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Unformatted text preview: MAT 472: INTERMEDIATE REAL ANALYSIS FALL 2005 Instructor: S. Kaliszewski Time: 10:4011:55 TTh / 3:154:30 TTh Location: ARCH 321 / EDB 212 Line Number: 52462 / 49027 Credits: 3 Prerequisites: MAT 300 (Mathematical Structures) and MAT 342 (Linear Algebra), or equivalents. Text: Rosenlicht  Course Description. Hhis course covers the fundamentals of analysis in metric spaces, with emphasis on the real line. Among the most important topics are continuity, compact- ness, uniform continuity, uniform convergence, and differentiation and Riemann integration of functions of one real variable. Advanced topics may include, but are not limited to: the Baire Category Theorem, the Weierstrass Approximation Theorem, and the Arzela-Ascoli Theorem. One of the primary functions of this course is to prepare students for graduate-level real analysis (MAT 570). The course also serves as preparation for the first half of the depart- ments graduate qualifying exam in Real Analysis. MAT 371 (Advanced Calculus) is strongly recommended as preparation for MAT 472, although it is not a formal prerequisite. Many students find MAT 371 useful as an intro- duction to both the subject matter of MAT 472, and to the process of reading mathematics and constructing proofs. References  Edward D. Gaughan, Introduction to analysis , 4th ed., Brooks/Cole Publishing Co., Pacific Grove, CA, 1993.MR1226448  Maxwell Rosenlicht, Introduction to analysis , Dover Publications Inc., New York, 1986. Reprint of the 1968 edition.MR851984 (87g:26001)  Walter Rudin, Principles of mathematical analysis , 3rd ed., McGraw-Hill Book Co., New York, 1976....
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