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Instructor:
E-mail: Office: Phone: Office hours: |
Victoria Sadovskaya sadovskaya@psu.edu 426 McAllister (814) 863-4140 Monday 1:30-3:00 p.m.; Wednesday 10:10-11:00 a.m.; and by appointment |
Course description:
This course provides rigorous development of the key concepts and results of real analysis.
The topics include
Real numbers. Metric spaces.
Sequences: convergence, limsup and liminf, Cauchy sequences, sequences in metric spaces.
Infinite series: convergence, convergence tests, power series.
Functions of one real variable:
limit and continuity, properties of continuous functions, uniform continuity,
differentiation, integration, the Fundamental Theorem of Calculus.
The course is focused on theory rather than computations. The students will learn and write proofs.
Mathematical exposition will be emphasized.
Prerequisites: Math 141 (required), and Math 311M or Math 311W (strongly recommended).
Text:
Elementary Analysis: The Theory of Calculus
by Kenneth A. Ross, second edition.
Math 312 students can download chapters or the entire book, free of charge, at
http://link.springer.com.ezaccess.libraries.psu.edu/book/10.1007/978-1-4614-6271-2
Syllabus
pdf