Three reviews and extends the previous explorations of the real number system, and the final part features a selection of topics in real function theory. Numerous and varied exercises range from articulating the steps omitted from examples and observing mechanical results at work to the completion of partial proofs within the text. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780486469133
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